Research ArticleThe Development and Application ofCrop Evaluation System Based on GRA

Ruihong Wang1 Liguo Zhang1 Lianjie Dong2 and Xiuying Lu3

1College of Information Science amp Technology Agricultural University of Hebei Baoding China2College of Science Agricultural University of Hebei Baoding China3Agricultural University of Hebei Baoding China

Correspondence should be addressed to Ruihong Wang xxwrhhebaueducn

Received 16 June 2016 Revised 15 October 2016 Accepted 24 October 2016

Academic Editor Alberto Borboni

Copyright copy 2016 Ruihong Wang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Ever since it was proposed grey system theory has attracted the attention of scientific researchers and scholars And it also has beenwidely used in many fields and solved a large number of practical problems in production life and scientific research With thedevelopment and popularization of computer science and network technology this traditional mathematical model can be appliedmore simply and efficiently to solve practical problems Firstly this paper to implement steps of grey relational analysis has madethe exclusive analysis and hasmade the simple introduction to grey relational analysis characteristicsThen based on grey relationaltheory and ASPNET technology the crop evaluation system is developed Lastly by using Excel and the crop evaluation systemthe paper carries out a comprehensive evaluation about eight features of Fuji apple which is from nine different producing areasrespectively The experiment results show that the crop evaluation system is effective and could greatly improve the work efficiencyof the researcher and expand the application scope

1 Introduction

Grey System In todayrsquos world society has been in the infor-mation age It contains a large number of known unknownand unascertained information We call it grey system whichcontains less incomplete and uncertain information pro-posed by Deng Julong in 1982 [1 2] Its research mainlyincludes grey system modeling theory grey system control-ling theory grey relational analysis (GRA) [3] grey pre-diction method grey planning method and grey decision-making method

Grey system is mainly used to solve the ldquolimited sampleless informationrdquo problem [4ndash6] which cannot be solved bystatistics and fuzzy mathematics On the basis of informationcoverage it seeks the practical regular by generating thesequence Its characteristic is ldquoless data modelrdquo [7ndash10]

Grey Relational Analysis GRA is not only an important partof grey systembut also the cornerstone of analysis predictionand decision-making of grey system [11ndash15]

When we study a system we should distinguish the mainfactors and secondary factors which promote the develop-ment of system or hinder that Because the information isincomplete and uncertain it is difficult to determine therelationship of all factors and is difficult to distinguish themain factors and secondary factors in the grey system Themain function of the GRA is to quantify and sort thosefactors so as to analyze the system

At first we calculate the relational coefficient of each pro-gram and the ideal program composed by best indicator andthen calculate the relational degree from coefficient Finallyaccording to the size of relational degree we sort analyzeand draw conclusion This approach is superior to classicalexact mathematical methods This method breaks throughconstraints of traditional precise mathematics which doesnot tolerate ambiguity It has many significant features suchas far from simple easy to grasp simple calculation clear sortno special requirements for the data distribution type andvariable type So it is widely used in many fields [16ndash23] suchas evaluation of citrus quality breeding selection of wheat

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 1815240 6 pageshttpdxdoiorg10115520161815240

2 Mathematical Problems in Engineering

Import strain data

Automatically generate database

Input the weights and each stainparameter of ideal strain

Dimensionless data

Generate the relational degree curve

Figure 1 Workflow of crop evaluation system

strain application of potato new strain breeding selection ofoil-tea application research of rice new strain and analysison yield and main characters of soybean strains

Grey Relational Degree The theory tool of GRA is the greyrelational degree It measures the relational degree amongfactors If two factors have similar changing trend the greyrelational degree is large On the other hand the grey rela-tional degree is small In turn we can use the grey relationaldegree to judge the degree of correlation between factors

When we analyze abstract system or phenomenon wefirstly select the right sequence data reflecting the character-istic of system behavior which is called mapping of seekingsystem behaviorThe sequence data is indirectly used to char-acterize the system behavior Then we also need to furtherclarify the effective factors that affect system main behaviorWhen we make the quantitative analysis we must transformthe system behavior characteristic and each effective factorfor similar dimensionless quantitative data and transformnegative relational factor for a positive relational factor

Since Professor Deng Julong proposed the system in 1982grey system has rapidly grown and developed but there isno software development So we develop crop evaluationsystem by using C program language The workflow of cropevaluation system is shown in Figure 1This evaluation systemcan greatly improve the work efficiency for the researcher andexpand the application scope of this method

2 Materials and Methods

Relational degree is a relevance measure between the thingsand factors We find it from the random time series so as toprovide evidence for factor analysis and forecasting accuracyanalysis And the relational degree is not only a basis fordecision-making but also a method to determine the mainfactors Therefore how to define a reasonable calculation

method of relational degree has important significance Com-mon relational degree definitions are the following Dengrelational degree absolute relational degree T relationaldegree B relational degree and C relational degree In thispaper we adopt Deng relational degree to carry out theevaluation model

According to Deng relational degree when we evaluatethe Fuji apple from 9 different producing areas [24] we set its8 features as a grey system and set each feature as a factor insystem Before evaluation we firstly set an ideal variety as anevaluation standard

Set the index of ideal variety constitute the sequence ofreference series 1198830 the rest varieties as test series 119883119894 andthen generate sequence1198830 = [1198830(1) 1198830(2) 1198830(119899)]119883119894 =[119883119894(1)119883119894(2) 119883119894(119899)] 119899 is the factor number 119894 denotes 119894thvariant We can use the following formulas to calculate therelational coefficient equal-weighted degree and weighteddegree

Relational coefficient [25ndash28] is

120585119894 (119896)

=minmin 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)

1003816100381610038161003816 + 120588maxmax 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)100381610038161003816100381610038161003816100381610038161199090 (119896) minus 119909119894 (119896)

1003816100381610038161003816 + 120588maxmax 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)1003816100381610038161003816

(1)

Equal-weighted degree is

119903119894 =1119899

119899

sum1

120585119894 (119896) (2)

Weighted degree is

119903lowast119894= 1119899

119899

sum1

120585119894 (119896)119882119894 (3)

Here |1198830(119870) minus 119883119894(119870)| = Δ 119894(119870) is the absolute dif-ference between 1198830 sequence and 119883119894 sequence at 119870 pointmin119894min119896|1198830(119870) minus 119883119894(119870)| is secondary minimum differ-ence max119894max119896|1198830(119870) minus 119883119894(119870)| is the secondary maximumdifference 120588 is the distinguishing coefficient and its valueranges from 0 to 1 usually taking 05 120585119894(119896) is the weightingcoefficient Its size was based on results of previous studiesexperience target selection and expert appraisal results119882119894 isweight coefficient of each character According to 119903119894 or 119903

lowast

119894 the

relational degrees of tested varieties are calculatedThe biggerthe value of tested variety the more excellent the variety Onthe contrary it is poor

3 Results

31 Performance of the Method In this paper with the Fujifor example we introduce the evaluation system process andcarry out the evaluation model We analyze 8 characters ofFuji apple from 9 different producing areas 8 characters arefruit volume (mL) skin color flesh color starch content ()the juice yield () solid acid ratio fruit firmness (g) andprotein content (g100 g) Raw data sheet was shown inTable 1

Mathematical Problems in Engineering 3

Table 1 Raw data

Input the crop name Apple Input characters number 8Input the weight 008 016 016 016 004 016 016 008Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Table 2 Dimensionless quantity

Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 100 100 100 100 100 100 100 1001 099 112 minus175 116 099 087 100 0532 071 118 minus044 161 127 118 092 0813 075 093 minus085 148 112 138 100 0654 100 144 minus032 165 131 088 091 0475 070 111 minus065 184 083 095 101 0546 086 082 100 248 090 100 090 0677 090 108 minus145 119 095 078 090 0798 095 091 minus125 248 074 089 083 0629 090 137 minus055 106 085 070 098 099

Table 3 Absolute difference

Charactersrsquo name 1 2 3 4 5 6 7 8100 001 012 275 016 001 013 000 047200 029 018 144 061 027 018 008 019300 025 008 185 048 012 038 000 035400 000 044 132 065 031 012 009 053500 030 011 165 084 017 005 001 046600 014 018 000 148 010 000 010 033700 010 008 245 019 005 022 010 021800 005 009 225 148 026 011 017 038900 010 037 155 006 015 030 002 001

First nondimensional treatment for the original data isdone According formula (4) calculate the nondimensionaldata as shown in Table 2

119871ℎ (119896) =119883119894 (119896)1198830 (119896) (4)

Here 119871ℎ(119896) denotes 119896th character of 119894th variantSecond according to the dimensionless quantity sheet

and formula (5) calculate each relevant absolute difference

Table 4 Correlative coefficients

Charactersrsquo name 100 200 300 400 500 600 700 8001 100 092 033 089 099 092 100 0742 083 089 049 069 084 089 095 0883 085 095 043 074 092 078 100 0804 100 076 051 068 082 092 094 0725 082 092 045 062 089 097 099 0756 091 089 100 048 093 100 093 0817 094 094 036 088 097 086 093 0878 097 094 038 048 084 093 089 0789 093 079 047 096 090 082 099 099

between reference sequence and comparative sequence andget absolute difference as shown in Table 3

Δ 119894 (119870) =10038161003816100381610038161198830 (119870) minus 119883119894 (119870)

1003816100381610038161003816 (5)

Third according to the relational coefficients sheet usingformula (1) get correlative coefficients as shown in Table 4

Inputting the weight in the raw data sheet using cor-relative coefficients and formula (3) we calculate weightedrelational degree of the Fuji apple quality fromdifferent originand get weighted relational degree as shown in Table 5

Using the chart function in Excel 2003 we generate theclumps bar graph as shown in Figure 2

4 Mathematical Problems in Engineering

Table 5 Relational degree

Charactersrsquo name Relational degree Sort100 083 300200 079 600300 079 700400 078 800500 080 500600 086 100700 082 400800 075 900900 083 200

Relational degree088086084082080078076074072070068

200 300 400 500 600 700 800 900100

Figure 2 The bar graph

If we input equal-weight in the raw data sheet (as shownin Table 6) then final equal-weighted relational degreeclumps bar graph is generated as shown in Figure 3

According to relational analysis principle the sequencein which relational degree is biggest ismost close to referencesequence that is the variety is more close to ldquoideal varietyrdquoAmong them 9th variety is most close to ldquoideal varietyrdquofollowed by 6th variety 8th variety has max difference withit indicating that its comprehensive quality is worst The restof origin Fuji apple is centeredTheweighted relational degreehas the same sort as the equal-weight mainly due to the sameimportance of quality indexes

32 Crop Evaluation System In the above section we haveestablished the evaluationmodel It can be seen that thewholeprocess is very cumbersome and complex In particular forthe less skilled computer user the biggest drawback is that[29 30] when the objects change performance indicatorsmay be different and the weight of each index may need tobe changed and then the user will not be able to simply andflexibly use the model In order to make the model becomemore widely used easily increase or decrease characteristicnumber and modify the characteristics weight we use Cprogram language to develop the software based on the abovemodel and analysis steps It achieves automatic calculationand analysis of data The software interface and operation isas follows

Relational degree

200 300 400 500 600 700 800 900100

088

086

084

082

080

078

076

074

072

Figure 3 The bar graph

Figure 4 Main interface

(1) Operating system is the main interface as shown inFigure 4

(2) First import each strain of data to be analyzed thedata is written in Excel format The data format is asshown in Figure 5

(3) Browse the file and find the data sheet to be analyzedand then click the button ldquodata importrdquo to importthe data The software automatically calculates thenumber of strains and indicators Interface is shownin Figure 6

(4) According the user requirement the operator inputsthe weight and each trait parameter of ideal strainthen click the button ldquorelational degree analysisrdquo andthe software generates the relational degree curveThis paper adopts the same data as introduced inExcel methods in Figure 5 The result was shown inFigure 7

4 Discussion

GRA method is one of the very popular methods to analyzevarious relationships among the discrete data sets The majoradvantages of the GRA method are that the results are basedon the original data and the calculations are simple andstraightforward Different from previous studies the paperestablished the crop evaluation model based on the basicideal of traditional grey relational analysis (GRA) methodand also developed the crop evaluation system based on themodel With friendly interface and being easy to operate thesoftware can be easily performed on computer and suitablefor different families genera and species of plants Thedisadvantages of the traditional grey correlation analysis areovercome In addition setting weights is the key step of cropevaluation the operator can give different weights accordingto different crop types in the evaluation system

Mathematical Problems in Engineering 5

Table 6 Equal-weight

Input the crop name Apple Input characters number 8Input the weight 0125 0125 0125 0125 0125 0125 0125 0125Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Figure 5 The data format

Figure 6 The operation interface

5 Conclusions

GRA is part of grey system theory which is suitable for solv-ing complicated interrelationships between multiple factorsand variables When used to evaluate different crops qualityit can make full use of all the information about fruit qualitytraits and can give an objective and reasonable sort As dis-cussed in the above sections traditional methods have manyshortcomings using weighted relational degree to evaluatedifferent crops quality the distribution of weight often needsto be changed The interface is not friendly The operation isnot convenient and calculation process is complex and so onThe developed crop evaluation system overcomes the aboveshortcomings Taking the Fuji data as experimental data thepaper made the relational degree analysis It shows that thedeveloped crop evaluation system can greatly improve the

Figure 7 Relational degree curve

work efficiency of the researcher and expand the applicationscope

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Science and Technology PlanProjects of Hebei province (nos 15210138 and 15ZN010)

References

[1] L Weizhong A Yinghui X Chongxiang et al ldquoPhenotypiccharacter and yield research of maizi inbred lines based onGRArdquo Crops vol 5 pp 105ndash108 2012

[2] W Ma Q Guo C Wei H Li C Peng and Z Liang ldquoCom-prehensive evaluation of new self-cultivated sugarcane lines bygrey relational analysisrdquo Asian Agricultural Research vol 6 no9 pp 85ndash88 2014

[3] X-F Yan and Y Shen ldquoComprehensive quality evaluation ofdehaired cashmere fiber based on grey relational analysisrdquoWoolTextile Journal vol 42 no 11 pp 46ndash50 2014

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

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Mathematical Problems in Engineering

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

Import strain data

Automatically generate database

Input the weights and each stainparameter of ideal strain

Dimensionless data

Generate the relational degree curve

Figure 1 Workflow of crop evaluation system

strain application of potato new strain breeding selection ofoil-tea application research of rice new strain and analysison yield and main characters of soybean strains

Grey Relational Degree The theory tool of GRA is the greyrelational degree It measures the relational degree amongfactors If two factors have similar changing trend the greyrelational degree is large On the other hand the grey rela-tional degree is small In turn we can use the grey relationaldegree to judge the degree of correlation between factors

When we analyze abstract system or phenomenon wefirstly select the right sequence data reflecting the character-istic of system behavior which is called mapping of seekingsystem behaviorThe sequence data is indirectly used to char-acterize the system behavior Then we also need to furtherclarify the effective factors that affect system main behaviorWhen we make the quantitative analysis we must transformthe system behavior characteristic and each effective factorfor similar dimensionless quantitative data and transformnegative relational factor for a positive relational factor

Since Professor Deng Julong proposed the system in 1982grey system has rapidly grown and developed but there isno software development So we develop crop evaluationsystem by using C program language The workflow of cropevaluation system is shown in Figure 1This evaluation systemcan greatly improve the work efficiency for the researcher andexpand the application scope of this method

2 Materials and Methods

Relational degree is a relevance measure between the thingsand factors We find it from the random time series so as toprovide evidence for factor analysis and forecasting accuracyanalysis And the relational degree is not only a basis fordecision-making but also a method to determine the mainfactors Therefore how to define a reasonable calculation

method of relational degree has important significance Com-mon relational degree definitions are the following Dengrelational degree absolute relational degree T relationaldegree B relational degree and C relational degree In thispaper we adopt Deng relational degree to carry out theevaluation model

According to Deng relational degree when we evaluatethe Fuji apple from 9 different producing areas [24] we set its8 features as a grey system and set each feature as a factor insystem Before evaluation we firstly set an ideal variety as anevaluation standard

Set the index of ideal variety constitute the sequence ofreference series 1198830 the rest varieties as test series 119883119894 andthen generate sequence1198830 = [1198830(1) 1198830(2) 1198830(119899)]119883119894 =[119883119894(1)119883119894(2) 119883119894(119899)] 119899 is the factor number 119894 denotes 119894thvariant We can use the following formulas to calculate therelational coefficient equal-weighted degree and weighteddegree

Relational coefficient [25ndash28] is

120585119894 (119896)

=minmin 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)

1003816100381610038161003816 + 120588maxmax 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)100381610038161003816100381610038161003816100381610038161199090 (119896) minus 119909119894 (119896)

1003816100381610038161003816 + 120588maxmax 10038161003816100381610038161199090 (119896) minus 119909119894 (119896)1003816100381610038161003816

(1)

Equal-weighted degree is

119903119894 =1119899

119899

sum1

120585119894 (119896) (2)

Weighted degree is

119903lowast119894= 1119899

119899

sum1

120585119894 (119896)119882119894 (3)

Here |1198830(119870) minus 119883119894(119870)| = Δ 119894(119870) is the absolute dif-ference between 1198830 sequence and 119883119894 sequence at 119870 pointmin119894min119896|1198830(119870) minus 119883119894(119870)| is secondary minimum differ-ence max119894max119896|1198830(119870) minus 119883119894(119870)| is the secondary maximumdifference 120588 is the distinguishing coefficient and its valueranges from 0 to 1 usually taking 05 120585119894(119896) is the weightingcoefficient Its size was based on results of previous studiesexperience target selection and expert appraisal results119882119894 isweight coefficient of each character According to 119903119894 or 119903

lowast

119894 the

relational degrees of tested varieties are calculatedThe biggerthe value of tested variety the more excellent the variety Onthe contrary it is poor

3 Results

31 Performance of the Method In this paper with the Fujifor example we introduce the evaluation system process andcarry out the evaluation model We analyze 8 characters ofFuji apple from 9 different producing areas 8 characters arefruit volume (mL) skin color flesh color starch content ()the juice yield () solid acid ratio fruit firmness (g) andprotein content (g100 g) Raw data sheet was shown inTable 1

Mathematical Problems in Engineering 3

Table 1 Raw data

Input the crop name Apple Input characters number 8Input the weight 008 016 016 016 004 016 016 008Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Table 2 Dimensionless quantity

Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 100 100 100 100 100 100 100 1001 099 112 minus175 116 099 087 100 0532 071 118 minus044 161 127 118 092 0813 075 093 minus085 148 112 138 100 0654 100 144 minus032 165 131 088 091 0475 070 111 minus065 184 083 095 101 0546 086 082 100 248 090 100 090 0677 090 108 minus145 119 095 078 090 0798 095 091 minus125 248 074 089 083 0629 090 137 minus055 106 085 070 098 099

Table 3 Absolute difference

Charactersrsquo name 1 2 3 4 5 6 7 8100 001 012 275 016 001 013 000 047200 029 018 144 061 027 018 008 019300 025 008 185 048 012 038 000 035400 000 044 132 065 031 012 009 053500 030 011 165 084 017 005 001 046600 014 018 000 148 010 000 010 033700 010 008 245 019 005 022 010 021800 005 009 225 148 026 011 017 038900 010 037 155 006 015 030 002 001

First nondimensional treatment for the original data isdone According formula (4) calculate the nondimensionaldata as shown in Table 2

119871ℎ (119896) =119883119894 (119896)1198830 (119896) (4)

Here 119871ℎ(119896) denotes 119896th character of 119894th variantSecond according to the dimensionless quantity sheet

and formula (5) calculate each relevant absolute difference

Table 4 Correlative coefficients

Charactersrsquo name 100 200 300 400 500 600 700 8001 100 092 033 089 099 092 100 0742 083 089 049 069 084 089 095 0883 085 095 043 074 092 078 100 0804 100 076 051 068 082 092 094 0725 082 092 045 062 089 097 099 0756 091 089 100 048 093 100 093 0817 094 094 036 088 097 086 093 0878 097 094 038 048 084 093 089 0789 093 079 047 096 090 082 099 099

between reference sequence and comparative sequence andget absolute difference as shown in Table 3

Δ 119894 (119870) =10038161003816100381610038161198830 (119870) minus 119883119894 (119870)

1003816100381610038161003816 (5)

Third according to the relational coefficients sheet usingformula (1) get correlative coefficients as shown in Table 4

Inputting the weight in the raw data sheet using cor-relative coefficients and formula (3) we calculate weightedrelational degree of the Fuji apple quality fromdifferent originand get weighted relational degree as shown in Table 5

Using the chart function in Excel 2003 we generate theclumps bar graph as shown in Figure 2

4 Mathematical Problems in Engineering

Table 5 Relational degree

Charactersrsquo name Relational degree Sort100 083 300200 079 600300 079 700400 078 800500 080 500600 086 100700 082 400800 075 900900 083 200

Relational degree088086084082080078076074072070068

200 300 400 500 600 700 800 900100

Figure 2 The bar graph

If we input equal-weight in the raw data sheet (as shownin Table 6) then final equal-weighted relational degreeclumps bar graph is generated as shown in Figure 3

According to relational analysis principle the sequencein which relational degree is biggest ismost close to referencesequence that is the variety is more close to ldquoideal varietyrdquoAmong them 9th variety is most close to ldquoideal varietyrdquofollowed by 6th variety 8th variety has max difference withit indicating that its comprehensive quality is worst The restof origin Fuji apple is centeredTheweighted relational degreehas the same sort as the equal-weight mainly due to the sameimportance of quality indexes

32 Crop Evaluation System In the above section we haveestablished the evaluationmodel It can be seen that thewholeprocess is very cumbersome and complex In particular forthe less skilled computer user the biggest drawback is that[29 30] when the objects change performance indicatorsmay be different and the weight of each index may need tobe changed and then the user will not be able to simply andflexibly use the model In order to make the model becomemore widely used easily increase or decrease characteristicnumber and modify the characteristics weight we use Cprogram language to develop the software based on the abovemodel and analysis steps It achieves automatic calculationand analysis of data The software interface and operation isas follows

Relational degree

200 300 400 500 600 700 800 900100

088

086

084

082

080

078

076

074

072

Figure 3 The bar graph

Figure 4 Main interface

(1) Operating system is the main interface as shown inFigure 4

(2) First import each strain of data to be analyzed thedata is written in Excel format The data format is asshown in Figure 5

(3) Browse the file and find the data sheet to be analyzedand then click the button ldquodata importrdquo to importthe data The software automatically calculates thenumber of strains and indicators Interface is shownin Figure 6

(4) According the user requirement the operator inputsthe weight and each trait parameter of ideal strainthen click the button ldquorelational degree analysisrdquo andthe software generates the relational degree curveThis paper adopts the same data as introduced inExcel methods in Figure 5 The result was shown inFigure 7

4 Discussion

GRA method is one of the very popular methods to analyzevarious relationships among the discrete data sets The majoradvantages of the GRA method are that the results are basedon the original data and the calculations are simple andstraightforward Different from previous studies the paperestablished the crop evaluation model based on the basicideal of traditional grey relational analysis (GRA) methodand also developed the crop evaluation system based on themodel With friendly interface and being easy to operate thesoftware can be easily performed on computer and suitablefor different families genera and species of plants Thedisadvantages of the traditional grey correlation analysis areovercome In addition setting weights is the key step of cropevaluation the operator can give different weights accordingto different crop types in the evaluation system

Mathematical Problems in Engineering 5

Table 6 Equal-weight

Input the crop name Apple Input characters number 8Input the weight 0125 0125 0125 0125 0125 0125 0125 0125Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Figure 5 The data format

Figure 6 The operation interface

5 Conclusions

GRA is part of grey system theory which is suitable for solv-ing complicated interrelationships between multiple factorsand variables When used to evaluate different crops qualityit can make full use of all the information about fruit qualitytraits and can give an objective and reasonable sort As dis-cussed in the above sections traditional methods have manyshortcomings using weighted relational degree to evaluatedifferent crops quality the distribution of weight often needsto be changed The interface is not friendly The operation isnot convenient and calculation process is complex and so onThe developed crop evaluation system overcomes the aboveshortcomings Taking the Fuji data as experimental data thepaper made the relational degree analysis It shows that thedeveloped crop evaluation system can greatly improve the

Figure 7 Relational degree curve

work efficiency of the researcher and expand the applicationscope

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Science and Technology PlanProjects of Hebei province (nos 15210138 and 15ZN010)

References

[1] L Weizhong A Yinghui X Chongxiang et al ldquoPhenotypiccharacter and yield research of maizi inbred lines based onGRArdquo Crops vol 5 pp 105ndash108 2012

[2] W Ma Q Guo C Wei H Li C Peng and Z Liang ldquoCom-prehensive evaluation of new self-cultivated sugarcane lines bygrey relational analysisrdquo Asian Agricultural Research vol 6 no9 pp 85ndash88 2014

[3] X-F Yan and Y Shen ldquoComprehensive quality evaluation ofdehaired cashmere fiber based on grey relational analysisrdquoWoolTextile Journal vol 42 no 11 pp 46ndash50 2014

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Table 1 Raw data

Input the crop name Apple Input characters number 8Input the weight 008 016 016 016 004 016 016 008Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Table 2 Dimensionless quantity

Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 100 100 100 100 100 100 100 1001 099 112 minus175 116 099 087 100 0532 071 118 minus044 161 127 118 092 0813 075 093 minus085 148 112 138 100 0654 100 144 minus032 165 131 088 091 0475 070 111 minus065 184 083 095 101 0546 086 082 100 248 090 100 090 0677 090 108 minus145 119 095 078 090 0798 095 091 minus125 248 074 089 083 0629 090 137 minus055 106 085 070 098 099

Table 3 Absolute difference

Charactersrsquo name 1 2 3 4 5 6 7 8100 001 012 275 016 001 013 000 047200 029 018 144 061 027 018 008 019300 025 008 185 048 012 038 000 035400 000 044 132 065 031 012 009 053500 030 011 165 084 017 005 001 046600 014 018 000 148 010 000 010 033700 010 008 245 019 005 022 010 021800 005 009 225 148 026 011 017 038900 010 037 155 006 015 030 002 001

First nondimensional treatment for the original data isdone According formula (4) calculate the nondimensionaldata as shown in Table 2

119871ℎ (119896) =119883119894 (119896)1198830 (119896) (4)

Here 119871ℎ(119896) denotes 119896th character of 119894th variantSecond according to the dimensionless quantity sheet

and formula (5) calculate each relevant absolute difference

Table 4 Correlative coefficients

Charactersrsquo name 100 200 300 400 500 600 700 8001 100 092 033 089 099 092 100 0742 083 089 049 069 084 089 095 0883 085 095 043 074 092 078 100 0804 100 076 051 068 082 092 094 0725 082 092 045 062 089 097 099 0756 091 089 100 048 093 100 093 0817 094 094 036 088 097 086 093 0878 097 094 038 048 084 093 089 0789 093 079 047 096 090 082 099 099

between reference sequence and comparative sequence andget absolute difference as shown in Table 3

Δ 119894 (119870) =10038161003816100381610038161198830 (119870) minus 119883119894 (119870)

1003816100381610038161003816 (5)

Third according to the relational coefficients sheet usingformula (1) get correlative coefficients as shown in Table 4

Inputting the weight in the raw data sheet using cor-relative coefficients and formula (3) we calculate weightedrelational degree of the Fuji apple quality fromdifferent originand get weighted relational degree as shown in Table 5

Using the chart function in Excel 2003 we generate theclumps bar graph as shown in Figure 2

4 Mathematical Problems in Engineering

Table 5 Relational degree

Charactersrsquo name Relational degree Sort100 083 300200 079 600300 079 700400 078 800500 080 500600 086 100700 082 400800 075 900900 083 200

Relational degree088086084082080078076074072070068

200 300 400 500 600 700 800 900100

Figure 2 The bar graph

If we input equal-weight in the raw data sheet (as shownin Table 6) then final equal-weighted relational degreeclumps bar graph is generated as shown in Figure 3

According to relational analysis principle the sequencein which relational degree is biggest ismost close to referencesequence that is the variety is more close to ldquoideal varietyrdquoAmong them 9th variety is most close to ldquoideal varietyrdquofollowed by 6th variety 8th variety has max difference withit indicating that its comprehensive quality is worst The restof origin Fuji apple is centeredTheweighted relational degreehas the same sort as the equal-weight mainly due to the sameimportance of quality indexes

32 Crop Evaluation System In the above section we haveestablished the evaluationmodel It can be seen that thewholeprocess is very cumbersome and complex In particular forthe less skilled computer user the biggest drawback is that[29 30] when the objects change performance indicatorsmay be different and the weight of each index may need tobe changed and then the user will not be able to simply andflexibly use the model In order to make the model becomemore widely used easily increase or decrease characteristicnumber and modify the characteristics weight we use Cprogram language to develop the software based on the abovemodel and analysis steps It achieves automatic calculationand analysis of data The software interface and operation isas follows

Relational degree

200 300 400 500 600 700 800 900100

088

086

084

082

080

078

076

074

072

Figure 3 The bar graph

Figure 4 Main interface

(1) Operating system is the main interface as shown inFigure 4

(2) First import each strain of data to be analyzed thedata is written in Excel format The data format is asshown in Figure 5

(3) Browse the file and find the data sheet to be analyzedand then click the button ldquodata importrdquo to importthe data The software automatically calculates thenumber of strains and indicators Interface is shownin Figure 6

(4) According the user requirement the operator inputsthe weight and each trait parameter of ideal strainthen click the button ldquorelational degree analysisrdquo andthe software generates the relational degree curveThis paper adopts the same data as introduced inExcel methods in Figure 5 The result was shown inFigure 7

4 Discussion

GRA method is one of the very popular methods to analyzevarious relationships among the discrete data sets The majoradvantages of the GRA method are that the results are basedon the original data and the calculations are simple andstraightforward Different from previous studies the paperestablished the crop evaluation model based on the basicideal of traditional grey relational analysis (GRA) methodand also developed the crop evaluation system based on themodel With friendly interface and being easy to operate thesoftware can be easily performed on computer and suitablefor different families genera and species of plants Thedisadvantages of the traditional grey correlation analysis areovercome In addition setting weights is the key step of cropevaluation the operator can give different weights accordingto different crop types in the evaluation system

Mathematical Problems in Engineering 5

Table 6 Equal-weight

Input the crop name Apple Input characters number 8Input the weight 0125 0125 0125 0125 0125 0125 0125 0125Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Figure 5 The data format

Figure 6 The operation interface

5 Conclusions

GRA is part of grey system theory which is suitable for solv-ing complicated interrelationships between multiple factorsand variables When used to evaluate different crops qualityit can make full use of all the information about fruit qualitytraits and can give an objective and reasonable sort As dis-cussed in the above sections traditional methods have manyshortcomings using weighted relational degree to evaluatedifferent crops quality the distribution of weight often needsto be changed The interface is not friendly The operation isnot convenient and calculation process is complex and so onThe developed crop evaluation system overcomes the aboveshortcomings Taking the Fuji data as experimental data thepaper made the relational degree analysis It shows that thedeveloped crop evaluation system can greatly improve the

Figure 7 Relational degree curve

work efficiency of the researcher and expand the applicationscope

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Science and Technology PlanProjects of Hebei province (nos 15210138 and 15ZN010)

References

[1] L Weizhong A Yinghui X Chongxiang et al ldquoPhenotypiccharacter and yield research of maizi inbred lines based onGRArdquo Crops vol 5 pp 105ndash108 2012

[2] W Ma Q Guo C Wei H Li C Peng and Z Liang ldquoCom-prehensive evaluation of new self-cultivated sugarcane lines bygrey relational analysisrdquo Asian Agricultural Research vol 6 no9 pp 85ndash88 2014

[3] X-F Yan and Y Shen ldquoComprehensive quality evaluation ofdehaired cashmere fiber based on grey relational analysisrdquoWoolTextile Journal vol 42 no 11 pp 46ndash50 2014

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Table 5 Relational degree

Charactersrsquo name Relational degree Sort100 083 300200 079 600300 079 700400 078 800500 080 500600 086 100700 082 400800 075 900900 083 200

Relational degree088086084082080078076074072070068

200 300 400 500 600 700 800 900100

Figure 2 The bar graph

If we input equal-weight in the raw data sheet (as shownin Table 6) then final equal-weighted relational degreeclumps bar graph is generated as shown in Figure 3

According to relational analysis principle the sequencein which relational degree is biggest ismost close to referencesequence that is the variety is more close to ldquoideal varietyrdquoAmong them 9th variety is most close to ldquoideal varietyrdquofollowed by 6th variety 8th variety has max difference withit indicating that its comprehensive quality is worst The restof origin Fuji apple is centeredTheweighted relational degreehas the same sort as the equal-weight mainly due to the sameimportance of quality indexes

32 Crop Evaluation System In the above section we haveestablished the evaluationmodel It can be seen that thewholeprocess is very cumbersome and complex In particular forthe less skilled computer user the biggest drawback is that[29 30] when the objects change performance indicatorsmay be different and the weight of each index may need tobe changed and then the user will not be able to simply andflexibly use the model In order to make the model becomemore widely used easily increase or decrease characteristicnumber and modify the characteristics weight we use Cprogram language to develop the software based on the abovemodel and analysis steps It achieves automatic calculationand analysis of data The software interface and operation isas follows

Relational degree

200 300 400 500 600 700 800 900100

088

086

084

082

080

078

076

074

072

Figure 3 The bar graph

Figure 4 Main interface

(1) Operating system is the main interface as shown inFigure 4

(2) First import each strain of data to be analyzed thedata is written in Excel format The data format is asshown in Figure 5

(3) Browse the file and find the data sheet to be analyzedand then click the button ldquodata importrdquo to importthe data The software automatically calculates thenumber of strains and indicators Interface is shownin Figure 6

(4) According the user requirement the operator inputsthe weight and each trait parameter of ideal strainthen click the button ldquorelational degree analysisrdquo andthe software generates the relational degree curveThis paper adopts the same data as introduced inExcel methods in Figure 5 The result was shown inFigure 7

4 Discussion

GRA method is one of the very popular methods to analyzevarious relationships among the discrete data sets The majoradvantages of the GRA method are that the results are basedon the original data and the calculations are simple andstraightforward Different from previous studies the paperestablished the crop evaluation model based on the basicideal of traditional grey relational analysis (GRA) methodand also developed the crop evaluation system based on themodel With friendly interface and being easy to operate thesoftware can be easily performed on computer and suitablefor different families genera and species of plants Thedisadvantages of the traditional grey correlation analysis areovercome In addition setting weights is the key step of cropevaluation the operator can give different weights accordingto different crop types in the evaluation system

Mathematical Problems in Engineering 5

Table 6 Equal-weight

Input the crop name Apple Input characters number 8Input the weight 0125 0125 0125 0125 0125 0125 0125 0125Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Figure 5 The data format

Figure 6 The operation interface

5 Conclusions

GRA is part of grey system theory which is suitable for solv-ing complicated interrelationships between multiple factorsand variables When used to evaluate different crops qualityit can make full use of all the information about fruit qualitytraits and can give an objective and reasonable sort As dis-cussed in the above sections traditional methods have manyshortcomings using weighted relational degree to evaluatedifferent crops quality the distribution of weight often needsto be changed The interface is not friendly The operation isnot convenient and calculation process is complex and so onThe developed crop evaluation system overcomes the aboveshortcomings Taking the Fuji data as experimental data thepaper made the relational degree analysis It shows that thedeveloped crop evaluation system can greatly improve the

Figure 7 Relational degree curve

work efficiency of the researcher and expand the applicationscope

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Science and Technology PlanProjects of Hebei province (nos 15210138 and 15ZN010)

References

[1] L Weizhong A Yinghui X Chongxiang et al ldquoPhenotypiccharacter and yield research of maizi inbred lines based onGRArdquo Crops vol 5 pp 105ndash108 2012

[2] W Ma Q Guo C Wei H Li C Peng and Z Liang ldquoCom-prehensive evaluation of new self-cultivated sugarcane lines bygrey relational analysisrdquo Asian Agricultural Research vol 6 no9 pp 85ndash88 2014

[3] X-F Yan and Y Shen ldquoComprehensive quality evaluation ofdehaired cashmere fiber based on grey relational analysisrdquoWoolTextile Journal vol 42 no 11 pp 46ndash50 2014

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Table 6 Equal-weight

Input the crop name Apple Input characters number 8Input the weight 0125 0125 0125 0125 0125 0125 0125 0125Charactersrsquo name Fruit volume Skin color Flesh color Starch content The juice yield Solid acid ratio Fruit firmness Protein contentIdeal variety 32000 1200 minus020 040 5800 5500 27371 0561 31822 1340 035 047 5752 4811 27371 0302 22722 1410 009 065 7347 6471 25286 0463 24033 1110 017 059 6413 7605 27305 0374 31933 1723 006 066 6846 4839 24893 0275 22467 1337 013 074 6249 5231 27593 0316 27567 989 minus020 099 6722 5526 24704 0387 28944 1297 029 048 5993 4296 24704 0458 30556 1087 025 099 6725 4917 22614 0359 28822 1645 011 043 6255 3833 26913 056

Figure 5 The data format

Figure 6 The operation interface

5 Conclusions

GRA is part of grey system theory which is suitable for solv-ing complicated interrelationships between multiple factorsand variables When used to evaluate different crops qualityit can make full use of all the information about fruit qualitytraits and can give an objective and reasonable sort As dis-cussed in the above sections traditional methods have manyshortcomings using weighted relational degree to evaluatedifferent crops quality the distribution of weight often needsto be changed The interface is not friendly The operation isnot convenient and calculation process is complex and so onThe developed crop evaluation system overcomes the aboveshortcomings Taking the Fuji data as experimental data thepaper made the relational degree analysis It shows that thedeveloped crop evaluation system can greatly improve the

Figure 7 Relational degree curve

work efficiency of the researcher and expand the applicationscope

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Science and Technology PlanProjects of Hebei province (nos 15210138 and 15ZN010)

References

[1] L Weizhong A Yinghui X Chongxiang et al ldquoPhenotypiccharacter and yield research of maizi inbred lines based onGRArdquo Crops vol 5 pp 105ndash108 2012

[2] W Ma Q Guo C Wei H Li C Peng and Z Liang ldquoCom-prehensive evaluation of new self-cultivated sugarcane lines bygrey relational analysisrdquo Asian Agricultural Research vol 6 no9 pp 85ndash88 2014

[3] X-F Yan and Y Shen ldquoComprehensive quality evaluation ofdehaired cashmere fiber based on grey relational analysisrdquoWoolTextile Journal vol 42 no 11 pp 46ndash50 2014

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

[4] Z Qifen and C Ruyi ldquoInfluence factors analysis of housingdemand by grey theory systemrdquo China Collective Economy vol10 no 28 pp 77ndash78 2014

[5] L Pei and Z Jian ldquoGrey relational analysis of producer servicesbased on panal datardquo Economic Research Guide no 28 pp 51ndash52 2014

[6] Y Kuo T Yang and G-W Huang ldquoThe use of grey relationalanalysis in solving multiple attribute decision-making prob-lemsrdquo Computers and Industrial Engineering vol 55 no 1 pp80ndash93 2008

[7] S-Q Jiang S-F Liu Z-X Liu and Z-G Fang ldquoGrey incidencedecision making model based on areardquo Control and Decisionvol 30 no 4 pp 685ndash690 2015

[8] Y Li and X Zhang ldquoApplication of grey relational analysisbased on entropy-weight in the assessment of urban sustainabledevelopmentrdquo Journal of University of Chinese Academy ofScience vol 31 no 5 pp 662ndash670 2014

[9] J-S Heh ldquoEvaluationmodel of problem solvingrdquoMathematicaland Computer Modelling vol 30 no 11-12 pp 197ndash211 1999

[10] W-C Chang K-L Wen H S Chen and T-C Chang ldquoSelec-tion model of pavement material via Grey relational graderdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics pp 3388ndash3391 October 2000

[11] Z Xianliang W Zhanqing H Zhibang et al ldquoGrey cor-relation multidimensional comprehensive evaluation of newwatermelon varietiesrdquo Journal of Shanxi Agricultural Sciencesvol 42 no 10 pp 1067ndash1070 2014

[12] G FenglianW Qiang and L Peipei ldquoApplication of grey corre-lation degree of evaluation of different organic fertilizer rottenproportionrdquo Journal of Anhui Agricultural Sciences vol 42 no29 pp 10054ndash10056 2014

[13] G-W Wei ldquoGRA method for multiple attribute decision mak-ing with incomplete weight information in intuitionistic fuzzysettingrdquo Knowledge-Based Systems vol 23 no 3 pp 243ndash2472010

[14] P N Singh K Raghukandan and B C Pai ldquoOptimization byGrey relational analysis of EDM parameters on machining Al-10 SiCP compositesrdquo Journal of Materials Processing Technol-ogy vol 155-156 no 1ndash3 pp 1658ndash1661 2004

[15] J Hou ldquoGrey relational analysis method for multiple attributedecision making in intuitionistic fuzzy settingrdquo Journal ofConvergence Information Technology vol 5 no 10 pp 194ndash1992010

[16] A Borboni and R Faglia ldquoStochastic evaluation and analysisof free vibrations in simply supported piezoelectric bimorphsrdquoJournal of AppliedMechanics Transactions ASME vol 80 no 2Article ID 021003 2013

[17] Q Song and A Jamalipour ldquoNetwork selection in an integratedwireless lan and UMTS environment using mathematical mod-eling and computing techniquesrdquo IEEE Wireless Communica-tions vol 12 no 3 pp 42ndash48 2005

[18] J Shen S Shi Y Zhou Y Zhang and Z Yao ldquoSurface waterenvironmental quality assessment of danjiangkou valley basedon improved grey correlation analysisrdquo EnvironmentalMonitor-ing in China vol 5 no 10 pp 41ndash46 2014

[19] Z Gu H Chen Y Wang Y Sun J Ding and Y Zhang ldquoSafetyevaluation of angelicae sinensis radix by grey incidence degreemethodrdquo Chinese Journal of Experimental Traditional MedicalFormulae vol 17 no 9 pp 60ndash64 2014

[20] A Tao andH Yin ldquoAn analysis on the energy consumption andeconomy increase based on grey relation theoryrdquo in Proceedings

of the International Conference on Engineering and BusinessManagement (EBM rsquo11) 2011

[21] J Zhao and XWang ldquoThe grey relational analysis of CO2 emis-sions and its influencing factorsrdquo in Proceedings of the IEEEInternational Conference on Engineering Technology and Eco-nomic Management (ICETEM rsquo12) Beijing China 2012

[22] G Li H-J Han and X-M Huang ldquoGray relational evalua-tion model with weights based on DEA cross-efficiencyrdquo inProceedings of the 2nd International Conference on IndustrialMechatronics and Automation (ICIMA rsquo10) pp 236ndash239 May2010

[23] Y Lu and H Wei ldquoResearch on the motivation of the customerparticipation based on gray relational analysisrdquo in Proceedingsof the International Conference on Business Management andElectronic Information (BMEI rsquo11) vol 3 pp 438ndash441 May 2011

[24] W Xuan B Jinfeng L Xuan et al ldquoGrey application of greycorrelation analysis for evaluating the overall quality of fujiapples from different growing areasrdquo Food Science vol 34 no23 pp 88ndash91 2013

[25] H Zhang T Han and J Liu ldquoEvaluation of peach quality basedon grey relational analysisrdquoNorthern Horticulture no 12 pp 9ndash13 2008

[26] W Xiuping Z Guoxin L Xuelin et al ldquoComprehensive eval-uation of rice new variety based on grey relational analysisrdquoChinese Agricultural Science Bulletin vol 22 no 8 pp 557ndash5592006

[27] C-K Ke and M-Y Wu ldquoA selection approach for optimizedproblem-solving process by grey relational utility model andmulticriteria decision analysisrdquoMathematical Problems in Engi-neering vol 2012 Article ID 293137 14 pages 2012

[28] S Ghosh P Sahoo and G Sutradhar ldquoTribological perfor-mance optimization of Al-75 SiCp composites using thetaguchi method and grey relational analysisrdquo Journal of Com-posites vol 2013 Article ID 274527 9 pages 2013

[29] C Lingguang ldquoApplication of grey relational analysis in oil-teabreedingrdquo Forest Inventory and Planning vol 34 no 4 pp 33ndash36 2009

[30] Z Shaorong and L Guo ldquoComprehensive evaluation of potatonew variety by grey relational analysisrdquo Journal of MountainAgriculture and Biology vol 23 no 3 pp 202ndash205 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of