ApAPPLICATION OF ADAPTIVE NEURO FUZZY INFERENCE SYSTEM IN THE PROCESS OF TRANSPORTATION SUPPORTjor Article Anfis

8/10/2019 ApAPPLICATION OF ADAPTIVE NEURO FUZZY INFERENCE SYSTEM IN THE PROCESS OF TRANSPORTATION SUPPORTj

1/32

Asia-Pacific Journal of Operational ResearchVol. 30, No. 2 (2013) 1250053 (32 pages)c World Scientific Publishing Co. & Operational Research Society of Singapore

DOI: 10.1142/S0217595912500534

APPLICATION OF ADAPTIVE NEURO FUZZY INFERENCE

SYSTEM IN THE PROCESS OF TRANSPORTATION SUPPORT

DRAGAN PAMUCAR

Military Academy, University of Defence

Pavla Jurisica Sturma 33, 11000 Belgrade, [email protected]

VESKO LUKOVAC

Military Academy, University of Defence

Pavla Jurisica Sturma 33, 11000 Belgrade, Serbia

[email protected]

SNEZANA PEJCIC-TARLE

Faculty of Transport and Traffic Engineering, University of Belgrade

Vojvode Stepe 305, 11000 Belgrade, [email protected]

Published 28 January 2013

The possibility for more confidential predictions, leaning on scientific methods andaccomplishments of information technology leaves more time for the realization of logisticneeds. Longstanding ambitions to acquire desired levels of efficiency within the systemwith minimal costs of resources, materials, energy and money are the features of executivestructures of logistic systems. A successful logistic process is based on validation of tech-nological development, indicating the need for a faster and more confidential integration

of logistic systems and instilling confidence with military units that provide criticalsupport (supply, transport and maintenance) will be reliably realized according to rele-vance and priority. Conclusions like these impose the necessity that the decision-makingprocess of logistic organs is accessed carefully and systematically, since any wrong deci-sion leads to a reduced state of readiness for military units. To facilitate the day-to-dayoperation of the Army of Serbia and the completion of both scheduled and unscheduledtasks it is necessary to satisfy the wide range of transport requirements. In this paper,the Adaptive Neuro Fuzzy Inference System (ANFIS) is described, thus making possiblea strategy of coordination of transport assets to formulate an automatic control strat-egy. This model successfully imitates the decision-making process of the chiefs of logisticsupport. As a result of the research, it is shown that the suggested ANFIS, which has theability to learn, has a possibility to imitate the decision-making process of the transport

support officers and show the level of competence that is comparable with the level oftheir competence.

Keywords: Logistic process; neuro-fuzzy model; vehicle assignment problem; fuzzy sets.

Corresponding author

1250053-1

AsiaPac.

J.Oper.Res.Downloade

dfromw

ww.worldscientific.com

by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.
http://dx.doi.org/10.1142/S0217595912500534http://dx.doi.org/10.1142/S0217595912500534


2/32

D. Pamucar, V. Lukovac & S. Pejcic-Tarle

1. Introduction

Increased mobility and subsequent consumption of supply lends itself to the conceptthat complex missions and tasks need to have an increased problem-solving input

by the custodians of the logistic system. The nature of military operations, by

definition, makes the accurate prediction of logistic requirement demanding and

uncertain. This is why maintenance of a reserve is needed, which, among other

things, imposes additional expense on the system.

In the Gulf War, the logistic support of the forces engaged is described as moun-

tain movement. A division in that time spent munitions, fuel and other expendables

as much as the army during World War II. A total of 1.2 million liters of petrols, oils

and lubricants were spent daily, approximately a million liters of drinking water andaround 200 tractors were engaged in the process. During Operation Desert Storm,

the division spent more than 8 million liters of fuel for 100 hours of offensive action,

the resupply of which took more than 400 tankers with the volume of more than

200m3.

The logistic system in the Army of Serbia has been created to protect and

maintain military readiness. During the execution of the military operations, the

structure of logistic force elements, equipment and resources is organized so that the

success in combat and operations is ensured. Improvement in information security

and in technology of transport enables a formation to change mass with speed andensures that everything will work properly. Full spectrum supportability means

support to a soldier from the supply resource to the point where it should be

necessary; in a tunnel, in a dome of military engines, on a ship, in an airplane cabin

or in the base.

In order to achieve certain systems for logistic support, systems are created

to meet the required tasks and adjust to environmental changes and new require-

ments. It is models that use the methods of operational research that are frequently

created.

The paper investigates the problem of an optimal choice of transport dependingon the needs of Serbian military units. Units of logistic support in the Serbian

Armed Forces need to respond to numerous transport requirements coming from

other military units. Each requirement comprises many elements, which means that

the choice of an adequate vehicle is by no means simple. The presented problem is

known as vehicle assignment problem (VAP) or an assignment problem in general

(Bradley et al., 1977; Zeleny, 1982).

In the last decades, there were many attempts to solve the assignment of vehi-

cles to transportation jobs (routes). In its simplest form, VAP can be formulated

as a linear programming problem (Abara, 1989) and solved with an application

of the simplex method (Cooke, 1985), an assignment algorithm called Hungarian

method (Bradleyet al., 1977), network algorithms (Cooke, 1985) or the transporta-

tion method (Lotfi and Pegels, 1989) as well as its extensions (Pilot and Pilot, 1999).

In real life situations, VAP is more complicated and requires more advanced methods

1250053-2

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


3/32

Application of Adaptive Neuro Fuzzy Inference System

to be solved. Some authors (Lobel, 1998; Rushmeier and Kantogiorgis, 1997; Ziarati

et al., 1999) formulate VAP in terms of the linear, integer or mixed integer program-

ming problem. Some others (Beaujon and Turnquist, 1991) transform in terms of

linear, discrete model into a nonlinear, continuous form. In both cases, the prob-

lems are formulated either in deterministic or nondeterministic form (Beaujon and

Turnquist, 1991; Milosavljevic et al., 1996). Many models are based on queuing

theory (Green and Guha, 1995; Whitt, 1992). They consider either a homogeneous

(Beaujon and Turnquist, 1991; Lobel, 1998) or a nonhomogeneous fleet (Rushmeier

and Kantogiorgis, 1997; Ziarati et al., 1999). Some of the models combine VAP

with other fleet management problems, such as: fleet sizing (Beaujon and Turn-

quist, 1991; Crainic and Laporte, 1997; Crainic, 2000), vehicle routing (Beaujon

and Turnquist, 1991) or vehicle scheduling (Booler, 1980; Lobel, 1998) with time

and capacity constraints (Crainic and Laporte, 1997; Crainic, 2000). The models

usually refer to specific transportation environments, such as urban transportation

(Lobel, 1998), rail transportation (Booler, 1980; Ziarati et al., 1999), or air trans-

portation (Rushmeier and Kantogiorgis, 1997). In most cases, the proposed vehicle

assignment models have a single objective character, however, different objective

functions are considered. The most popular are total transportation costs (Ziarati

et al., 1999), profit (Beaujon and Turnquist, 1991; Rushmeier and Kantogiorgis,

1997), or empty rides (flows) (Lobel, 1998). Depending on specific characteristics

of VAP and complexity of the decision models, various solution procedures and

algorithms are applied to solve concrete instances of VAP.

Ziaratiet al.(1999) consider the problem of assigning locomotives to trains that

operate on certain routes. The demand on specific routes influences the composi-

tion and length of each train, which imposes certain conditions on selection of a

locomotive for a particular train. The decision problem is formulated in terms of

linear integer programming and solved by a customized branch and cutalgorithm

(Bradley et al., 1977; Hillier et al., 1990).

Ichoua et al. (2003) present an original formulation of a dial-a-ride problem.

As opposed to traditional formulations of travel time as a function of distance in adial-a-ride problem, the authors propose travel time differentiation based on various

factors, including time of the day, traffic congestion and others. They construct

a mathematical model that involves a relationship between the travel speed and

the time of day. Their model is experimentally evaluated in static and dynamic

conditions.

Rushmeiner and Kantogiorgis (1997) present interesting considerations on

assignment of airplanes to particular transportation jobs (flights). They formulated

VAP in terms of mixed integer mathematical programming with price-wise linear

constraints. The decision problem is solved by a Cplex solver for GAMS system anda heuristic procedure for rounding of noninteger solutions.

The most up-to-date approaches to modeling and solving VAP involve stake-

holders analysis leading to multiple objective formulations of the problem (Singh

and Saxena, 2003), analysis of uncertainty and imprecision of data (Milosavljevic

1250053-3

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


4/32


et al., 1996; Zak, 2002), and application of artificial intelligence methods in the

solution procedures of the problem (Vukadinovic et al., 1996; Vukadinovic et al.,

1999).

Zeleny (1982) and Singh and Saxena (2003) claim that multiple criteria formu-

lations of different categories of transportation decision-making problems are more

realistic than their single criterion equivalents. Zeleny (1982) proposes one of the

first multiple criteria formulations of a classical transportation problem.

Singh and Saxena (2003) investigate another variant of a transportation prob-

lem focused on optimization of the total transportation time between certain

origins and destinations. The authors consider three nonlinear, time-oriented cri-

teria, such as riding time, loading and unloading time, and a set numerous con-

straints. The problem is solved by a heuristic procedure that utilizes a specific

and original structure of the problem. The optimal solution defines a minimal flow

of materials in the transportation network and a minimal time required to dis-

tribute this flow in a network. Computational efficiency of the proposed algorithm

is analyzed on a real life case study focused on transportation of iron in a steel

industry.

Milosaviljevic et al. (1996) formulate a VAP for a road transportation com-

pany. The authors consider a heterogeneous fleet operating from a central depot

and define types of vehicles allocated to concrete transportation jobs. The decision-

making problem is formulated in terms of fuzzy mathematical programming and

solved by an original heuristic procedure. Fuzzy numbers are applied to model the

dispatchers preferences and different categories of constraints associated with fleet

assignment. Further extension of this research is presented in the articles of Vukadi-

novic et al. (1999) in which neural networks are applied to generate a set of fuzzy

decision rules allocating vehicles to transportation jobs. Due to the fact that in many

real life situations VAP is characterized by high computational complexity, espe-

cially when it is combined with other fleet management problems, several authors

apply heuristic procedures to solve the analyzed problems. In some cases, heuristics

are combined with other well-known techniques, such as branch-and-bound algo-rithm (Rushmeier and Kantogiorgis, 1997; Henn, 2000). In the last several years,

metaheuristic algorithms earned great popularity as a solution procedures for an

assignment problem (Jaszkiewicz, 1997; Taillard, 1995).

In the vehicle asignment model presented in this paper, experience of officers

commanding logistic support units is accumulated into the neuro-fuzzy network

that can provide a generalized approach. Adaptive neuro-fuzzy network is trained

to make optimal choices based not only on standard criteria (reliability of the means

of transport, mobility of the means of transport in field conditions, exploitation of

the cubage of means of transport and the price per tonal kilometer), but also onadditional criteria. Additional criteria are rank units, terrorist activity along lines of

logistic support, combat activity in the vicinity of the unit being supplied, protection

of human and material resources from hostile activity.

1250053-4

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


5/32


2. Structure of the Neuro-Fuzzy System

Fuzzy neural nets are based on joining of fuzzy logics concepts and artificial neuralnets are based on the theories that have found their place on top of interest of

researchers in the field of artificial intelligence.

Fuzzy logics, Zadeh (1988, 1989), enables a mathematical potential for descrip-

tion of indefiniteness related to cognitive processes with man, such as thinking and

reasoning. It enables reasoning with incomplete and insufficiently precise informa-

tion, which is also called approximate reasoning(Zadeh, 1975).

Fuzzy logics is mostly used for modeling complex systems in which it is hard

to define, by using other methods, interdependence that exists between certain

variables. The models based upon the fuzzy logics are based on IF-THEN rules,Lee et al. (2003). Each rule establishes a relation between the linguistic values

through an IF-THEN statement

IFx1is Aj1AND. . . ANDxiis AjiAND. . . ANDxnisAjnTHENy is Bj,

where xi, i = 1, 2, . . . , n are the input variables, y is the output variable Aj and

Bj are linguistic values labeling fuzzy sets. The degree with which the output vari-

able y matches the corresponding fuzzy set Bj, depends on the degrees of match-

ing of the input variables xi, i = 1, 2, . . . , n to their fuzzy sets, Aj and on the

logic format (AND, OR) of the antecedent part of the rule (Delgado et al., 2002).

So, it is immediate calculating the degree of matching in each rule as shown in

Fig. 1.

Each rule gives a fuzzy set, with a membership function cut in the higher zone.

By all the rules is given a set of fuzzy sets with differently cut membership func-

tions, whose deterministic values all have a share in the inferential result, Teodor-

ovic (1999). A single value is needed to have a useful result. The resulting fuzzy

set has to be converted to a real number. This operation is called defuzzification,

Fig. 2.

On the other hand, artificial neural nets, with their different architectures built

on the concept of artificial neuron, are developed in such a way that they act

as biological neural systems in performing functions as learning and recognition of

samples, Vemuriet al.(1998). While fuzzy logics enables the mechanism of reasoning

with incomplete and insufficiently precise information, artificial neural nets offer

certain extraordinary possibilities, such as the possibility of learning, adaptation

and generalization, Wang and Keerthipala (1998).

Artificial neurons, like biological ones have simple structure and similar functions

as biological neurons. The body of neuron is called the node or a unit, as it is shown

in the Fig. 3.

Artificial neuron is a simple element of processing that performs a simple math-ematical function. Input values in a neuron are shown with x1, x2, . . . , xn, wheren

is the overall number of inputs in the neuron. Each input value is firstly multiplied

with weight coefficient wij , j = 1, 2, . . . , n, wherei is order number of the neuron in

1250053-5

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


6/32


ACTIVATION

IF OR THEN

IF OR THEn

X

1x

2x

2x

1x

ACCUM

ULATION

X

-100 10030.8

Fig. 1. Applying rules.

the neural net, Takagi (2000). These multiplied values are then summed and result

in pi.

pi=nj=1

wijxj . (1)

This value is used as an input in a nonlinear function , which depends on the

parameter the point of activation. The dependence is most frequently such

that is subtracted from pi and hence their difference is used as the input in the

outy

Fig. 2. Defuzzification.

1250053-6

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


7/32


x1

x2

x3

xn

w1

w2

w3

wn

nnwxwxwxNET +++= ...2211 )(NETFOUT =

Fig. 3. Artificial neuron.

nonlinear function , Park (2002). In this way, we get the value of the input i

neuron:

yi=(pi ) =

nj=1

wijxj

. (2)Values of the weight factors wij, j = 1, 2, . . . , n can be changed i.e., adjusted to

input and output data to acquire minimal error with respect to given data. Thisprocess of adjustment of the weight factors is called learningi.e., training of neural

net.

Both neural nets and fuzzy logics deal with important aspects of demonstration

of knowledge, reasoning and learning, but they use different approaches and possess

their own advantages and disadvantages. Neural nets can learn from the example,

but it is almost impossible to describe the knowledge acquired in this way. On

the other hand, fuzzy logics enables approximate reasoning, but does not have the

feature of self adjustment (Table1).

The main idea of this neuro-adaptive technique is based on the methods of fuzzymodeling and learning on the given composite of data. This method of learning is

similar to the method of learning with neural nets. By using the given input/output

data, Adaptive Neuro Fuzzy Inference System (ANFIS) forms fuzzy system of rea-

soning in which the parameters of affiliation function are set by using algorithm

of back propagation or combined with method of the smallest square error. This

approach enables that the fuzzy system learns on the data it models. The general

structure of ANFIS is shown on Fig. 4.

Table 1. Comparative features of fuzzy logics and neural nets.

Neural nets and fuzzy logic Advantages Disadvantages

Fuzzy logics Approximate reasoning No adjustment

Neural nets Learning from example Hard description of knowledge

1250053-7

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


8/32


x

y

min

min

S

V

M

M

S

V

min

min

min

min

min

min

min

NORMALIZATION

1

4

2

3

5

6

7

8

9

x

y

f

Fig. 4. Structure of ANFIS.

3. Choice of Transportation Using ANFIS Model

The purpose of logistics in the Army of Serbia is to create forces, armament and

military equipment and enable constant support in military actions. The primary

goal of military logistics is to contribute to national protection through security ofneeded systems and means of armament and military equipment whose features are

reliability, effectiveness and efficiency, high degree of readiness and technological

superiority of potential antagonists.

According to the draft of military doctrine of the Army of Serbia, principal

functions of logistics are:

Maintenance,

Fabrication,

Services,

Transport, Facilities.

One of the most important functions of logistics is supply and transport. Supply

means purchase, spreading, storing and keeping stored material reserves, including

a definition of the type and amount of reserves on each level.

The units of transportation support (UTS) every day activities and receive

a number of transportation requests from other units of the Army of Serbia

that want to transport various types of loads to different destination. Every request

of transport is featured by greater number of attributes amongst which the most

important are the type of goods, the amount of goods (weight and cubage), the

place of loading and unloading, desired hours of loading and/or unloading and the

distance on which the products are being transported.

Given that in many fleets in the Army of Serbia there are various types of

vehicles the dispatchers have to make decisions every day about the most suitable

1250053-8

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


9/32


type of vehicle to carry out the task. In logistic bases, the following vehicles are used

for performing the task TAM 4500/5000 with the cubage of 5t, FAP 1314 with the

cubage of 8t, TAM150 T11 with the cubage of 12t and FAP 2026 with the cubage

of 20t.

The criteria upon which the organ of logistic support makes a selection and

brings conclusions for the vehicle that will be directed to the task are:

Reliability of the means of transport,

Mobility of the means of transport in field conditions,

Exploitation of the cubage of means of transport,

The price for tonal kilometer.

During the conduct of military operations in Bosnia and in the area of Kosovo,

it has been demonstrated that the UTS that have been actively included in com-

bat required active logistic support that is primarily shown through supplies of the

necessary amounts of munitions for infantry and artillery. Usage of munitions dur-

ing combat operations is large, and the impossibility of forehand supplies with the

aforementioned units means the battle readiness of the units is jeopardized. Expe-

riences of the officers from the logistic force elements that took part in supplying

the units during the war fighting have shown that, besides basic criteria that serve

for choosing the means of transport for completing the mission, it is necessary to

get to see additional criteria that are primarily based upon the experience of thekey decision makers.

Officers with experience have established criteria that they use to choose a vehi-

cle whose construction and technical characteristics satisfy the conditions for trans-

portation of a particular type of load. By fuzzy collections qualitative and imprecise

information can be quantified. Hence, fuzzy reasoning can be used as a technique

by which descriptive heuristic rules are transformed into automatic strategy.

The basic problem that an analyst faces while developing fuzzy systems is defin-

ing the basis of fuzzy rules and parameters relating to the function of adherence of

fuzzy collections that describe input and output variables.

3.1. Description of the problem

The considered problem is a daily timetable of vehicles at disposal on certain number

of requirements of transport. Means of transport go to completion of the mission

from the logistic base and return there upon completion of the task. Reasons for

this tactic of servicing are insufficient transport of various types of load by the same

vehicle and the fact that various types of load belong to different units of the Army

of Serbia. Figure 5 shows the logistic base with certain number of units that needto be serviced.

Each transport requirement features the following attributes:

The unit where the load needs to be delivered (place and rough time of loading

and unloading),

1250053-9

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


10/32


Fig. 5. Logistic base with units that need to be serviced.

The amount of the load transported (type of the load, weight, and volume) and

The distance on which the load is being transported (the distance between thelogistic base and certain unit).

Depending on the requirement of transport the classification of the vehicles on

transporting missions can be made daily, weekly, monthly and yearly. Here, a case

of daily supply was considered.

The considered problem belongs to the task of assigning. The problem of classi-

fication falls into the problem of linear programming. It consists of classification of

n resources and activities to m places and performers, where maximal efficiency is

wanted. In our case, it means that it is necessary to define the function of the aim,that is, classify the vehicles on transporting missions with minimal costs of transport

with limitations and treating problems as problems of mathematical programming.

The main drawback of the approach based on mathematical programming is the

fact that it is not simple to formulate the objective function and set hard limita-

tions. Besides, the information available to dispatchers are frequently imprecise or

given in the descriptive form:

Often it is impossible to determine the costs of transport precisely,

Units of higher rank have priority compared to units of lower rank,

Some vehicles are more suitable for completing transport tasks on specific con-figuration of the field and in certain climatic conditions,

Performance of the battle actions near the units that need to be supplied with

material means requires direction of vehicles that give a certain level of protection

to drivers and load,

1250053-10

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.
http://www.worldscientific.com/action/showImage?doi=10.1142/S0217595912500534&iName=master.img-083.jpg&w=182&h=209


11/32


Activities of terrorist or insurgent groups near arterial routes along which resup-

ply of units is performed.

This is why, the conventional approach cannot comprise all relevant imprecise

parameters. In most of the cases, this phase of the process of determining the UTS is

reduced to practiced knowledge of those who make decisions. However, the problem

arises when the decision about engagement of certain types of vehicles is to be made

by individuals who do not possess enough practiced knowledge. A solution of the

given problem is proposed in this work, by creating an ANFIS model.

3.2. Design of ANFIS model

An integral part of an ANFIS model is fuzzy system of inference. Problems thatan analyst faces when developing fuzzy system are determining of composites of

linguistic rules that a dispatcher uses and parameters of the function of adherence

of incoming/outgoing couples.

Generation of the function of adherence of fuzzy composites and couples by

means of which dispatchers behave imply long communication with a great number

of dispatchers with experience. Membership functions of fuzzy composites, which

describe the same notion proposed by various dispatchers, can be really different.

This is why, the features of developed fuzzy system depend on the number of dis-

posable dispatchers and the ability to formulate the strategy of distribution.It is thought that the fuzzy system is composed of four input variables: reliability,

mobility, tonnage use and the price by tonal kilometer and, one output variable,

preference of the dispatcher to supply a certain transport requirement with certain

type of vehicle.

ANFIS implements a Takagi Sugeno Kang fuzzy inference system in which the

conclusion of a fuzzy rule is constituted by a weighted linear combination of the

crisp inputs rather than by a fuzzy set. The described criteria are listed in Table 2.

The composite ofKi(i= 1, 2, . . . , 4) is made of two subsets:

K+, subset of the criteria of beneficial type, higher values desirable and

K, subset of the criteria of cost type, lower values desirable.

Values of input variables are described by means of linguistic descriptors S =

{l1, l2, . . . , li}, i H, H={1, 2, . . . , T }, where Tis the overall number of linguistic

Table 2. Criteria for evaluating the offered means of transportation.

Criterion Min Max Numerical Linguistic

Reliability of the means of transport (RMT)

Mobility of the means of transport in fieldconditions (MMTFC)

Exploitation of the cubage of transport (ECMT) Cost of tonal kilometer (CTK)

1250053-11

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


12/32


descriptors. Linguistic variables are presented by triangle fuzzy number, which is

defined as (,,) (Martinez, 2007).

li(x) =

0, x <

x

, x

x

, x

0, x >

. (3)

In our example, the number of linguistic variables is T= 5: very low VL, low

L, medium M, high H and very high VH. Linguistic descriptors have the

following values (Fig. 6).

Membership functions of fuzzy linguistic descriptors lki(i = 1, T , k = 1, K) are

defined as:

lVL =

0, 0< x


13/32


Since linguistic values lki(i = 1, T , k = 1, K) are described by fuzzy numbers

lki{lki, elki}, the process of normalization is realized according to the following(Herreraet al., 2008):(a) for beneficial criterion k(k K), the process is realized according to the

form

(lki)n =lki

lmaxk, (9)

where lmaxk is maximal value of fuzzy number lki(k = 1, 2, . . . , K ), for lki

(lki)= 0.(b) for cost criterionk(kK), the process is realized according to the following

(lki)n = 1 lki lmink

lmaxk, (10)

wherelmink is minimal value in the area of fuzzy number lki(k= 1, 2, . . . , K ) for

flki(lki)= 0.

Defuzzification of linguistic descriptors is done through application of the Centre

of Gravity method as per expression (Pamucar et al., 2011):

lki=

x2x1

lki(x) x dxx2x1

lki(x) dx, lH =

0.620.5

x0.50.12 x dx+

0.770.62

0.77x0.15 x dx0.62

0.5x0.50.12 dx+

0.770.62

0.77x0.15 dx

= 0.6382 0.64.

The main problem, which the analyst faces, while creating fuzzy system is deter-

mining of base for fuzzy rules and parameters of the membership functions of fuzzy

composites that describes input and output variables (Table 3). In fuzzy systems,as functions of adherence, Gaussian curves are depicted (Fig. 7).

In order for the base of rules to be defined, it is necessary to determine the

relative importance of criterion wk, k = 1, 2, . . . , K (K= 4). After the survey with

dispatchers in units and delivered prognosis the data are statistically elaborated

(Table4).

Table 3. Values of function parameters before the training of ANFIS.

Membership function/Input value MF 1 MF 2 MF 3RMT (11.5, 14.43) (12.9, 33.1) (11.7, 83.92)

MMTFC (0.12, 0.15) (0.153, 0.53) (0.19, 0.99)

ECMT (5.18, 1.74) (5.78, 21.75) (7.11, 42.70)

CTK (14.2, 2.62) (13.4, 47.25) (11.5, 98.38)

1250053-13

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


14/32


15/32


x1

x2

x3

x4

A2A2

A1A1

A3A3

B1B1

B2B2

B3B3

C1C1

CC2

C3C3

D1D1

DD2

D3D3

yy

Reliability of the means

of transport

Mobility of the means of

transport in field conditions

Cost of tonal kilometer

Exploitation of the cubage oftransport

v1(y)

v2(y)

v3(y)

v4(y)

v5(y)

Preferential dispatcher

O1i O

2i O

3i O

4i O

5i

Layer 1Layer 1 Layer 2Layer 2 Layer 3Layer 3 Layer 4Layer 4 Layer 5Layer 5

Fig. 8. Structure of the ANFIS.

Kj=1

wk = 1,wk[0, 1], [0, 1], (12)where j is the preference of a decision maker, i.e., the degree of confidence.

The initial fuzzy system, which determines the preference of dispatcher that

certain transport requirement is served with vehicle of tonnage of 5, 8, 12 or 20

tons is projected into adaptive neural net (Fig. 8). The main aim of ANFIS model

is to decrease the role of a dispatcher while constructing fuzzy system and leaningon concrete examples of the decisions made in practice while choosing the motor

vehicle for completion of the tasks given.

Layer 1. The junctions of the first layer represent verbal categories of input vari-

ables that are quantified by fuzzy composites. Each junction of the first

layer is adaptive junction and is described by the function of adherence

xi(xi), i= 1, . . . , 4. Functions of adherence are described by the form of

Gaussian curves that are featured by two parameters cand .

Gaussian(x,c,) =e

1

2( xc

)2

. (13)Since fuzzy rules are expressed in the form IF the condition THEN the

consequence, the categories of output variables that are quantified by

fuzzy composites are shown as adaptive junctions of the first layer (Altug

et al., 1999; Chiclana et al., 2007).

1250053-15

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


16/32


Layer2. Each junction of this layer counts minimal value of four input values.

Output values of the junction of the second layer are the importance of

rules.

O21 =wi=Ai(x1) Bi(x2) Ci(x3) Di(x4). (14)

Layer 3. Every ith node in this layer calculates the ratio of the ith rules firing

strength to the sum of all rules firing strength.

O31 = wi = wi4i=1wi

, i= 1, . . . , 4. (15)

Layer4. The fourth layer has five adaptive junctions that represent the preference

of dispatchers that certain transport requirement serves certain type ofvehicle. Each junction of this layer counts the section of certain fuzzy

composite with maximal value of input importance of rules.

O41 = wifi. (16)

Layer5. The only junction of the fifth layer is fixed junction by which the out-

put result of fuzzy system is gained. This is fuzzy composite with cer-

tain degrees of adherence of possible preference of dispatchers to direct

the transport task to certain vehicle considered. The output value is real

number that is found in the interval of zero to one (Sneider and Frank,1996).

O51 =Overall output=i

wifi=

iwifiiwi

. (17)

By training the neural net with numerical examples of made decisions, initial forms

of input/output functions of adherence to the phase of composites are readjusted.

The values of the membership functions after the training of ANFIS are shown in

the Table5.

The change of function of adherence is trained by backpropagation algorithm.Neuro-fuzzy modeling requires possession of useable numerical data. Trust in the

gained result is increased if we dispose of high enough representative pattern that

would be used for training (Fig. 9).

Proposed neural net is trained on 298 dispatcher decisions. Table6gives a set

of 40 transportation requests used in neuro fuzzy network training. The remaining

Table 5. Values of function parameters after the training of ANFIS.

Membership function/Input value MF 1 MF 2 MF 3RMT (64.45, 50.92) (66.5, 72.6) (58.42, 77.62)

MMTFC (3.828, 0.39) (5.085, 7.37) (3.14, 4.41)

ECMT (79.1, 33.45) (52.57, 63.29) (76.38, 74.16)

CTK (31.2, 21.78) (29.87, 41.33) (29.61, 26.79)

1250053-16

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


17/32


18/32


Table 6. Characteristics of 40 transportation requests (training pairs).

Transport request RMT MMTFC ECMT PTK ftraining fANFIS

1. 0.9922 0.6693 57 0.3398 0.757 0.755

2. 0.7953 0.8124 19 0.9660 0.573 0.584

3. 0.9131 0.6571 46 0.7189 0.660 0.649

4. 0.0711 0.3116 80 0.7497 0.343 0.342

5. 0.5092 0.9209 11 0.2234 0.560 0.571

6. 0.6383 0.6250 21 0.7729 0.486 0.497

7. 0.9248 0.7278 68 0.1035 0.802 0.813

8. 0.0879 0.9519 35 0.1928 0.485 0.496

9. 0.9153 0.4948 74 0.6161 0.692 0.68810. 0.2705 0.8124 31 0.7957 0.436 0.447

11. 0.2317 0.1518 96 0.9435 0.372 0.383

12. 0.0661 0.3429 19 0.4298 0.230 0.241

13. 0.0373 0.0557 16 0.1477 0.155 0.166

14. 0.9051 0.2470 69 0.3356 0.630 0.641

15. 0.5994 0.7485 35 0.1591 0.606 0.610

16. 0.5677 0.2906 23 0.7142 0.372 0.383

17. 0.5511 0.3710 33 0.2741 0.459 0.470

18. 0.9544 0.5018 85 0.1118 0.786 0.79019. 0.4887 0.3786 5 0.7599 0.321 0.332

20. 0.6365 0.6405 92 0.1253 0.732 0.737

21. 0.7354 0.8459 97 0.7547 0.778 0.789

22. 0.6663 0.3996 40 0.6245 0.491 0.502

23. 0.0173 0.9084 89 0.8082 0.520 0.531

24. 0.9503 0.6196 69 0.7286 0.718 0.729

25. 0.4674 0.1280 14 0.6886 0.268 0.268

26. 0.0259 0.5208 31 0.0271 0.340 0.337

27. 0.3702 0.0164 80 0.4119 0.393 0.38928. 0.9153 0.3949 91 0.5340 0.713 0.719

29. 0.0431 0.0631 78 0.4626 0.283 0.294

30. 0.8732 0.8251 74 0.1495 0.823 0.834

31. 0.1771 0.2776 90 0.4120 0.429 0.440

32. 0.8289 0.4331 81 0.1777 0.705 0.694

33. 0.7716 0.4607 40 0.5255 0.556 0.567

34. 0.3447 0.1692 38 0.7060 0.296 0.313

35. 0.9198 0.2518 61 0.3962 0.610 0.621

36. 0.9785 0.0300 48 0.7878 0.493 0.50437. 0.2659 0.2888 28 0.9728 0.252 0.263

38. 0.3539 0.9993 60 0.3016 0.643 0.632

39. 0.1168 0.9127 15 0.0024 0.452 0.463

40. 0.0429 0.6778 60 0.2126 0.447 0.436

1250053-18

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


19/32


0.2

0.4

0.6

0.8

20

40

60

80

0.4

0.5

0.6

0.7

Mobility of the

means of transport

in field conditions

Dispatcher'spreferences

Exploitation of the

cubage of transport 2040

6080

0.2

0.4

0.6

0.8

0.4

0.5

0.6

0.7


Mobility of the

means of transport

in field conditions

Reliability of the

means of transport

2040

6080

10

20

30

0.4

0.5

0.6

0.7

Reliability of themeans of transport



10

20

30

20

40

60

80

0.4

0.5

0.6

0.7

Exploitation of thecubage of transport



Fig. 10. Graphic representation of the set of the possible solutions of input variables.

Fig. 11. Training data ANFIS output.

After that, the next value xk is transmitted. Neural net is trained if it can

successfully solve the tasks it is trained for. After training the neural net can gen-

eralize new input data that it is not trained for (Figure 10).

1250053-19

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.
http://www.worldscientific.com/action/showImage?doi=10.1142/S0217595912500534&iName=master.img-190.jpg&w=357&h=159


20/32


Comparative values of ANFIS model criteria functions (fANFIS) and training set

criteria functions (ftraining) is shown in Fig. 11. Figure 11 shows the negligible error

at ANFIS model output.

Five-layered adaptive net is tested on 25 dispatcher decisions. For each type

of vehicle, the data from transport requirement are transmitted through ANFIS,

hence, gaining certain values of input functions. Transport vehicle is chosen as:

fVi = max(fVi), i= 1, . . . , 4. (20)

4. Results

A total of 25 transport requirements are considered for units that are found onthe tasks of security of administrative line of Kosovo and Metohija. Features of

transport tasks are shown in Table7.

Besides shown features, transport task is described by the time of loading

and unloading, location where the unit is set, the degree of danger that the

Table 7. Features of transport tasks.

Transport task Priority units Type of cargo The amount of Type of roadcargo tons

1. First Infantry ammunition 32 Rural2. Second Infantry mine 20 Country

3. First Gun ammunition 226 Asphalt

4. First Infantry ammunition 35 Rural

5. Second Food 15 Rural

6. Third Food 9 Asphalt

7. First Infantry ammunition 15 Country

8. Second Infantry mine 19 Rural

9. First Anti-tank mine 23 Country

10. First Anti-tank mine 28 Rural

11. Second Infantry mine 9 Asphalt12. Third Infantry mine 11 Country

13. Third Food 12 Rural

14. First Gun ammunition 126 Rural

15. First Infantry ammunition 75 Asphalt

16. Second Gun ammunition 21 Rural

17. Third Food 61 Country

18. Third Food 19 Asphalt

19. Second Infantry mine 147 Country

20. First Gun ammunition 97 Country

21. Second Infantry ammunition 73 Asphalt

22. First Infantry mine 33 Asphalt

23. First Gun ammunition 371 Rural

24. First Gun ammunition 27 Asphalt

25. Second Anti-tank mine 55 Asphalt

1250053-20

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


21/32


itinerary is found in by hostile forces, as well as the possibility to use alternative

directions.

Where V1 = TAM 4500/5000 with the cubage of 5t, V2 = FAP 1314 with the

cubage of 8t, V3= TAM150 T11 with the cubage of 12t and V4 = FAP 2026 with

the cubage of 20t.

The numerical results of Tables6and8imply the applicability of the proposed

model used as a decision-making tool for vehicle assignment. As is shown in Table8,

decisions on vehicle assignment at ANFIS model output are identical to those made

by dispatchers. In transportation requirements 1, 8, 10, 13, 14, 15, 17, 19, 20 and

23, ANFIS model gave alternative types of vehicle, which is acceptable, in some

cases it is even preferable, as units of Serbian armed forces have a heterogeneous

motor pool at their disposal.

Table 8. Comparative review of decisions and ANFIS model.

Transport Selection of vehicles for the transport requestrequest Dispatcher ANFIS

1. V3 V2,V3

2. V3 V3

3. V4 V4

4. V3 V3

5. V2 V2

6. V1 V1

7. V3 V3

8. V3 V3, V4

9. V3 V3

10. V3 V3, V4

11. V1 V1

12. V3 V3

13. V3 V3, V4

14. V3 V3, V4

15. V1 V1, V2

16. V3 V3

17. V3 V3, V4

18. V4 V4

19. V3 V3, V4

20. V1 V1, V2

21. V4 V422. V4 V4

23. V1 V1, V2

24. V1 V1

25. V4 V4

1250053-21

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


22/32


23/32


AppendixA

.

Transport

RMT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

1.

0.6182

0.9

736

19

0.4292

0.6

13

0.6

24

19

.

0.8

912

0.1

472

66

0.7

199

0.5

49

0

.538

2.

0.1478

0.7

022

25

0.9113

0.3

34

0.3

23

20

.

0.5

870

0.7

121

97

0.9

199

0.6

70

0

.681

3.

0.4267

0.9

621

90

0.5811

0.7

05

0.7

16

21

.

0.8

173

0.6

970

59

0.3

273

0.7

10

0

.721

4.

0.0765

0.3

166

51

0.1723

0.3

32

0.3

43

22

.

0.9

714

0.5

910

10

0.1

988

0.6

22

0

.633

5.

0.9023

0.3

239

30

0.1851

0.5

69

0.5

80

23

.

0.4

999

0.3

143

32

0.3

147

0.4

18

0

.429

6.

0.3747

0.8

341

29

0.9633

0.4

58

0.4

69

24

.

0.6

665

0.7

380

43

0.1

915

0.6

43

0

.654

7.

0.7263

0.3

727

69

0.0167

0.6

37

0.6

26

25

.

0.1

474

0.2

599

63

0.7

649

0.3

11

0

.294

8.

0.3086

0.3

272

53

0.4412

0.3

95

0.4

06

26

.

0.2

040

0.0

446

32

0.7

240

0.1

92

0

.203

9.

0.9170

0.9

662

20

0.2928

0.7

32

0.7

15

27

.

0.7

670

0.0

816

90

0.3

832

0.5

80

0

.591

10

.

0.4404

0.9

939

23

0.8214

0.5

28

0.5

39

28

.

0.3

449

0.6

802

98

0.4

060

0.6

29

0

.640

11

.

0.4976

0.7

909

16

0.1984

0.5

32

0.5

49

29

.

0.9

806

0.3

013

93

0.7

142

0.6

95

0

.706

12

.

0.8888

0.0

450

77

0.2891

0.5

88

0.5

99

30

.

0.6

126

0.9

733

43

0.2

085

0.6

93

0

.704

13

.

0.5104

0.9

445

34

0.5685

0.5

90

0.6

01

31

.

0.9

757

0.8

277

85

0.1

788

0.8

84

0

.893

14

.

0.1288

0.5

407

34

0.0540

0.3

87

0.3

98

32

.

0.7

299

0.3

604

47

0.6

965

0.5

11

0

.522

15

.

0.8072

0.1

618

65

0.2002

0.5

74

0.5

85

33

.

0.1

137

0.4

296

95

0.8

935

0.4

17

0

.428

16

.

0.5766

0.1

717

84

0.7058

0.4

93

0.5

04

34

.

0.4

628

0.9

424

76

0.4

715

0.6

88

0

.697

17

.

0.1524

0.1

639

40

0.5265

0.2

50

0.2

33

35

.

0.6

119

0.4

832

59

0.1

435

0.5

92

0

.603

18

.

0.1431

0.6

921

81

0.9760

0.4

63

0.4

74

36

.

0.7

644

0.8

584

43

0.0

815

0.7

24

0

.735

1250053-23

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


24/32


AppendixA

.(Continued)

Transport

R

MT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

37

.

0.5219

0.4

409

23

0.8039

0.3

92

0.4

03

55

.

0.0

583

0.5

834

22

0.3

221

0.3

18

0

.301

38

.

0.2897

0.7

096

36

0.1710

0.4

87

0.4

98

56

.

0.0

415

0.3

525

63

0.9

172

0.2

86

0

.297

39

.

0.9696

0.4

158

95

0.6110

0.7

40

0.7

49

57

.

0.8

449

0.5

687

24

0.5

899

0.5

67

0

.576

40

.

0.5300

0.1

436

69

0.3318

0.4

68

0.4

79

58

.

0.9

298

0.8

110

45

0.5

244

0.7

29

0

.740

41

.

0.5907

0.0

718

53

0.9324

0.3

68

0.3

79

59

.

0.9

545

0.7

615

53

0.2

026

0.7

75

0

.786

42

.

0.1434

0.7

342

57

0.0932

0.5

04

0.5

15

60

.

0.2

007

0.0

046

68

0.9

514

0.2

46

0

.229

43

.

0.1811

0.5

185

47

0.9885

0.3

38

0.3

49

61

.

0.1

335

0.9

993

24

0.3

322

0.4

73

0

.482

44

.

0.8318

0.4

420

29

0.9196

0.5

04

0.5

13

62

.

0.8

831

0.8

840

49

0.8

620

0.7

11

0

.722

45

.

0.3403

0.2

080

22

0.7023

0.2

66

0.2

77

63

.

0.5

373

0.5

298

62

0.2

138

0.5

81

0

.598

46

.

0.9491

0.8

599

78

0.5130

0.8

34

0.8

45

64

.

0.4

258

0.7

625

34

0.8

082

0.4

82

0

.491

47

.

0.9936

0.6

113

51

0.8120

0.6

77

0.6

88

65

.

0.4

719

0.6

780

60

0.6

176

0.5

57

0

.568

48

.

0.8635

0.7

655

83

0.3698

0.8

02

0.8

13

66

.

0.2

868

0.2

104

27

0.8

484

0.2

46

0

.263

49

.

0.4818

0.7

990

28

0.2517

0.5

53

0.5

64

67

.

0.2

852

0.7

573

30

0.6

865

0.4

33

0

.444

50

.

0.6440

0.2

698

68

0.0776

0.5

69

0.5

78

68

.

0.8

377

0.4

050

29

0.3

517

0.5

52

0

.563

51

.

0.4223

0.7

147

36

0.7544

0.4

77

0.4

88

69

.

0.5

550

0.4

460

30

0.6

459

0.4

38

0

.455

52

.

0.4873

0.0

699

12

0.2837

0.2

93

0.3

04

70

.

0.3

307

0.9

545

92

0.3

814

0.6

94

0

.703

53

.

0.7877

0.4

373

66

0.3557

0.6

36

0.6

47

71

.

0.4

648

0.2

506

65

0.3

421

0.4

66

0

.477

54

.

0.4820

0.6

259

93

0.3861

0.6

50

0.6

61

72

.

0.7

315

0.5

164

54

0.0

572

0.6

40

0

.657

1250053-24

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


25/32


AppendixA

.(Continued)

Transport

RMT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

73

.

0.2231

0.0

527

58

0.2148

0.3

17

0.3

28

90

.

0.1

069

0.9

207

48

0.8

871

0.4

45

0

.454

74

.

0.3495

0.1

387

26

0.1521

0.3

14

0.3

31

91

.

0.5

502

0.0

624

42

0.3

761

0.3

79

0

.390

75

.

0.9296

0.0

291

41

0.4016

0.4

96

0.5

05

92

.

0.1

522

0.3

088

97

0.2

154

0.4

67

0

.476

76

.

0.2383

0.3

263

76

0.2602

0.4

45

0.4

56

93

.

0.3

311

0.7

984

36

0.8

076

0.4

65

0

.476

77

.

0.2373

0.1

277

40

0.7209

0.2

49

0.2

66

94

.

0.6

187

0.0

217

74

0.4

415

0.4

64

0

.475

78

.

0.3293

0.0

086

60

0.1234

0.3

55

0.3

66

95

.

0.2

585

0.0

097

86

0.5

109

0.3

57

0

.366

79

.

0.7084

0.7

965

63

0.9349

0.6

51

0.6

62

96

.

0.5

271

0.2

217

59

0.7

324

0.4

25

0

.436

80

.

0.8383

0.7

469

21

0.7534

0.5

95

0.6

04

97

.

0.6

900

0.7

537

49

0.7

298

0.6

17

0

.628

81

.

0.2929

0.0

414

82

0.1017

0.4

10

0.4

21

98

.

0.0

705

0.7

492

82

0.8

604

0.4

68

0

.479

82

.

0.8887

0.2

989

79

0.0079

0.6

97

0.7

06

99

.

0.6

093

0.9

149

67

0.1

894

0.7

36

0

.745

83

.

0.6281

0.1

611

34

0.5610

0.3

97

0.4

08

100

.

0.9

769

0.7

602

39

0.1

754

0.7

50

0

.761

84

.

0.5810

0.1

277

92

0.9062

0.4

81

0.4

92

101

.

0.0

126

0.3

678

94

0.3

817

0.4

12

0

.423

85

.

0.4488

0.7

788

87

0.1212

0.6

96

0.7

07

102

.

0.2

974

0.3

709

77

0.9

542

0.4

12

0

.423

86

.

0.0810

0.6

392

72

0.0457

0.4

96

0.5

05

103

.

0.8

057

0.9

312

77

0.0

597

0.8

48

0

.859

87

.

0.9190

0.5

066

44

0.6947

0.6

14

0.6

25

104

.

0.4

681

0.3

179

73

0.5

386

0.4

88

0

.497

88

.

0.9958

0.4

511

98

0.9153

0.7

37

0.7

48

105

.

0.4

102

0.8

868

12

0.2

718

0.5

12

0

.521

89

.

0.1817

0.6

262

57

0.0295

0.4

91

0.5

02

106

.

0.2

836

0.3

709

80

0.1

778

0.4

93

0

.504

1250053-25

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


26/32


AppendixA

.(Continued)

Transport

R

MT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

107

.

0.2199

0.0

718

23

0.6240

0.1

94

0.2

05

126

.

0.3

672

0.1

995

81

0.5

460

0.4

36

0

.447

108

.

0.1191

0.3

902

50

0.2002

0.3

64

0.3

75

127

.

0.8

868

0.6

656

69

0.5

148

0.7

31

0

.740

109

.

0.7481

0.5

147

78

0.3468

0.6

77

0.6

86

128

.

0.9

452

0.8

830

70

0.4

294

0.8

28

0

.839

110

.

0.8175

0.4

269

26

0.3478

0.5

44

0.5

55

129

.

0.5

273

0.8

628

65

0.5

749

0.6

48

0

.659

111

.

0.2159

0.3

829

43

0.7157

0.3

26

0.3

37

130

.

0.2

375

0.8

440

28

0.4

611

0.4

60

0

.471

112

.

0.7881

0.8

936

21

0.8227

0.6

14

0.6

25

131

.

0.7

535

0.7

988

24

0.4

370

0.6

20

0

.631

113

.

0.6130

0.4

332

93

0.5201

0.6

25

0.6

36

132

.

0.2

572

0.7

403

63

0.0

550

0.5

64

0

.575

114

.

0.7129

0.0

025

55

0.4676

0.4

41

0.4

52

133

.

0.6

959

0.7

766

77

0.4

711

0.7

22

0

.733

115

.

0.4967

0.5

283

93

0.7637

0.5

88

0.5

99

134

.

0.4

689

0.4

429

21

0.5

352

0.3

96

0

.405

116

.

0.7122

0.0

863

89

0.4111

0.5

57

0.5

68

135

.

0.4

376

0.4

717

58

0.2

588

0.5

14

0

.525

117

.

0.0351

0.1

628

69

0.0903

0.3

25

0.3

36

136

.

0.3

219

0.4

097

86

0.2

480

0.5

26

0

.535

118

.

0.5883

0.6

395

86

0.3425

0.6

78

0.6

89

137

.

0.9

924

0.8

284

46

0.5

532

0.7

56

0

.767

119

.

0.3248

0.8

340

49

0.2046

0.5

66

0.5

77

138

.

0.0

883

0.9

011

88

0.4

175

0.5

79

0

.568

120

.

0.9471

0.9

362

45

0.4397

0.7

81

0.7

92

139

.

0.8

243

0.7

478

27

0.2

827

0.6

52

0

.663

121

.

0.2934

0.8

952

46

0.8776

0.4

99

0.5

10

140

.

0.3

583

0.0

263

36

0.5

285

0.2

70

0

.281

122

.

0.1169

0.4

249

15

0.9892

0.2

07

0.2

16

141

.

0.0

998

0.8

350

10

0.2

111

0.3

89

0

.400

123

.

0.5291

0.9

245

81

0.4257

0.7

22

0.7

33

142

.

0.2

155

0.6

113

95

0.9

298

0.5

03

0

.512

124

.

0.8001

0.9

910

93

0.1575

0.8

94

0.9

05

143

.

0.6

612

0.9

371

91

0.7

499

0.7

65

0

.776

125

.

0.6958

0.0

250

64

0.9622

0.4

15

0.4

26

144

.

0.6

578

0.2

661

52

0.4

367

0.4

96

0

.507

1250053-26

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


27/32


AppendixA

.(Continued)

Transport

RMT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

145

.

0.4296

0.0

041

90

0.9457

0.3

82

0.3

93

163

.

0.9

658

0.6

718

89

0.8

295

0.7

79

0

.788

146

.

0.7685

0.9

092

95

0.0910

0.8

70

0.8

59

164

.

0.9

650

0.6

077

58

0.4

078

0.7

24

0

.735

147

.

0.0755

0.7

115

63

0.0131

0.4

96

0.5

05

165

.

0.5

480

0.0

235

48

0.9

143

0.3

27

0

.338

148

.

0.3463

0.6

957

24

0.0731

0.4

83

0.4

94

166

.

0.6

790

0.7

874

70

0.2

876

0.7

20

0

.731

149

.

0.1777

0.4

094

78

0.7143

0.4

09

0.4

20

167

.

0.8

422

0.7

671

86

0.5

055

0.7

89

0

.798

150

.

0.0972

0.0

737

23

0.7651

0.1

37

0.1

48

168

.

0.5

371

0.2

171

82

0.2

500

0.5

33

0

.544

151

.

0.6539

0.5

951

8

0.6324

0.4

64

0.4

75

169

.

0.5

478

0.0

566

87

0.8

779

0.4

38

0

.449

152

.

0.2826

0.4

037

67

0.0657

0.4

81

0.4

90

170

.

0.4

395

0.2

819

38

0.6

992

0.3

63

0

.372

153

.

0.8100

0.2

526

89

0.1581

0.6

66

0.6

77

171

.

0.1

587

0.1

542

23

0.3

119

0.2

28

0

.239

154

.

0.2007

0.1

389

63

0.5684

0.3

13

0.3

24

172

.

0.1

775

0.0

317

25

0.9

966

0.1

34

0

.145

155

.

0.5185

0.4

171

83

0.1250

0.6

02

0.6

13

173

.

0.4

930

0.2

880

38

0.3

404

0.4

20

0

.431

156

.

0.7630

0.0

928

48

0.3848

0.4

76

0.4

87

174

.

0.5

132

0.8

995

57

0.3

116

0.6

61

0

.670

157

.

0.8211

0.4

804

30

0.4517

0.5

61

0.5

72

175

.

0.5

097

0.0

198

80

0.5

007

0.4

34

0

.445

158

.

0.8009

0.4

360

36

0.1060

0.5

91

0.6

00

176

.

0.9

354

0.1

485

26

0.5

465

0.4

82

0

.493

159

.

0.6579

0.8

603

14

0.8561

0.5

38

0.5

49

177

.

0.4

699

0.2

690

48

0.4

384

0.4

21

0

.432

160

.

0.0446

0.1

011

39

0.5303

0.1

90

0.2

01

178

.

0.9

080

0.8

943

44

0.8

914

0.7

07

0

.718

161

.

0.3187

0.6

439

34

0.3463

0.4

55

0.4

66

179

.

0.2

421

0.0

257

45

0.3

805

0.2

67

0

.278

162

.

0.0746

0.2

211

28

0.7594

0.1

86

0.1

97

180

.

0.0

082

0.4

992

77

0.8

407

0.3

61

0

.370

1250053-27

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


28/32


AppendixA

.(Continued)

Transport

R

MT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

181

.

0.0510

0.3

640

41

0.4677

0.2

83

0.2

94

199

.

0.3

886

0.8

010

21

0.8

030

0.4

48

0

.459

182

.

0.8145

0.7

660

63

0.5634

0.7

16

0.7

27

200

.

0.2

820

0.0

055

61

0.7

966

0.2

73

0

.262

183

.

0.1838

0.1

397

64

0.0599

0.3

60

0.3

71

201

.

0.3

678

0.1

577

44

0.5

703

0.3

29

0

.340

184

.

0.6399

0.9

684

32

0.7447

0.6

20

0.6

31

202

.

0.5

258

0.4

244

20

0.4

423

0.4

17

0

.428

185

.

0.1450

0.2

499

41

0.7135

0.2

57

0.2

66

203

.

0.6

407

0.2

684

99

0.4

112

0.6

11

0

.622

186

.

0.3732

0.6

965

98

0.6422

0.6

20

0.6

31

204

.

0.6

903

0.2

295

58

0.1

485

0.5

41

0

.552

187

.

0.0545

0.7

869

62

0.0401

0.5

06

0.5

17

205

.

0.0

546

0.9

642

47

0.6

908

0.4

57

0

.446

188

.

0.3501

0.3

713

12

0.6354

0.3

00

0.3

11

206

.

0.9

607

0.1

857

60

0.5

378

0.5

88

0

.599

189

.

0.6842

0.3

967

81

0.2204

0.6

39

0.6

50

207

.

0.3

571

0.0

958

71

0.6

743

0.3

64

0

.375

190

.

0.2707

0.1

414

55

0.0579

0.3

69

0.3

78

208

.

0.9

487

0.8

688

91

0.0

235

0.9

18

0

.929

191

.

0.7091

0.8

808

97

0.6023

0.7

95

0.8

60

209

.

0.8

985

0.5

060

44

0.3

510

0.6

41

0

.652

192

.

0.3288

0.1

693

83

0.3106

0.4

42

0.4

53

210

.

0.2

604

0.7

167

94

0.0

633

0.6

35

0

.644

193

.

0.0931

0.3

497

63

0.7006

0.3

25

0.3

14

211

.

0.3

901

0.3

457

96

0.3

396

0.5

46

0

.557

194

.

0.4239

0.4

596

69

0.0733

0.5

51

0.5

62

212

.

0.0

784

0.3

734

77

0.7

237

0.3

60

0

.371

195

.

0.8447

0.5

661

14

0.1537

0.5

85

0.5

96

213

.

0.6

320

0.6

999

10

0.8

374

0.4

72

0

.483

196

.

0.9029

0.6

165

68

0.4828

0.7

23

0.7

32

214

.

0.5

760

0.4

807

57

0.7

147

0.5

17

0

.526

197

.

0.1880

0.5

403

80

0.8307

0.4

45

0.4

56

215

.

0.9

294

0.0

117

89

0.1

064

0.6

41

0

.652

198

.

0.8074

0.4

451

77

0.4466

0.6

64

0.6

53

216

.

0.1

408

0.9

371

69

0.2

606

0.5

77

0

.588

1250053-28

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


29/32


AppendixA

.(Continued)

Transport

RMT

MMTF

C

ECMT

C

TK

ftraining

fANFIS

Tra

nsport

RMT

MMTF

C

ECMT

CTK

ftraining

fANFIS

reques

t

request

217

.

0.5541

0.3

715

16

0.4527

0.4

00

0.4

11

238

.

0.2

471

0.3

997

87

0.4

705

0.4

77

0

.466

218

.

0.7737

0.0

412

20

0.0321

0.4

30

0.4

41

239

.

0.2

404

0.0

781

62

0.8

200

0.2

81

0

.292

219

.

0.8891

0.2

448

17

0.0325

0.5

24

0.5

35

240

.

0.1

120

0.3

330

45

0.6

416

0.2

87

0

.304

220

.

0.7809

0.2

288

12

0.8511

0.3

87

0.3

96

241

.

0.5

851

0.0

026

92

0.8

409

0.4

51

0

.460

221

.

0.7456

0.0

840

69

0.5115

0.5

08

0.5

19

242

.

0.4

754

0.3

572

79

0.3

101

0.5

40

0

.557

222

.

0.6071

0.1

918

37

0.1538

0.4

47

0.4

58

243

.

0.0

663

0.1

448

29

0.7

755

0.1

62

0

.179

223

.

0.6025

0.5

495

10

0.4296

0.4

58

0.4

67

244

.

0.9

030

0.7

253

15

0.7

132

0.6

00

0

.609

224

.

0.5639

0.9

766

25

0.9121

0.5

62

0.5

73

245

.

0.6

849

0.6

495

26

0.7

252

0.5

27

0

.516

225

.

0.8334

0.8

487

51

0.4990

0.7

24

0.7

35

246

.

0.8

056

0.8

330

34

0.9

402

0.6

23

0

.634

226

.

0.2099

0.5

794

89

0.8592

0.4

84

0.4

95

247

.

0.1

950

0.0

141

85

0.5

646

0.3

29

0

.340

227

.

0.2310

0.1

310

58

0.5107

0.3

14

0.3

23

248

.

0.8

455

0.3

718

100

0.3

643

0.7

21

0

.730

228

.

0.7203

0.7

654

82

0.4170

0.7

45

0.7

56

249

.

0.3

078

0.9

302

40

0.4

068

0.5

46

0

.557

229

.

0.9372

0.8

576

57

0.7968

0.7

48

0.7

59

250

.

0.2

377

0.7

404

61

0.7

237

0.4

85

0

.474

230

.

0.8001

0.7

958

86

0.6571

0.7

68

0.7

79

251

.

0.1

467

0.8

734

38

0.3

172

0.4

77

0

.488

231

.

0.3370

0.9

944

64

0.9242

0.5

84

0.5

95

252

.

0.5

894

0.0

162

77

0.5

834

0.4

45

0

.454

232

.

0.1403

0.1

855

75

0.4482

0.3

47

0.3

56

253

.

0.7

586

0.7

369

44

0.6

550

0.6

31

0

.642

233

.

0.4001

0.3

165

48

0.5440

0.4

01

0.4

12

254

.

0.5

225

0.4

025

12

0.0

284

0.4

31

0

.442

234

.

0.7808

0.3

362

75

0.7799

0.5

84

0.5

93

255

.

0.1

036

0.1

809

62

0.1

875

0.3

27

0

.338

235

.

0.0566

0.2

599

93

0.4886

0.3

81

0.3

92

256

.

0.7

389

0.4

540

100

0.9

822

0.6

47

0

.664

236

.

0.5002

0.6

127

63

0.7568

0.5

41

0.5

30

257

.

0.5

256

0.5

343

53

0.5

615

0.5

21

0

.530

237

.

0.3455

0.8

515

76

0.8720

0.5

79

0.5

96

258

.

0.5

093

0.1

627

45

0.7

144

0.3

68

0

.357

1250053-29

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


30/32


References

Abara, J (1989). Applying integer linear programming to the fleet assignment problem.Interfaces, 19(4), 2028.

Altug, S, MY Chow and HJ Trussell (1999). Fuzzy inference systems implemented onneural architectures for motor fault detection and diagnosis. IEEE Transaction onindustrial Electronics, 6, 10691079.

Beaujon, GJ and MA Turnquist (1991). A model for fleet sizing and vehicle allocation.Transportation Science, 1, 1945.

Booler, JM (1980). The solution of railway locomotive scheduling problem. Journal ofOperations Research Society, 31, 943948.

Bradley, SP, A Hex and T Magnanti (1977). Applied Mathematical Programming. MA:Addison-Wesley.

Chiclana, F, F Herrera, E Herrera-Viedma and S Alonso (2007). Some induced orderedweighted averaging operators and their use for solving group decision-making prob-lems based on fuzzy preference relations. European Journal of Operational Research,182, 383399.

Cooke, WP (1985). Quantitative Methods for Management Decision. New York: McGraw-Hill Book Company.

Crainic, TG (2000). Service network design in freight transportation. European Journal ofOperational Research, 122, 272288.

Crainic, TG and G Laporte (1997). Planning models for freight transportation. EuropeanJournal of Operational Research, 97, 409439.

Delgado, M, F Herrera, E Herrera-Viedma, MJ Martn-Bautista, L Martnez and MA Vila(2002). Communication model based on the 2-tuple fuzzy linguistic representationfor a distributed intelligent agent system on internet. Soft Computing, 6, 320328.

Green, LV and D Guha (1995). On the efficiency of imbalance in multi-facility multi-serverservice systems. Management Science, 41, 179187.

Henn, V (2000). Fuzzy route choice model for traffic assignment. Fuzzy Sets and Systems,116, 77101.

Herrera, F, E Herrera-Viedma and L Martnez (2008). A fuzzy linguistic methodology todeal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy Systems, 16,354370.

Hillier, FS and GJ Lieberman (1990). Introduction to Operations Research, New York:

McGraw-Hill.Ichoua, S, M Gendreau and JY Potrin (2003). Vehicle dispatching with timedependenttravel times. European Journal of Operational Research, 2, 379396.

Jang, JSR (1993). ANFIS: Adaptive network based fuzzy inference systems. IEEE Trans-actions on Systems, Man, and Cybernetics, 3, 665685.

Jaszkiewicz, A (1997). A metaheuristic approach to multiple objective nurse scheduling.Foundations of Computing and Decision Sciences, 3, 169184.

Khosravi, A, HA Talebi and M Karrari (2005). Fault detection and isolation for unknownnonlinear systems using expert methods. Proceedings of the 2005 IEEE Conferenceon Control Applications, Canada, 14861490.

Lee, B, A Fujiwara, Y Sugie and M Namgung (2003). A sequential method for combining

random utility model and fuzzy inference model.Journal of Advanced ComputationalIntelligence and Intelligent Informatics, 3, 117121.

Lobel, A (1998). Vehicle scheduling in public transit and lagrangean pricing. ManagementScience, 44, 16371649.

Lotfi, V and C Pegels (1989). Decision Support Systems for Management Science/Operations Research. Homewood: Irwin.

1250053-30

AsiaPac.


dfromw


by178.2

22.6

7.1

65on03/20

/13.

Forpersonaluseonly.


31/32


32/32


Dragan S. Pamucar was born in Rijeka, Croatia. He received his BS degree from

the Technical Military Academy in Belgrade, 2003 and MS degree from the Faculty

of Transport and Traffic Engineering in Belgrade, 2009. His main research inter-

ests, as a PhD student at the Military Academy in Belgrade, are: Organization

Design, Fuzzy Logic, Genetic algorithms, Neural nets, Multicriteria Decision Mak-

ing Models, etc.

He is an assistant professor at the Military Academy in Belgrade, teaching Opera-

tions Research and Organization in Transport. He has published several academic

articles or papers in international journals, including Yugoslav lournal of operations

researh and International Journal of Physical Sciences.

Vesko M. Lukovac was born in Kolasin, Montenegro. He received his BS degree

from the Technical Military Academy in Belgrade, 2000 and MS degree from the

Faculty of Transport and Traffic Engineering in Belgrade, 2010. His main

Documents

ApAPPLICATION OF ADAPTIVE NEURO FUZZY INFERENCE SYSTEM IN THE PROCESS OF TRANSPORTATION SUPPORTjor Article Anfis