Research Article A Note on Hypertension …downloads.hindawi.com/archive/2013/342970.pdfcoronary heart disease (CHD). Srivastava and Sharma [ ] designed a so computing diagnostic system

Hindawi Publishing CorporationISRN BiomathematicsVolume 2013, Article ID 342970, 11 pageshttp://dx.doi.org/10.1155/2013/342970

Research ArticleA Note on Hypertension Classification Scheme andSoft Computing Decision Making System

Pankaj Srivastava,1 Amit Srivastava,2 Anjali Burande,3 and Amit Khandelwal2

1 Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211004, India2 Applied Mechanics Department, Motilal Nehru National Institute of Technology, Allahabad 211004, India3 Department of Mathematics, Dayanand College of Commerce, Latur 413512, India

Correspondence should be addressed to Pankaj Srivastava; [email protected]

Received 22 July 2013; Accepted 28 August 2013

Academic Editors: V. P. Emerenciano and J. R. C. Piqueira

Copyright © 2013 Pankaj Srivastava et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Nowadays young professionals are a soft target of hypertension due to the increased work pressure and poor tolerance.Many peoplehave high blood pressure for years without knowing it. Most of the time, there are no symptoms, but when this condition goesuntreated it damages arteries and vital organs throughout the body and that is why it is also termed as the silent killer. Complicationsarising from hypertension could lead to stroke and heart failure. Soft computing approach provides a sharper conclusion fromvague, ambiguous, and imprecise data (generally found in medical field) using linguistic variables. In this study, a soft computingdiagnostic support system for the risk assessment of hypertension is proposed.

1. Introduction

A human body is a complex system and there are a numberof variables that affect its functioning. The abnormalityin its functioning causes a number of symptoms in theform of primary stages of different diseases although therecognition of these symptoms and their mapping with thediseases precisely is not an easy one. Sometimes compicationsin human body may be caused by improper diagnosis orimproper management of the disease or due to the inac-cessibility of medical personnel [1]. The quickening speedof change and adoption of western lifestyles by people indeveloping countries have led to a sharp rise in the incidenceof hypertension [2]. Hypertension is a medical term for highblood pressure which is a condition that occurs when thepressure in the arteries is above the normal range. Accordingto one of the studies “Recession has had an adverse impacton jobs in India and perhaps this is one of the reasons whycases of Hypertension have gone up in past two years amongyoung IT professionals”. Recent analysis has predicted thatmore than 1.56 billon people will be living with hypertensionworldwide by the year 2025. It has been declared by a surveyreport that one of four adults in India has high BP which

kills 7.5million people worldwide each year; moreover, AIDS,diabetes, road accidents, and tuberculosis are put together. InIndia 23.1% men and 22.6% women have high BP a notchlower than the global prevalence of one in three adults saysthe World Health statistics 2012 released, 16 May 2012. Jain[3] established a decision making process phenomenon inthe presence of fuzzy variables. Poli et al. [4] developed aneural network expert system for diagnosing and treatinghypertension. Degani [5] discussed computerized electrocar-diogram diagnosis using fuzzy approach. Charbonnier et al.[6] proposed the statistical and fuzzy models of ambulatorysystolic blood pressure for hypertension diagnosis. Jena et al.[7] discussed the application of soft computing in medicalscience. Pandey et al. [8] proposed a rule based systemfor cardiac analysis based on electrocardiography. Further,Allahverdi et al. [9] proposed a fuzzy expert system forthe determination of coronary heart disease risk (CHD) ofpatient for the next ten years. Nalayini and Wahidabanu[10] were of the view that most of the cardiac diseasesare characterized by varied degrees of intricacy and theconventional procedures are not capable of dealing with theseintricacies very efficiently. Djam and Kimbi [1] developed a

2 ISRN Biomathematics

Table 1

Systolic BP in mmHg Diastolic BP in mmHgDesirable 90–120 60–80Above desirable 120–130 80–85Moderate 130–140 85–90Above moderate 140–150 90–95Little high 150–160 95–100High 160–170 100–110Very high >168 >108

fuzzy expert system for the management of hypertension.Recently, P. Srivastava and A. Srivastava [11] proposed a softcomputing diagnostic system to evaluate the risk factor forcoronary heart disease (CHD). Srivastava and Sharma [12]designed a soft computing diagnostic system that classifiesECG beats in different phases and enables us to identifythe status of cardiac health as per available ECG graphs.The present paper introduces a new soft computing modelthat measures risk factor on the basis of newly designedalgorithm; a number of cases have been discussed as peravailable database.

2. Methodology

For complex systems, fuzzy tools are quite suitable becauseof its tolerance to some imprecision. In the present study, theinputs consist of age, systolic blood pressure (SBP), diastolicblood pressure (DBP), bodymass index (BMI), heart rate, lowdensity lipoprotein (LDL), high density lipoprotein (HDL),triglyceride, smoking, and exercise, while the output is therisk grade of hypertension.

In order to design a user friendly informative system forevaluating risk percentage of hypertension, we propose fuzzyAlgorithm 1.

2.1. Input Variables

2.1.1. Blood Pressure. In this fieldwe use systolic BP (SBP) anddiastolic BP (DBP).The input variables for SBP andDBPwereclassified into seven fuzzy sets (see Table 1).

Systolic Blood Pressure (SBP). Consider

𝜇desirable =

{{{{{{{{

{{{{{{{{

{

1 𝑥 ≤ 90

(

𝑥 − 90

15

)

2

90 ≤ 𝑥 < 105

1 − (

𝑥 − 105

15

)

2

105 ≤ 𝑥 < 120

0 𝑥 ≥ 120,

𝜇above desirable =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 120

𝑥 − 120

3

120 < 𝑥 ≤ 123

1 123 < 𝑥 ≤ 127

130 − 𝑥

3

127 < 𝑥 ≤ 130

0 𝑥 ≥ 130,

𝜇moderate =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 130

𝑥 − 130

3

130 < 𝑥 ≤ 133

1 133 < 𝑥 ≤ 137

140 − 𝑥

3

137 < 𝑥 ≤ 140

0 𝑥 ≥ 140,

𝜇above moderate =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 140

𝑥 − 140

3

140 < 𝑥 ≤ 143

1 143 < 𝑥 ≤ 147

150 − 𝑥

3

147 < 𝑥 ≤ 150

0 𝑥 ≥ 150,

𝜇little high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 150

𝑥 − 150

3

150 < 𝑥 ≤ 153

1 153 < 𝑥 ≤ 157

160 − 𝑥

3

157 < 𝑥 ≤ 160

0 𝑥 ≥ 160,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 160

𝑥 − 160

3

160 < 𝑥 ≤ 163

1 163 < 𝑥 ≤ 167

170 − 𝑥

3

167 < 𝑥 < 170

0 𝑥 ≥ 170,

𝜇very high =

{{{{{{{{

{{{{{{{{

{

0 𝑥 ≤ 168

(

𝑥 − 168

6

)

2

168 ≤ 𝑥 < 174

1 − (

𝑥 − 174

6

)

2

174 ≤ 𝑥 < 180

1 𝑥 ≥ 180.

(1)

Diastolic Blood Pressure (DBP)

𝜇normal =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 60

(

𝑥 − 60

10

)

2

60 ≤ 𝑥 < 70

1 − (

𝑥 − 70

10

)

2

70 ≤ 𝑥 < 80

0 𝑥 ≥ 80,

ISRN Biomathematics 3

(I) Initial fuzzification mechanismBEGIN

(1) Input-Fuzzy system with suitable “𝑛” parameters 𝐴𝑖

(2) Initialize 𝑖 ← 1

DOUNTIL (𝑖 > 𝑛)Categorize 𝑛

𝑖fuzzy sets in𝑋

𝑗linguistic variables

DOUNTIL (𝑗 > 𝑛𝑖)

(1) Construction of suitable membership function 𝜇𝑋𝑗

(2) Increment 𝑗ENDDOUNTILIncrement 𝑖END

(II) Construction of Fuzzy StringsBEGIN

(1) Input: “𝑛𝑖” fuzzy sets in linguistic variables

𝑋𝑗; 𝑖 = 1, 2, . . ., 𝑛 and 𝑗 = 1, 2, . . . , 𝑛

𝑖

(2) Input:𝑚 output parameters 𝑌𝑜, 𝑜 = 1, 2, . . . , 𝑚.

(3) Develop 𝑡 = 𝑘1, 𝑘2, . . . , 𝑘

𝑟linguistic strings 𝐽

𝑘; 𝑘 = 1, 2, . . . , 𝑡

using AND operation on each linguistic term𝑋𝑗; 𝑗 = 1, 2, . . . , 𝑛

𝑖

(4) Initialize 𝑘 ← 1

DOUNTIL (𝑘 > 𝑡)Increment 𝑗ENDDOUNTILIncrement 𝑘END

(III) Output EvaluationBEGIN

(1) Construct Utility matrix 𝑈 of pxq order.(2) Construct 𝑟 utility fuzzy sets 𝑈

𝐼; 𝐼 = 1, 2, . . . 𝑟

using 𝑥 ⊕ 𝑦 = 𝑥 + 𝑦 − 𝑥𝑦 for each 𝑥, 𝑦 ∈ 𝑈

(3) Initialize 𝐼 ← 1

DOUNTIL (𝐼 > 𝑟)(4) Construct 𝑟maximizing sets 𝑈

𝑀𝐼, 𝐼 = 1, 2 . . . 𝑟

corresponding to each alternative.(5) Develop 𝑟 optimal fuzzy utility sets 𝑈

𝑂𝐼, 𝐼 = 1, 2 . . . 𝑟.

Each optimal fuzzy set 𝑈𝑂𝐼

is obtained by fuzzyintersection⋀ on fuzzy utility set and maximizingset such that 𝜇

𝑈𝑂𝐼(𝑥) = 𝜇

𝑈𝐼(𝑥)⋂𝜇

𝑈𝑀𝐼(𝑥) = min(𝜇

𝑈𝐼(𝑥) , 𝜇

𝑈𝑀𝐼(𝑥))

for each utility value 𝑥.(6) Take maximum membership value from each optimal utility fuzzy set.(7) The optimal alternative 𝐴

𝑂with corresponding maximum

membership grades obtained in step 10 such as𝐴𝑂= {((max) 𝜇

𝑈𝑂𝐼(𝑥) , 𝐵

𝐼) : ⋁𝑥 ∈ 𝑈

𝑂𝐼} for 𝐼 = 1, 2 . . . 𝑟.

ENDDOUNTILIncrement 𝐼END

Algorithm 1

𝜇above normal =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 80

𝑥 − 80

2

80 < 𝑥 ≤ 82

85 − 𝑥

3

82 < 𝑥 ≤ 85

0 𝑥 ≥ 85,

𝜇moderate =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 85

𝑥 − 85

2

85 < 𝑥 ≤ 87

90 − 𝑥

3

87 < 𝑥 ≤ 90

0 𝑥 ≥ 90,


Table 2

Cholesterol (mg/dL)LDL HDL

Normal ≤100 Very high ≤30Above normal 100–130Borderline high 130–160 High 30–50High 160–190 Nearly normal 50–60Very high ≥180 Normal ≥58

𝜇above moderate =

{{{{{{{{

{{{{{{{{

{

0 𝑥 ≤ 90

𝑥 − 90

2

90 < 𝑥 ≤ 92

95 − 𝑥

3

92 < 𝑥 ≤ 95

0 𝑥 ≥ 95,

𝜇little high =

{{{{{{{{

{{{{{{{{

{

0 𝑥 ≤ 95

𝑥 − 95

2

95 < 𝑥 ≤ 97

100 − 𝑥

3

97 < 𝑥 ≤ 100

0 𝑥 ≥ 100,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 100

𝑥 − 100

5

100 < 𝑥 ≤ 105

110 − 𝑥

5

105 < 𝑥 ≤ 110

0 𝑥 ≥ 110,

𝜇very high =

{{{{{{{{

{{{{{{{{

{

0 𝑥 ≤ 108

(

𝑥 − 108

6

)

2

108 ≤ 𝑥 < 114

1 − (

𝑥 − 114

6

)

2

114 ≤ 𝑥 < 120

1 𝑥 ≥ 120.

(2)

2.1.2. Cholesterol. In this studywe have classified total choles-terol into low density lipoprotein (LDL) cholesterol and highdensity lipoprotein (HDL). HDL cholesterol level has beenclassified into four fuzzy sets. LDL cholesterol level has beenclassified into five fuzzy sets.High levels of LDL are associatedwith coronary artery disease, whereas high levels of HDLappear to protect against coronary artery disease.These fuzzysets have been shown in Table 2.

Low Density Lipoprotein (LDL). Consider

𝜇normal =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 50

(

𝑥 − 50

25

)

2

50 ≤ 𝑥 < 75

1 − (

𝑥 − 75

25

)

2

75 ≤ 𝑥 < 100

0 𝑥 ≥ 100,

𝜇above normal =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 100

𝑥 − 100

10

100 < 𝑥 ≤ 110

1 110 ≤ 𝑥 ≤ 120

130 − 𝑥

10

120 < 𝑥 ≤ 130

0 𝑥 ≥ 130,

𝜇borderline high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 130

𝑥 − 130

10

130 < 𝑥 ≤ 140

1 140 ≤ 𝑥 ≤ 150

160 − 𝑥

10

150 < 𝑥 ≤ 160

0 𝑥 ≥ 160,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 160

𝑥 − 160

10

160 < 𝑥 ≤ 170

1 170 ≤ 𝑥 ≤ 180

190 − 𝑥

10

180 < 𝑥 ≤ 190

0 𝑥 ≥ 190,

𝜇very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 180

(

𝑥 − 190

20

)

2

180 ≤ 𝑥 < 200

1 − (

𝑥 − 200

20

)

2

200 ≤ 𝑥 < 220

1 𝑥 ≥ 220.

(3)

High Density Lipoprotein (HDL). Consider

𝜇very high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 0

𝑥 − 0

10

0 < 𝑥 ≤ 10

1 10 < 𝑥 ≤ 20

30 − 𝑥

10

20 < 𝑥 ≤ 30

0 𝑥 ≥ 30,


𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 30

𝑥 − 30

5

30 < 𝑥 ≤ 35

1 35 < 𝑥 ≤ 45

50 − 𝑥

5

45 < 𝑥 ≤ 50

0 𝑥 ≥ 50,

𝜇nearly normal =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 50

𝑥 − 50

3

50 < 𝑥 ≤ 53

1 53 < 𝑥 ≤ 57

60 − 𝑥

3

57 < 𝑥 ≤ 60

0 𝑥 ≥ 60,

𝜇normal =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 58

(

𝑥 − 58

7

)

2

58 ≤ 𝑥 < 65

1 − (

𝑥 − 65

5

)

2

65 ≤ 𝑥 < 70

1 𝑥 ≥ 70.

(4)

2.1.3. Age. This input field is classified into six fuzzy sets. Thefuzzy sets with their range are shown in Table 3. Consider

𝜇young =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 0

(

𝑥 − 0

15

)

2

0 ≤ 𝑥 < 15

1 − (

𝑥 − 15

15

)

2

15 ≤ 𝑥 < 30

0 𝑥 ≥ 30,

𝜇adult =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 < 25

𝑥 − 25

5

25 ≤ 𝑥 ≤ 30

1 30 ≤ 𝑥 ≤ 40

48 − 𝑥

8

40 ≤ 𝑥 ≤ 48

0 𝑥 ≥ 48,

𝜇mid aged =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 < 45

𝑥 − 45

5

45 ≤ 𝑥 ≤ 50

1 50 ≤ 𝑥 ≤ 56

60 − 𝑥

4

56 ≤ 𝑥 ≤ 60

0 𝑥 ≥ 60,

𝜇aged =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 < 58

𝑥 − 58

4

58 ≤ 𝑥 ≤ 62

1 62 ≤ 𝑥 ≤ 66

72 − 𝑥

6

66 ≤ 𝑥 ≤ 72

0 𝑥 ≥ 72,

Table 3

Age (in years)Young <30Adult 25–48Midaged 45–60Aged 58–72Old 70–86Very old >80

Table 4

Body mass index (kg/m2)Low (underweight) 10–18Medium (normal weight) 15–26Above medium (overweight) 25–34High (obese) 32–40Very high (severe obese) 38–46Very very high (super obese) 44–50

𝜇old =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 < 70

𝑥 − 70

4

70 ≤ 𝑥 ≤ 74

1 74 ≤ 𝑥 ≤ 78

86 − 𝑥

8

78 ≤ 𝑥 ≤ 86

0 𝑥 ≥ 86,

𝜇very old =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 80

(

𝑥 − 80

7

)

2

80 ≤ 𝑥 < 87

1 − (

𝑥 − 87

8

)

2

87 ≤ 𝑥 < 95

1 𝑥 ≥ 95.

(5)

2.1.4. BMI. Body mass index is defined as the individual’sbody weight divided by square of his or her height.This inputfield is classified into four fuzzy sets.The fuzzy sets with theirrange are shown in Table 4. Consider

𝜇low =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 10

(

𝑥 − 10

4

)

2

10 ≤ 𝑥 < 14

1 − (

𝑥 − 14

4

)

2

14 ≤ 𝑥 < 18

0 𝑥 ≥ 18,

𝜇medium =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 15

𝑥 − 15

3

15 < 𝑥 ≤ 18

1 18 < 𝑥 ≤ 24

26 − 𝑥

2

24 < 𝑥 ≤ 26

0 𝑥 ≥ 26,


Table 5

Heart rate (beats/min)Low 50–65Normal 60–80High 78–110Very high 105–125

𝜇above medium =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 25

𝑥 − 25

2

25 < 𝑥 ≤ 27

1 27 < 𝑥 ≤ 30

34 − 𝑥

4

30 < 𝑥 ≤ 34

0 𝑥 ≥ 34,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 32

𝑥 − 32

2

32 < 𝑥 ≤ 34

1 34 < 𝑥 ≤ 38

40 − 𝑥

2

38 < 𝑥 ≤ 40

0 𝑥 ≥ 40,

𝜇very high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 38

𝑥 − 38

2

38 < 𝑥 ≤ 40

1 40 < 𝑥 ≤ 44

46 − 𝑥

2

44 < 𝑥 ≤ 46

0 𝑥 ≥ 46,

𝜇very very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 44

(

𝑥 − 44

3

)

2

44 ≤ 𝑥 < 47

1 − (

𝑥 − 47

3

)

2

47 ≤ 𝑥 < 50

1 𝑥 ≥ 50.

(6)

2.1.5. Heart Rate. This input field is classified into fourlinguistic variables.The fuzzy sets with their range are shownin Table 5. Consider

𝜇low =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 50

(

𝑥 − 50

6

)

2

50 ≤ 𝑥 < 56

1 − (

𝑥 − 56

9

)

2

56 ≤ 𝑥 < 65

0 𝑥 ≥ 65,

Table 6

Triglyceride (mg/dL)Normal <150A little bit high 150–200High 200–500Very high ≥500

𝜇normal =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 60

𝑥 − 60

10

60 < 𝑥 ≤ 70

1 70 < 𝑥 ≤ 75

80 − 𝑥

5

75 < 𝑥 ≤ 80

0 𝑥 ≥ 80,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 78

𝑥 − 78

12

78 < 𝑥 ≤ 90

1 90 < 𝑥 ≤ 100

110 − 𝑥

10

100 < 𝑥 ≤ 110

0 𝑥 ≥ 110,

𝜇very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 105

(

𝑥 − 105

10

)

2

105 ≤ 𝑥 < 115

1 − (

𝑥 − 115

10

)

2

115 ≤ 𝑥 < 125

1 𝑥 ≥ 125.

(7)

2.1.6. Triglyceride. Triglycerides have been identified to play amajor role in heart disease and hypertension.This input fieldis classified into four fuzzy sets.The fuzzy setswith their rangeare shown in Table 6. Consider

𝜇normal =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 0

(

𝑥 − 75

75

)

2

0 ≤ 𝑥 < 75

1 − (

𝑥 − 75

75

)

2

75 ≤ 𝑥 < 150

0 𝑥 ≥ 150,

𝜇a little bit high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 150

𝑥 − 150

15

150 < 𝑥 ≤ 165

1 165 ≤ 𝑥 ≤ 185

200 − 𝑥

15

185 < 𝑥 ≤ 200

0 𝑥 ≥ 200,


Table 7

Exercise (in Min)Low effective 5–30medium effective 30–60High effective 60–100Very high effective 90–120

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 200

𝑥 − 200

100

200 < 𝑥 ≤ 300

1 300 ≤ 𝑥 ≤ 400

500 − 𝑥

100

400 < 𝑥 ≤ 500

0 𝑥 ≥ 500,

𝜇very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 500

(

𝑥 − 500

100

)

2

500 ≤ 𝑥 < 600

1 − (

𝑥 − 600

100

)

2

600 ≤ 𝑥 < 700

1 𝑥 ≥ 700.

(8)

2.1.7. Physical Exercise. This input field is classified into fourfuzzy sets. The fuzzy sets with their range are shown inTable 7. If a person is not doing exercise, then input value iszero. Consider

𝜇low =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 5

(

𝑥 − 5

12

)

2

5 ≤ 𝑥 < 17

1 − (

𝑥 − 17

13

)

2

17 ≤ 𝑥 < 30

0 𝑥 ≥ 30,

𝜇medium =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 30

𝑥 − 30

10

30 < 𝑥 ≤ 40

1 40 ≤ 𝑥 ≤ 50

60 − 𝑥

10

50 < 𝑥 ≤ 60

0 𝑥 ≥ 60,

𝜇high =

{{{{{{{{{

{{{{{{{{{

{

0 𝑥 ≤ 60

𝑥 − 60

10

60 < 𝑥 ≤ 70

1 70 ≤ 𝑥 ≤ 90

100 − 𝑥

10

90 < 𝑥 ≤ 100

0 𝑥 ≥ 100,

Table 8

Smoking (per day)Low smoker 5–10 cigarettesMedium smoker 8–20 cigarettesHigh smoker 18–30 cigarettesVery high smoker 28–35 cigarettes

𝜇very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 90

(

𝑥 − 90

15

)

2

90 ≤ 𝑥 < 105

1 − (

𝑥 − 105

15

)

2

105 ≤ 𝑥 < 120

1 𝑥 ≥ 120.

(9)

2.1.8. Smoking. This input field is classified into four fuzzysets. The fuzzy sets with their range are shown in Table 8. Ifperson is not smoking, then input value is zero. Consider

𝜇low =

{{{{{{{

{{{{{{{

{

1 𝑥 ≤ 5

(

𝑥 − 5

2

)

2

5 ≤ 𝑥 < 7

1 − (

𝑥 − 7

3

)

2

7 ≤ 𝑥 < 10

0 𝑥 ≥ 10,

𝜇medium =

{{{{{{

{{{{{{

{

0 𝑥 ≤ 8

𝑥 − 8

6

8 < 𝑥 ≤ 14

20 − 𝑥

6

14 < 𝑥 ≤ 20

0 𝑥 ≥ 20,

𝜇high =

{{{{{{

{{{{{{

{

0 𝑥 ≤ 18

𝑥 − 18

6

18 < 𝑥 ≤ 24

30 − 𝑥

6

24 < 𝑥 ≤ 30

0 𝑥 ≥ 30,

𝜇very high =

{{{{{{{

{{{{{{{

{

0 𝑥 ≤ 28

(

𝑥 − 28

4

)

2

28 ≤ 𝑥 < 32

1 − (

𝑥 − 32

3

)

2

32 ≤ 𝑥 < 35

1 𝑥 ≥ 35.

(10)

2.2. Output Variable. The output contains risk grade ofhypertension which is classified in five linguistic variables,very low, low, moderate, high, and very high. The outputoptimal alternatives indicate patient’s present grade of hyper-tension. These optimal alternatives have been graphicallyshown in the form of Sugeno’s spikes.


3. Result

Nowwe have developed various linguistic strings to representthe state of the patient using the input variables such as age,LDL, HDL, SBP, DBP, triglyceride, BMI, HR, exercise, andsmoking. Some of the linguistic strings are given as follows.

J1

= YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglyceride MBMINormalHRNoExcerciseNoSmoking

J2

= YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglyceride MBMINormalHRLowExcerciseLowSmoking

J3

= YoungAgeNormalLDLNormalHDL DesirableSBPDesirableDBPNormalTriglyceride MBMINormalHRMediumExcerciseLowSmoking

J400

= YoungAgeNormalLDLNormalHDLNormalSBPNormalDBPNormalTriglycerideAMBMI NormalHRMediumExcerciseLowSmoking

J401

= YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideAMBMI HighHRMediumExcerciseMedSmoking

J2500

= AdultAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMI NormalHRNoExcerciseNoSmoking

J6500

= AdultAgeHighLDLHighHDLDesirableSBP Mode-rateDBPNormalTriglyceride AMBMIHighHRLowExcerciseLowSmoking

J10001

= AdultAgeHighLDLHighHDLDesirableSBP Mo-derateDBPNormalTriglycerideAMBMI HighHRLowExcerciseMediumSmoking

J17009

= MidagedAgeNormalLDLNormalHDL De-sirableSBPDesirableDBPNormalTriglycerideMBMI Nor-malHRNoExcerciseNoSmoking

J17010

= MidagedAgeNormalLDLNormalHDL Desir-ableSBPDesirableDBPNormalTriglycerideMBMI HighHRNoExcerciseLowSmoking

J200080

= AgedAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMI NormalHRNoExcerciseNoSmoking

J405001

= AgedAgeHighLDLHighHDLModerateSBP Mod-erateDBPNormalTriglycerideVHBMI VHHRLowExcerciseMediumSmoking

J966080

= AgedAgeVeryHighLDLNVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideVHBMINormalHRLowExcercisehighSmoking

J1200200

= OldAgeHighLDLNormalHDL AboveDesira-bleSBPModerateDBPNormalTriglyceride AMBMI Nor-malHRLowExcercise NoSmoking

J2344569

= OldAgeVeryHighLDLNVeryhighHDL Ver-yhighSBPhighDBPVeryhighTriglyceride AMBMIHighHRNoExcerciseVery highSmoking

J5676880

= VeryOldAgeVeryhighLDLNormalHDL Mod-erateSBPADesirableDBPNormalTriglyceride AMBMINor-malHRLowExcercise LowSmoking

J7566780

= VeryoldAgeHighLDLHighHDL VeryhighSBPVeryhighDBPVeryhighTriglyceride HighBMIVHHRNoExcerciseVeryhighSmoking

J8545200

= VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPHighDBPV.highTriglyceride VHBMIHighHRNoExcercisehighSmoking

J9031678

= VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglyceride VHBMIVHHRLowExcerciseVery highSmoking

J9031680

= VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideMVVHBMIVHHRNoExcerciseVery highSmoking.

On the basis of our proposed technique to investigate thehealth status of a personwhosemedical data is available, threedifferent cases have been discussed as follows.

Case 1. The input variables of first patient are

(1) Age = {(0, young), (0.8, adult), (0,midaged), (0, aged),(0, old), (0, very old)}.

(2) LDL = {(0.71, normal), (0, above normal), (0, border-line high), (0, high), (0, very high)}.


(3) HDL = {(0, very high), (0, high), (0, nearly normal),(1, normal)}.

(4) SBP = {(0, desirable), (0.8, above desirable), (0, mod-erate), (0, above moderate), (0, little high), (0, high),(0, very high)}.

(5) DBP = {(0, desirable), (1, above desirable), (0, moder-ate), (0, above moderate), (0, little high), (0, high), (0,very high)}.

(6) Triglyceride = {(0.72, normal), (0, a little bit high), (0,high), (0, very high)}.

(7) BMI = {(0, low), (0.99, medium), (0, above medium),(0, high), (0, very high), (0, very very high)}.

(8) HR = {(0, low), (0.86, normal), (0, high), (0, veryhigh)}.

(9) Exercise = {(1, low), (0, medium), (0, high), (0, veryhigh)}.

(10) Smoking = {(1, low), (0, medium), (0, high), (0, veryhigh)}.

This is the fuzzy set which represents the state of con-cerned patient:

𝑋 = {(0.71, 𝐽𝐴,𝑁,𝑁,𝐴𝐷,𝐴𝐷,𝑁,𝑀,𝑁,𝐿,𝐿

)} . (11)

The utility matrix 𝑈 of order 5𝑥 9031680 by using thefuzzy rule base designed is as follows:

𝑈 = (

98 95 ⋅ ⋅ ⋅ 10 ⋅ ⋅ ⋅ 10 ⋅ ⋅ ⋅ 05

68 80 ⋅ ⋅ ⋅ 20 ⋅ ⋅ ⋅ 30 ⋅ ⋅ ⋅ 10

30 25 ⋅ ⋅ ⋅ 45 ⋅ ⋅ ⋅ 62 ⋅ ⋅ ⋅ 40

20 20 ⋅ ⋅ ⋅ 92 ⋅ ⋅ ⋅ 90 ⋅ ⋅ ⋅ 86

10 10 ⋅ ⋅ ⋅ 55 ⋅ ⋅ ⋅ 20 ⋅ ⋅ ⋅ 95

) . (12)

The five fuzzy utilities are

(1) 𝑈1= {(0.71, 98)},

(2) 𝑈2= {(0.71, 68)},

(3) 𝑈3= {(0.71, 30)},

(4) 𝑈4= {(0.71, 20)},

(5) 𝑈5= {(0.71, 10)}.

The maximum sets corresponding to each alternative are

(1) 𝑈1m = {(1, 98)},

(2) 𝑈2m = {(0.69, 68)},

(3) 𝑈3m = {(0.30, 30)},

(4) 𝑈4m = {(0.20, 20)},

(5) 𝑈5m = {(0.10, 10)}.

Now, the optimal fuzzy utilities using fuzzy utilities andmaximizing sets are

(1) 𝑈1o = {(0.71, 98)},

(2) 𝑈2o = {(0.69, 68)},

(3) 𝑈3o = {(0.30, 30)},

0.18

0.37

0.560.66 0.62

0

0.2

0.4

0.6

0.8

1

Very low Low Moderate High Very high

Mem

bers

hip

valu

e

Grade of hypertension

Case 1

Figure 1: View of Sugeno’s spikes.

(4) 𝑈4o = {(0.20, 20)},

(5) 𝑈5o = {(0.10, 10)}.

Using these utilities, the optimal alternatives are given by

𝐴𝑜= {(0.71, very low) , (0.69, low) , (0.30,moderate) ,

(0.20, high) , and (0.10, very high)} .(13)

This optimal alternative indicates that the patientpresently is in very low grade of hypertension. The optimalalternatives have been graphically shown in Figure 1 in theform of Sugeno’s spikes.

Case 2. The input variables of the second patient are asfollows.

(1) Age = {(0, young), (0, adult), (1, midaged), (0, aged),(0, old), (0, very old)}.

(2) LDL = {(1, normal), (0, above normal), (0, borderlinehigh), (0, high), (0, very high)}.

(3) HDL= {(0, very high), (0.6, high), (0, nearly normal),(0, normal)}.

(4) SBP = {(0, desirable), (0.8, above desirable), (0, mod-erate), (0, above moderate), (0, little high), (0, high),(0, very high)}.

(5) DBP = {(0, desirable), (0.66, above desirable), (0,moderate), (0, above moderate), (0, little high), (0,high), (0, very high)}.

(6) Triglyceride = {(0.66, normal), (0, a little bit high), (0,high), (0, very high)}.

(7) BMI = {(0, low), (0, medium), (0.86, above medium),(0, high), (0, very high), (0, very very high)}.

(8) HR = {(0, low), (0.76, normal), (0, high), (0, veryhigh)}.

(9) Exercise = {(0, low), (0.79, medium), (0, high), (0,very high)}.



𝑋 = {(0.6, 𝐽𝑀𝐴,𝑁,𝐻,𝐴𝐷,𝐴𝐷,𝑁,𝐴𝑀,𝑁,𝑀,𝐿

)} . (14)


0.18

0.37

0.560.66 0.62

00.10.20.30.40.50.60.7


Mem

bers

hip

valu

e


Case 2


The utility matrix is the same as in Case 1.The five fuzzy utilities are

(1) 𝑈1= {(0.6, 55)},

(2) 𝑈2= {(0.6, 92)},

(3) 𝑈3= {(0.6, 40)},

(4) 𝑈4= {(0.6, 24)},

(5) 𝑈5= {(0.6, 10)}.


(1) 𝑈1m = {(0.59, 55)},

(2) 𝑈2m = {(1, 92)},

(3) 𝑈3m = {(0.43, 35)},

(4) 𝑈4m = {(0.26, 24)},

(5) 𝑈5m = {(0.10, 10)}.


(1) 𝑈1o = {(0.59, 55)},

(2) 𝑈2o = {(0.6, 92)},

(3) 𝑈3o = {(0.43, 35)},

(4) 𝑈4o = {(0.26, 24)},

(5) 𝑈5o = {(0.10, 10)}.




This optimal alternative indicates that the patientpresently is in low grade of hypertension. The optimalalternatives have been graphically shown in Figure 2 in theform of Sugeno’s spikes.

Case 3. The input variables of the third patient are as follows.

(1) Age = {(0, young), (0, adult), (0, midaged), (0, aged),(0.75, old), (0, very old)}.

(2) LDL = {(0, normal), (0, above normal), (0, borderlinehigh), (0.8, high), (0, very high)}.

(3) HDL = {(0, very high), (1, high), (0, nearly normal),(0, normal)}.

(4) SBP = {(0, desirable), (0, above desirable), (0.8, mod-erate), (0, above moderate), (0, little high), (0, high),(0, very high)}.

(5) DBP = {(0, desirable), (1, above desirable), (0, moder-ate), (0, above moderate), (0, little high), (0, high), (0,very high)}.

(6) Triglyceride = {(1, normal), (0.66, a little bit high), (0,high), (0, very high)}.

(7) BMI = {(0, low), (0, medium), (0, above medium),(0.78, high), (0, very high), (0, very very high)}.

(8) HR = {(0, low), (0, normal), (0.96, high), (0, veryhigh)}.

(9) Exercise = {(0, low), (1, medium), (0, high), (0, veryhigh)}.



𝑋 = {(0.66, 𝐽𝑂,𝐻,𝐻,𝑀,𝐴𝐷,𝐿𝐻,𝐻,𝐻,𝑀,𝐿

)} . (16)

The utility matrix 𝑈 is the same as in Case 1.The five fuzzy utilities are

(1) 𝑈1= {(0.66, 15)},

(2) 𝑈2= {(0.66, 30)},

(3) 𝑈3= {(0.66, 45)},

(4) 𝑈4= {(0.66, 80)},

(5) 𝑈5= {(0.66, 50)}.


(1) 𝑈1m = {(0.187, 15)},

(2) 𝑈2m = {(0.375, 30)},

(3) 𝑈3m = {(0.562, 45)},

(4) 𝑈4m = {(1, 80)},

(5) 𝑈5m = {(0.62, 50)}.


(1) 𝑈1o = {(0.187, 15)},

(2) 𝑈2o = {(0.375, 30)},

(3) 𝑈3o = {(0.562, 45)},

(4) 𝑈4o = {(0.66, 80)},

(5) 𝑈5o = {(0.62, 50)}.





0.18

0.37

0.560.66 0.62

00.10.20.30.40.50.60.7


Mem

bers

hip

valu

e


Case 3


This optimal alternative indicates that the patient ispresently in high grade of hypertension.

The optimal alternatives have been graphically shown inthe form of Sugeno’s spikes in Figure 3.

4. Conclusion

The present research paper confirms that the soft computingdiagnostic system can represent the expert’s thinking in anefficient manner to handle complex cases. The design anddevelopment of soft computing risk assessment system on thebasis of the proposed technique will assist medical experts tomeasure grade classification of hypertension efficiently.

References

[1] X. Y. Djam and Y. H. Kimbi, “Fuzzy expert system for themanagement of hypertension,”ThePacific Journal of Science andTechnology, vol. 12, no. 1, p. 390, 2011.

[2] X. Y. Djam and Y. H. Kimb, “A medical diagnostic supportsystem for the management of Hypertension (MEDDIAG),”Journal ofMedical andApplied Biosciences, vol. 3, pp. 41–55, 2011.

[3] R. Jain, “Decision making in the presence of fuzzy variables,”IEEE Transactions on Systems, Man and Cybernetics, vol. 6, no.10, pp. 698–703, 1976.

[4] R. Poli, S. Cagnoni, R. Livi et al., “A neural network expertsystemfor diagnosing and treating hypertension,” Computer,vol. 24, no. 3, pp. 64–71, 1991.

[5] R. Degani, “Computerized electrocardiogram diagnosis: fuzzyapproach,” Methods of Information in Medicine, vol. 31, no. 4,pp. 225–233, 1992.

[6] S. Charbonnier, S. Galichet, G. Mauris, and J. P. Siche, “Statisti-cal and fuzzy models of ambulatory systolic blood pressure forhypertension diagnosis,” IEEE Transactions on Instrumentationand Measurement, vol. 49, no. 5, pp. 998–1003, 2000.

[7] R. K. Jena, M. M. Aqel, P. Srivastava, and P. K. Mahanti, “Softcomputingmethodologies in bioinformatics,” European Journalof Scientific Research, vol. 26, no. 2, pp. 189–203, 2009.

[8] D. Pandey, M. Vaishali, and S. Pankaj, “Rule-based system forcardiac analysis,” National Academy Science Letters, vol. 29, no.7-8, pp. 299–309, 2006.

[9] N. Allahverdi, S. Torun, and I. Saritas, “Design of a fuzzy expertsystem for determination of coronary heart disease risk,” inInternational Conference on Computer Systems and Technologies(CompSysTech ’07), June 2007.

[10] N. Nalayini and R. S. D. Wahidabanu, “Design methodology ofa controller to forecast the uncertain cardiac arrest using fuzzylogic approach,” in Proceedings of the International ConferenceIntelligent Systems and Controls, pp. 46–52, Karpagam Collegeof Engineering, Coimbatore, India, 2008.

[11] P. Srivastava and A. Srivastava, “A soft computing approachfor cardiac analysis,” Journal of Basic and Applied ScientificResearch, vol. 2, no. 1, pp. 376–385, 2012.

[12] P. Srivastava and N. Sharma, “Soft computing criterion for ECGbeat classification and cardiac analysis,” communicated, 2012.

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Research Article A Note on Hypertension …downloads.hindawi.com/archive/2013/342970.pdfcoronary heart disease (CHD). Srivastava and Sharma [ ] designed a so computing diagnostic system