Expert Systems with Applications 40 (2013) 4090–4095

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Determining the number of postal units in the network – Fuzzy approach,Serbia case study

Mladenka Blagojevic a, Milica Šelmic a,⇑, Dragana Macura a, Dragana Šarac b

a University of Belgrade, Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, 11000 Belgrade, Serbiab University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia

a r t i c l e i n f o

Keywords:Network accessPermanent postal unitsFuzzy logicWang–Mendel’s method

0957-4174/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.eswa.2013.01.038

⇑ Corresponding author. Tel.: +381 11 3091207; faxE-mail addresses: m.blagojevic@sf.bg.ac.rs (M. Bla

(M. Šelmic), d.macura@sf.bg.ac.rs (D. Macura), dsarac

a b s t r a c t

One of the main, current, goals of the public postal operators in developing countries is to define themodel for proper postal network design and access. The access to the postal network represents a setof different elements that interact with each other and have a common aim of providing continuous,of high quality, reliable and sustainable universal postal service. Worldwide experience suggests differentapproaches in defining the components and criteria for establishing the system of access to the postalnetwork of the public operator. In this paper we present two different approaches. The first one is basedon criteria determined in previous study and, here, we develop proper mathematical formulation. Thesecond one is new, general, method created to generate fuzzy rules from numerical data, well knownas Wang–Mendel’s method. The authors apply both methods on real data collected from Serbian munic-ipalities and finally, compare results obtained by them.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The universal postal service is a service of general interest andrepresents a set of postal services which are performed continu-ously on the territory of any country, within the prescribed quality,at affordable prices and under the same conditions for all users,without any discrimination (European Parliament and Council,2008). The universal postal service is being developed in line withtechnological and economic development and the needs of users.

The providing of the universal postal service depends on prop-erly designed postal network and locations of access points. Accesspoints include the admission points, including mailboxes intendedfor the population, either in public places or in the premises of theuniversal postal service provider, where postal items can behanded in by the users of postal services (ERGP Report, 2012).

Worldwide experience suggests different approaches in defin-ing the components and criteria for establishing the system of ac-cess to the postal network of the public operator. As can be noticedfrom NERA (2007) different countries have different approaches toaccess to the postal network, established in relation with criterionas a density, minimum number of post offices, distribution, etc. Inaccordance with these criteria, for example, in Australia wereestablished 4000 post offices, of which 2500 in the rural area. InDenmark, there must be at least one post office offering full servicein a settlement with more than 5000 people. Post offices in cities

ll rights reserved.

: +381 112638912.gojevic), m.selmic@sf.bg.ac.rs@uns.ac.rs (D. Šarac).

with the population of 2500 to 5000 inhabitants should not beclosed unless there is some other service. Post offices in rural areasshould not be closed unless the postman can provide the service orthe distance to the next nearest post office does not exceed 10 km,measured in a straight line.

Following mentioned criteria, in Germany, postal network con-sists of 12000 post offices. Settlements with more than 2000 peo-ple must have at least one post office, or be the center of the overallplan. Public postal operator has pledged to set up a stationary postin settlements of over 2000 people, and that it is not posted on ahigher distance than 2 km in settlements with more than 4000inhabitants. In Hungary, settlements with more than 600 peoplemust have a permanent post office, except that in settlements of600 to 1000 people a mobile building can be set, if permitted todo so by local authorities. In cities, the distance of post office fromusers must not be greater than 3 km, but for every 20000 residentsthere should be a permanent post office. In Japan and Norway, onepost office in each municipality was established.

This paper considers the postal network of public postal opera-tor in Serbia, as a representative of the postal operators in region.The current trend of public postal operator and regulatory bodyin Serbia is to optimize the access points, universal postal serviceand public postal network. One possible way to achieve this goalis to minimize the number of permanent postal units of postal net-work. This process would reduce costs of postal operator, as well asthe total number of employees.

In this paper two different approaches to optimize the publicpostal network are presented. The first one relies on research

M. Blagojevic et al. / Expert Systems with Applications 40 (2013) 4090–4095 4091

Kujacic, Šarac, and Jovanovic (2012) and indicates the need for cri-teria which would determine the minimum required number ofpermanent postal units. For the Republic of Serbia, the authors ofKujacic et al. (2012) defined four relevant criteria. Based on theirconclusions we developed mathematical formulation and thus pro-vide an easier application of existing criteria.

The second, new, approach for determining the required numberof permanent postal units is also developed in this paper. Theauthors use well known Wang–Mendel’s (WM’s) method whichconsists of five steps. Step 1 divides the input and output spacesof the given numerical data into fuzzy regions. Step 2 generates fuz-zy rules from the given data. Step 3 assigns a degree of each of thegenerated rules for the purpose of resolving conflicts among gener-ated rules. Step 4 creates a combined fuzzy rule base based on boththe generated rules and linguistic rules of human expert. Finally,Step 5 determines a mapping from input space to output spacebased on combined fuzzy rule base using defuzzifying procedure.

The proposed model is general and with slightly modificationscan be implemented in numerous scenarios of determining re-quested number of postal units. The main advantage of describedmodel is in the fact that experts’ opinion and experience are embed-ded. This is a reason why we decided to use WM’s method whichcombines the importance of numerical information and experts’knowledge. The authors of the paper use a case study of municipal-ities’ characteristics in Serbia for numerical evaluation and testing,but the model can be applied on any postal network worldwide.

After comparing results obtained by both, exact formulae andfuzzy model, it is observed that the second model is better in orderto optimize the number of access points in public postal network.

The paper is organized as follows. The Section 2 gives the foun-dations of access to the public postal operator’s (PPO) network. Thethird Section describes models for determining the number of per-manent postal units. In the following Section results and discussionare presented. The last Section 5 is devoted to concluding remarks.

2. Access to the public postal operator’s (PPO) network

The issue of access to public postal operator’s network is ofgreat importance. There is no transparent methodology for the def-inition of particular criteria values (density of access points, mini-mum number of post offices, distribution/allocation of post officeson urban and rural network and other).

During the research, the authors Kujacic et al. (2012) have esti-mated the importance of certain factors for determining admissioncriteria. Based on that, they came to a conclusion that it is neces-sary to make certain measurements and comparisons and system-atize the decision making process. In this regard, they suggest thatthe tests are carried out in several steps:

� Step 1 – Stating the scope of the universal postal service (insome countries in the realm of the universal postal service, inaddition to the transfer of letter post items up to 2 kg and par-cels up to 20 kg, postal and financial services for vulnerablepopulation were included). This step affects significantly thedetermination of the minimum number of post offices withwhich public postal operator (PPO) must operate;� Step 2 – Determining the socio-economic and demographic

characteristics of the observed country and establishing the rel-evant factors for the development of postal services;� Step 3 – Determining the existing infrastructure of PPO and the

structure of the universal postal service’s scope and other ser-vices provided by PPO;� Step 4 – Determining the degree of correlation between envi-

ronmental factors and the requirements for the universal postalservice;

� Step 5 – Determining the criteria related to the density, distri-bution and minimum number of access points, post offices, etc.;� Step 6 – Mapping and testing of access points on the observed

territory and determining the minimum number of units inpublic postal network.

The authors of Kujacic et al. (2012) defined following criteria forurban settlements:

In every settlement with more than 1000 inhabitants (andmunicipality) should be provided with at least one permanent unitof postal network;

In settlements with more than 20000 inhabitants, there has tobe at least one permanent unit of postal network on every 20000inhabitants.

3. Models for determining the number of permanent postalunits in the public postal operators’ network

In the next time period, the Serbian postal operator is planningreorganization of the postal network. Since this is extremelyimportant activity, which influence on total costs and number ofemployees, it is necessary to adopt some models in order to deter-mine the number of requested permanent postal units in urbansettlements.

3.1. Exact approach

According to previously mentioned criteria, from Section 2, wedevelop following mathematical equation to determine number ofrequired permanent postal units:

Ni is the number of permanent postal units per municipality i, Ris the the total number of settlements per municipality i with apopulation between 1000 and 20000 inhabitants, M is the the totalnumber of settlements per municipality i with more than 20000inhabitants, S is the the total number of inhabitants in settlementswith a population of over 20000 inhabitants, and j is the counterfor settlements per municipality i with more than 20000inhabitants.

xi¼1; exist settlement with population between 1000 and 200000; otherwise

�

xi ¼1; exist settlement with population over 200000; otherwise

�

Ni ¼ xiRþ yi

XM

j¼1

Sj

20000

& ’ð1Þ

This equation gives an opportunity for mathematical interpretationof defined criteria. Obviously, Eq. (1) sublimates two criteria. Thefirst one concerns that a permanent postal unit has to be locatedin every settlement with more than 1000 inhabitants. The binaryvariable xi embeds this condition into Eq. (1). The second binaryvariable, yi, allows criteria that, in settlements with more than20000 inhabitants, at least one permanent postal unit has to existon every 20000 inhabitants.

3.2. Fuzzy approach

For most real-world control and design network problems, theinformation concerning modeling, tuning, evaluation, realization,etc. can be classified into two classes: numerical information ob-tained from some kind of measurements and linguistic informationobtained from human experts. Fuzzy logic provides a formal meth-odology for representing, and implementing a human’s heuristic

Table 2Domain intervals for x1, x2 and y.

Variable Domain

x1 [0,30]x2 [0,200]Y [1,25]

Fig. 1. Input variable x1 (the total number of settlements with a population

4092 M. Blagojevic et al. / Expert Systems with Applications 40 (2013) 4090–4095

knowledge. Up to know fuzzy logic have been applied on numer-ous problems related to transportation, optimization and design(Kikuchi & Pursula, 1998; Paek, Lee, & Napier, 1992; Sun & Gu,2011; Turskis, Zavadskas, & Peldschus, 2009; Yang & Soh, 2000).

In this paper we propose a general method, known as WangMendel’s method for combining both numerical and linguisticinformation into a common framework – a fuzzy rule base andapply it to the problem of determination of required number ofpermanent units in public postal operator’s network.

Generally, WM’s rule generation method is used to derive fuzzyrule base Wang and Mendel (1992). This method could becombined with some other methods, such as: Genetic algorithms(Casillas, Martinez, & Benitez, 2009; Cordon, Herrera, & Villar,2001), Swarm optimization algorithm (Carmona & Castro, 2005;Yang, Yuan, Yuan, & Mao 2010), Simulated annealing (Yanar &Akyurek, 2011), etc. Giving the literature review of the fuzzy sys-tems in the transportation fields, Teodorovic (1999) representedseveral papers with WM’s method application. Teodorovic empha-sized that WM’s method represents a nonlinear mapping, with thepossibility to approximate any real continuous function to arbi-trary accuracy. Wang (2003) extended WM’s method to enhancethe practicality. The author presented the approach for rankingthe importance of input variables and proposed an algorithm forsolving pattern recognition problems. Chen, Zhang, and Jia (2007)emphasized that WM’s rule generation method is the one of theearliest algorithms, but with one disadvantage. This method selectsthe rules with the maximum degree, without taking into consider-ation other conflicting rules. The authors compared three methods,and the main conclusion of the paper is that the weighted meanmethod has the best robustness and error-tolerance, consequentlythis approach is suitable for extracting rules from the real datawith noise. The results obtained by Yanar and Akyurek (2011) indi-cated that WM’s method provides better starting configuration forsimulated annealing compared to fuzzy C-means clusteringmethod.

According to the authors’ knowledge, there is no paper dealingwith WM’s method in designing postal network or determining re-quested number of postal units.

In this paper, the input variables of proposed, fuzzy, model are:

� the total number of settlements with a population between1000 and 20000 (labeled as x1)� the total number of inhabitants in settlements with a popula-

tion of over 20000 (labeled as x2).

As output variable of fuzzy model the authors of the paperadopt the number of permanent postal units in each settlement(denoted as y). The data for the variables x1, x2 and y (from Table 1)were collected from whole territory of the Republic of Serbia.

The values for input variable and output variable can be seenfrom Table 1. As it can be noticed each set of desired input–outputdata is given in the form of:

fðxð1Þ1 ; xð1Þ2 ; yð1ÞÞ; ðxð2Þ1 ; xð2Þ2 ; yð2ÞÞ; . . . ; ðxð40Þ1 ; xð40Þ

2 ; yð40ÞÞg:

Table 1Values for input and output variables.

Municipality xðiÞ1 xð1Þ2y(i)

1 8 0 82 5 156,280 133 13 26,549 144 10 25,526 11� � � � � � � � � � � �39 14 47,485 1640 18 75,743 22

A sample of 40 municipalities from Table 1 is formed randomlywith respect to all of the analyzed municipalities in the Republic ofSerbia.

The first step in WM’s method divides the input and outputspaces into fuzzy regions. Assume that the domain intervals ofx1, x2 and y are [x�1 ; x

þ1 ], [x�2 ; x

þ2 ] and [y-,y+], respectively. We divide

each domain interval into 2N + 1 regions (N may vary from variableto variable) and assign each region a fuzzy membership function(Table 2).

On following figures we show both input variables and outputvariable. The shape of each membership function is triangular. Ofcourse, other divisions the domain regions and other shapes ofmembership functions are possible.

The membership functions of following fuzzy sets are shown onFig. 1: very, very small number of settlements with a populationbetween 1000 and 20000 (VVS), very small number of settlementswith a population between 1000 and 20000 (VS), small number ofsettlements with a population between 1000 and 20000 (S), mid-dle number of settlements with a population between 1000 and20000 (M), large number of settlements with a population be-tween 1000 and 20000 (L), very large number of settlements witha population between 1000 and 20000 (VL), and very, very largenumber of settlements with a population between 1000 and20000 (VVL).

The domain of the second input variable x2 is covered by the fol-lowing fuzzy sets (Fig. 2).

Fig. 2 shows the membership functions of following fuzzy set:no settlements with over 20000 inhabitants (N), very, very smallnumber of inhabitants in settlements with a population of over20000 (VVS), very small number of inhabitants in settlements witha population of over 20000 (VS), small number of inhabitants in

between 1000 and 20000).

1N VV S ST M MT L

0 2 6 108 1612 X24 14 18

V V VV

ig. 2. Input variable x2 (the total number of inhabitants in settlements with aopulation of over 20 000) measured in thousands.

Fp

Table 3Rules based on input–output pairs of data.

Input–output pair Rule

xð1Þ1 ; xð1Þ2 ; y(1) 1: If x1 is S And x2 is N Then y is M

xð2Þ1 ; xð2Þ2 ; y(2) 2: If x1 is VS And x2 is VL Then y is L

xð3Þ1 ; xð3Þ2 ; y(3) 3: If x1 is M And x2 is VVS Then y is L

xð4Þ1 ; xð4Þ2 ; y(4) 4: If x1 is S And x2 is VVS Then y is M

� � � � � � � � � � � �xð39Þ

1 ; xð39Þ2 ; y(39) 39: If x1 is M And x2 is VS Then y is L

xð40Þ1 ; xð40Þ

2 ; y(40) 40: If x1 is L And x2 is STM Then y is VL

Table 4Final fuzzy rule base.

X2 N VS S M L VL VVL VVLVVS S S M L VL VVL VVLVS VS S M L VL VVL VVLS S M L VL VVL VVL VVLSTM S M L VL VL VVL VVLM S M L VL VVL VVL VVLMTL M M L VL VVL VVL VVLL S M VL VL VVL VVL VVLVL M L VL VL VVL VVL VVLVVL M L VL VVL VVL VVL VVL

VVS VS S M L VL VVLX1

M. Blagojevic et al. / Expert Systems with Applications 40 (2013) 4090–4095 4093

settlements with a population of over 20000 (S), small to mediumnumber of inhabitants in settlements with a population of over20000 (STM), medium number of inhabitants in settlements witha population of over 20000 (M), medium to large number of inhab-itants in settlements with a population of over 20000 (MTL), largenumber of inhabitants in settlements with a population of over20000 (L), very large number of inhabitants in settlements witha population of over 20000 (VL), very, very large number of inhab-itants in settlements with a population of over 20000 (VVL).

The domain of the output variable y is covered by the followingfuzzy sets (Fig. 3).

The domain of output variable is divided into six intervals(N = 6). Fig. 3. presents membership functions of following fuzzysets: very small number of permanent units (VS), small numberof permanent units (S), medium number of permanent units (M),large number of permanent units (L), very large number of perma-nent units (VL) and very, very large number of permanent units(VVL).

The second step of proposed model is to generate fuzzy rulesfrom given data pairs. We, first, determine the degrees of given in-put–output pairs (xðiÞ1 ; x

ðiÞ2 ; yðiÞ) in different regions. For example

xð20Þ1 ¼ 24 in Fig. 1 has degree 5/6 in VL, and degree 1/6 in L and

zero degrees in all other regions. Second, we assign a givenxðiÞ1 ; xðiÞ2 or y(i) to the region with maximum degree. Finally, we ob-tain one rule from one pair of desired input–output data, e.g.

� (xð1Þ1 ; xð1Þ2 ; y(1))) [xð1Þ1 (0.833 in VL, max), xð1Þ2 (1 in N, max);� y(1) (0.7 in M, max)]) Rule 1.� IF x1 is VL and x2 is N, THEN y is M

After this procedure we made 40 fuzzy rules, the one for eachinput–output pair of data. The part of these rules is shown inTable 3.

Next step is to eliminate same or conflict rules i.e. rules thathave same IF part but a different THEN part. One way to resolvethis conflict is to assign a degree to each rule generated from datapairs, and accept only the rule from a conflict group that has max-imum degree. In our case study we don’t have any conflict rules, sowe just remove same rules from existing rule base. In this way thenumber of rules is greatly reduced (total number of rules is 17).

Most often, available pairs of input–output data are not suffi-cient to ‘‘cover’’ all the different situations that can happen in aparticular system. Fuzzy rule base is more complete if the numberof different input–output data pairs is bigger. In order to obtainbetter results fuzzy rule base may be amended with additional fuz-zy rules generated by an expert. The final fuzzy rule base in thecase of determining the required number of permanent postalunits per municipalities in Serbia is shown in Table 4. Fuzzy rulesgenerated by the experts are underlined.

1

VS S M L VL VVL

0 5 10 20 15 25 X1

Fig. 3. Output variable y (the number of permanent postal units in eachsettlement).

4. Results and discussion

4.1. General information

The Republic of Serbia occupies the territory of 88361 km2.According to the last census (Statistical Office of the Republic ofSerbia, 2011) Serbia had an estimated population of 7576837inhabitants, distributed in 6167 settlements.

Of the total population in Serbia, more than 42% live in urbanareas, i.e. towns with above 20000 inhabitants. The Republic ofSerbia has 52 populated areas (settlements) with over 20000 citi-zens. Fig. 4. shows the map of counted cities and municipalities inSerbia.

4.2. Obtained results

After applying Matlab software and fuzzy logic toolbox the re-quired numbers of permanent postal units per municipalities inSerbia are obtained. These results are shown in Table 5.

The authors compare current number of permanent postal unitsper municipality with results obtained by exact Eq. (1) and fuzzylogic model. These results are shown in following Table 6. The firstcolumn presents observed municipalities. The second column pre-sents current number of permanent postal units per municipality.The third column shows results obtained by Eq. (1). The fourth col-umn consists of the number of permanent postal units obtained byWM’s method.

From Table 6 and Figs. 5 and 6 it can be seen that the developedWM’s method is able to find the exact number of permanent postalunit for 34 cases, and for 6 cases the model make some deviationsfrom existing number. In 5 of 6 cases, our fuzzy logic model gavethe number of required permanent unit less than current numberfor one unit. This fact is very encouraging for the furtherimplementation of this model. The obtained results indicate thatthe proposed model can be used in some future restructuring the

Fig. 4. Cities and municipalities in Serbia (Source: www.agropress.org.rs).

Table 5Values for input and output variables by Wang–Mendel method.

Municipality x1(i) x2

(i) y(i)

1 8 0 82 5 156,280 133 13 23,314 134 10 24,568 10� � � � � � � � � � � �39 14 52,693 1540 18 33,837 22

Table 6Comparison of obtained results.

Municipality Current number ofpermanent postal unitsper municipality

Resultsobtainedby Eq. (1)

Number ofpermanent postalunits by WM’S

1 8 8 82 13 13 133 14 14 134 11 11 10� � � � � � � � � � � �39 16 16 1540 22 22 22

Fig. 5. Comparison of the results.

Fig. 6. Linear interpretation of obtained results.

4094 M. Blagojevic et al. / Expert Systems with Applications 40 (2013) 4090–4095

postal system, in which certainly one of the main targets will bethe reduction of the number of permanent units per municipalities.

The WM’s method gives good results because of the fact thatwhen we created fuzzy rule database, we involved the experts withPh.D. and Master’s degrees in the postal traffic.

5. Conclusions

The postal network capacity is a unique, strategic advantage ofany post, because it allows access to the service on the internalmarket, and at the same time, supports the pursuit of expansionand global integration.

The universal postal service network has to meet the require-ments of users’ access, i.e. to effectively cover the entire territoryfor which it is organized. That is exactly the reason why we devel-op two different approaches for the access to the postal network ofthe public operator. The first one is based on exact mathematicalformulation, and second one relies on fuzzy logic and WM’smethod.

We apply both approaches on real data collected from Serbianmunicipalities. The obtained results, i.e. number of permanentpostal units per municipalities in Republic of Serbia, show thatthese two models are complementary and they converge to eachother. In 85% cases our fuzzy logic model gave the same numberof required permanent units as by mathematical equation whichrelies on previously defined criteria. This fact is very encouragingfor the further implementation of this model.

From this point of view combination of described models issuitable for application to other, similar, problems related to opti-mization of the postal network. The further research in this areashould take into account more parameters into analysis, such asthe demands for services and costs.

Acknowledgment

This research is partially supported by the Ministry of Science ofSerbia, Grant Numbers 36002, 36022.

M. Blagojevic et al. / Expert Systems with Applications 40 (2013) 4090–4095 4095

References

Carmona, P. & Castro, J. (2005). Interpretability enhancement of fuzzy modelingusing Ant colony optimization. In First international workshop on genetic fuzzysystems, Proceedings of the paper (pp. 148–154).

Casillas, J., Martinez, P., & Benitez, A. (2009). Learning consistent, complete andcompact sets of fuzzy rules in conjunctive normal form for regression problems.Soft Computing, 13(5), 451–465.

Chen, D., Zhang, J., & Jia, Sh. (2007). WM method and its application in traffic flowmodeling. In International conference on transportation engineering (pp. 339–345).

Cordon, O., Herrera, F., & Villar, P. (2001). Generating the knowledge base of a fuzzyrule-based system by the genetic learning of the data base. IEEE Transactions onFuzzy Systems, 9(4), 667–674.

ERGP. (2012). ‘‘ERGP REPORT on ‘‘access’’ to the postal network and elements ofpostal infrastructure’’.

European Parliament and the Council (2008). ‘‘Accompanying document to theReport from the Commission to the European Parliament and the Council on theapplication of the Postal Directive (Directive 97/67/EC as amended by Directive2002/39/EC) {COM(2008) 884 final}’’ pp. 19–20.

Kikuchi, S., & Pursula, M. (1998). Treatment of uncertainty in study oftransportation: Fuzzy set theory and evidence theory. Journal ofTransportation Engineering, 124(1), 1–8.

Kujacic, M., Šarac, D, & Jovanovic, B. (2012). Access to the postal network of thepublic operator. In Proceedings of international conference ‘‘the role of strategic

partnerships and re-engineering of the public postal network in the sustainableprovision of universal service’’ (pp. 18–26). Berane, Montenegro.

Paek, J., Lee, Y., & Napier, T. (1992). Selection of design/build proposal using fuzzylogic system. Journal of Construction Engineering and Management, 118(2),303–317.

Statistical Office of the Republic of Serbia (2011). ‘‘Census of Population, Householdsand Dwellings in the Republic of Serbia’’ (33–75). Belgrade

Sun, L., & Gu, W. (2011). Pavement condition assessment using fuzzy logic theoryand analytic hierarchy process. Journal of Transportation Engineering, 137(9),648–655.

Teodorovic, D. (1999). Fuzzy logic systems for transportation engineering: The stateof the art. Transportation Research Part A, 33, 337–364.

Turskis, Z., Zavadskas, E. K., & Peldschus, F. (2009). Multi-Criteria OptimizationSystem For Decision Making in Construction Design and Management.Inzinerine Ekonomika-Engineering Economics, 1, 7–17.

Wang, L. X. (2003). The WM method completed: A flexible fuzzy system approach todata mining. IEEE Transactions on Fuzzy Systems, 11(6), 768–782.

Wang, L., & Mendel, J. (1992). Generating fuzzy rules by learning from examples.IEEE Transactions on Systems, Man and Cybernetics, 22(6), 1414–1427.

Yanar, T. A., & Akyurek, Z. (2011). Fuzzy model tuning using simulated annealing.Expert Systems with Applications, 38, 8159–8169.

Yang, Y., & Soh, C. (2000). Fuzzy logic integrated genetic programming foroptimization and design. Journal of Computing in Civil Engineering, 14(4), 249–254.

Yang, X., Yuan, J., Yuan, J., & Mao, H. (2010). An improved WM method based on PSOfor electric load forecasting. Expert Systems with Applications, 37, 8036–8041.