a study of rural logistics center location based on...

Research ArticleA Study of Rural Logistics Center Location Based onIntuitionistic Fuzzy TOPSIS

Yan Zhang Yingying Zhang Yanfeng Li Sen Liu and Junai Yang

School of Logistics Yunnan University of Finance and Economics Kunming 650221 China

Correspondence should be addressed to Sen Liu liusencool163com

Received 3 March 2017 Accepted 14 May 2017 Published 18 June 2017

Academic Editor Franck Massa

Copyright copy 2017 Yan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In recent years with the development of the rural e-commerce the importance of rural logistics has been widely recognized Theselection of rural logistics center is a crucial part in products circulation because an unreasonable location of rural logistics cancause a circulation problem and product waste In this paper we propose a rural logistics center locationmodel based on the theoryof intuitionistic fuzzy TOPSIS First we integrate the information according to expertsrsquo score based on the evaluation index systemSecond we use the entropy weight method to determine the weight of each evaluation indexThird we rank the results by using theintuitionistic fuzzy TOPSISmethod Finally an illustrative example will be used to prove the validity and feasibility of the proposedmethod

1 Introduction

Agriculture plays an important role in production Howeverfarmers focus on agricultural production more than thecirculation process that leads to agricultural product backlogrot and poor harvests This not only damages the interests offarmers but also causes the waste of agricultural resourcesImperfect rural infrastructure construction seriously hindersthe development of the rural logistics industry which leadsto the current difficulty To a large extent inconvenient rurallogistics affects the development of economy Rural logistics isrelative to the concept of urban logistics Rural logistics refersto rural resident production and life and other economicactivities to provide transportation handling loading andunloading packaging processing and storage and all itsrelated activities [1] Not only does it benefit the farmersrsquo livesand improves the economic income of farmers but also itaccelerates the production and development of agricultureRural logistics has distinct features of distinct seasonalitybiology decentralization diversity and complexity [2 3]

At present there is small scale and a little quantity in rurallogistics Agricultural products can only be circulated withina small scale which cannot meet the development require-ments of the rural logistics industryThere aremany problemsin the existing logistics centers that need to replanned and

rebuilt The unreasonable location of rural logistics cancause a circulation problem and products waste It also canaggravate the waste of labor and the urban-rural economicgap [4] Therefore not only can reasonable rural logisticscenter location selection achieve the outward transportationof agricultural products but also it implements effectiveproduct circulation between cities other regions and evenother countries and forms two-way logistics leading to thedevelopment of the economy

Experts have different opinions on the rural logisticscenter location Amini used fuzzy TOPSIS methodology inrural industrial site selection [5] Rao et al proposed a fuzzyTOPSIS method in city logistics centers location selectionand evaluation criteria are transformed into linguistic 2-tuples in this method [6] Li et al presented a comprehensivemethodology combined with Axiomatic Fuzzy Set and TOP-SIS for logistics center location selection [7] Compared withother methods [8] TOPSIS is widely used in all aspects of themultiple attribute decision-making such as the evaluationof suppliers electronic commerce electronic informationand logistics node location However many criteria andlinguistic variables are difficult to accurately describe andorder [9] The existing methods based on interval num-bers and fuzzy numbers need to use prior knowledge thatmakes the evaluation result subjective [10 11] Hence these

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 2323057 7 pageshttpsdoiorg10115520172323057

2 Mathematical Problems in Engineering

researchesmake conclusion unreasonable by using processeddata Compared with these methods intuitionistic fuzzinesscan effectively reduce the fuzziness andmake the resultsmorerealistic and accurate by using raw date [11ndash13] Intuitionisticfuzzy improved TOPSIS can effectively deal with uncertaintyevaluation information

In the rural logistics center location of the existingresearch most theoretical models and algorithms focus ona single project model where application value is not highand model accuracy and science degrees are not perfectAnd part of the studies also stay on a level that onlyconsiders a single objective and aims at cost or benefit [210 14] They considered other indicators as a constraint andthe establishment of the evaluation index system is not tocarry out the green circulation and sustainable developmentconcept

This paper studies rural logistics center location selectionbased on the theory of intuitionistic fuzzy TOPSIS Basedon the existing theories and empirical studies this paperestablishes the evaluation index system of logistics centerlocation standing in the rural demand angle that combineslogistics center location of the relevant theories and the char-acteristics of the rural logistics Based on the rural electricityunder the incomplete information logistics center locationselection problem this paper establishes the rural electricbusiness logistics center location decision model using thetheory of intuitionistic fuzzy sets and TOPSIS decision-making This model calculates the weight with intuitionisticfuzzy weight and uses TOPSIS decision-making method fora final decision This method is easy to operate and can helpdecision-makers quickly find out the suitable criteria for thedevelopment of the rural logistics center location Finallywe give an illustrative example that proves the validity andfeasibility of evaluation methods

2 The Proposed Method

21 Intuitionistic Fuzzy Set The intuitionistic fuzzy set isrelative to the expansion of the traditional fuzzy sets Intu-itionistic fuzzy sets take into account the membership degreeand information such as the degree of membership andhesitation [15] Therefore the intuitionistic fuzzy set is moreflexible than traditional fuzzy sets and practical in dealingwith vagueness and uncertainty Compared with fuzzy setsthe intuitionistic fuzzy collective shows the fuzziness anduncertainty in the real world and it can better deal withthe uncertain information in the decision-making process[7 9 15ndash17] This method has good performance in terms oftheory and application At present the intuitionistic fuzzyset applies to decision-making medical diagnosis logic pro-gramming pattern recognition machine learning marketprediction and so forth [16]

Definition 1 Set 119883 is a nonempty set then the theory ofdomain 119883 on intuitionistic fuzzy sets can be represented as119860

119860 = ⟨120594 120583119860 (120594) ]119860 (120594)⟩ | 120594 isin 119883 (1)

Among them 120583119860 is the membership degree for 119860 ]119860 isthe nonmembership degree for 119860 and 120583119860(120594) and ]119860(120594) arefor the 119883 element that belongs to 119860 membership and thenonmembership degree120583119860 119883 997888rarr [0 1] 120594 isin 119883 997888rarr 120583119860 (120594) isin [0 1]

]119860 119883 997888rarr [0 1] 120594 isin 119883 997888rarr ]119860 (120594) isin [0 1] (2)

They meet the condition0 le 120583119860 (120594) + ]119860 (120594) le 1 (3)

For the theory of domain intuitionistic fuzzy set 119860 of119883120587119860 = 1 minus 120583119860 (120594) minus ]119860 (120594) (4)

The element in 120594 belongs to 119860 degree of hesitation oruncertainty

Obviously for any 120594 isin 119883 we have 0 lt 120587119860(120594) lt 1In particular any fuzzy set 119860 in the theory of domain 119883

can be established in the following equation120587119860 (120594) = 1 minus 120583119860 (120594) minus ]119860 (120594) (5)

Sets 119860 and 119861 are two fuzzy sets in the theory field 119883multiplication is defined as119860 otimes 119861 = 120583119860 (120594) sdot 120583119861 (120594) ]119860 (120594) + ]119861 (120594) minus ]119860 (120594)

sdot ]119861 (120594) | 120594 isin 119883 (6)

22TheProposedAlgorithm Unlike traditional TOPSIS deci-sion the elements of the decision matrix are intuitionisticfuzzy numbers under the environment of intuitionistic fuzzyTOPSIS multiple attribute decision-making method Wecalculated each scheme and the distance between the idealsolution and the negative ideal solution with intuition fuzzynumber related calculation formulas First experts integrateassessment information according to the evaluation indexsystem Then entropy weight method is used to determinethe weight of each evaluation index Finally we determinethe decision scheme of sorting by intuitionistic fuzzy TOPSISmethod for logistics center

The specific decision-making steps are as follows

Step 1 (determine theweight of decision-makers) We assumethat the decision-making group has 119894 The data of decision-maker is represented by intuitionistic fuzzy numbers119863119896 = [120583119896 ]119896 120587119896] is the rating fuzzy number directly ofDM119896 The weight of DM119896 is as follows

120582119896 = (120583119896 + 120587119896 (120583119896 (120583119896 + ]119896)))sum119897119896=1 (120583119896 + 120587119896 (120583119896 (120583119896 + ]119896))) (7)

Under the conditionsum119897119896=1 120582119896 = 1Step 2 (construct intuitionistic fuzzy matrix) Intuitionisticfuzzy decision matrix is 119877(119896) = (119877(119896)119894119895 )119898times119899 The weight of each

Mathematical Problems in Engineering 3

decider is 120582 = 1205821 1205822 120582l under the conditionsum119897119896=1 120582119896 =1 120582119896 isin [0 1] In the process of group decision-makingIFWA (direct fuzzy weighted average) is presented becauseall personal opinion decisions need to be integrated into thegroup opinion structure polymerization intuitionistic fuzzymatrix

119877(119896) = (119877(119896)119894119895 )119898times119899119877119894119895 = IFWA120582 (119903(1)119894119895 119903(2)119894119895 119903(119897)119894119895 ) = 1205821119903(1)119894119895 oplus 1205822119903(2)119894119895

oplus 1205823119903(3)119894119895 oplus 120582119897119903(119897)119894119895 = [1 minus 119897prod119896=1

(1 minus 120583(119896)119894119895 )120582119896 119897prod119896=1

(](119896)119894119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119894119895 )120582119896 minus 119897prod119896=1

(](119896)119894119895 )120582119896] (8)

Under the condition 119903119894119895 = (120583119860119894(120594119895) ]119860119894(120594119895) 120587119860119894(120594119895)) (119894 =1 2 119898 119895 = 1 2 119899)Aggregated direct fuzzy matrix structure is as follows

119877 = ( 1205831198601 (1205941) ]1198601 (1205941) 1205871198601 (1205941) sdot sdot sdot 1205831198601 (120594119899) ]1198601 (120594119899) 1205871198601 (120594119899) d120583119860119898 (1205941) ]119860119898 (1205941) 120587119860119898 (1205941) sdot sdot sdot 120583119860119898 (120594119899) ]119860119898 (120594119899) 120587119860119898 (120594119899))

119877 = (11990311 sdot sdot sdot 1199031119898 d1199031198991 sdot sdot sdot 119903119899119898)

(9)

Step 3 (determine the weight of the evaluation criteria)Evaluation criteria are unlikely to be equally important 119882represents a series of important degree levels We get 119882 byintegrating the importance of the decision-maker opinionsand standards

The intuitionistic fuzzy standard 119883119895 of DM119896 is 119882(119896)119895 =[120583(119896)119895 ](119896)119895 120587(119896)119895 ]Calculate the weight of the standard with IFWA

119882119895 = IFWA120582 (119882(1)119895 119882(2)119895 119882(119897)119895 ) = 1205821119903(1)119895 oplus 1205822119903(2)119895oplus sdot sdot sdot oplus 120582119897119903(119897)119895 = [1 minus 119897prod

119896=1

(1 minus 120583(119896)119895 )120582119896 119897prod119896=1

(](119896)119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119895 )120582119896 minus 119897prod119896=1

(](119896)119895 )120582119896]119882 = [119882111988221198823 119882119895]

(10)

Among them119882 = (120583119895 ]119895 120587119895) (119895 = 1 2 3 119899)Step 4 (build weighted aggregation of intuitionistic fuzzydecision matrix) After determining weights of criteria (119882)we construct weighted aggregation of intuitionistic fuzzydecision matrix

119877 otimes119882 = ⟨120594 120583119860119894 (120594) sdot 120583119908 (120594) ]119860119894 (120594) + ]119908 (120594)minus ]119860119894 (120594) sdot ]119908 (120594)⟩ | 120594 isin 119883

120587119860119894 (120594) sdot 119882 (120594) = 1 minus ]119860119894 (120594) minus ]119908 (120594) minus 120583119860119894 (120594)sdot ]119908 (120594) + ]119860119894 (120594) sdot ]119908 (120594)

(11)

Weighted aggregation intuitionistic fuzzy matrix is asfollows



(12)

1199031015840119894119895 = (1205831015840119894119895 ]1015840119894119895 1205871015840119894119895) = (120583119860119894 sdot 119908(120594119895) ]119860119894 sdot ](120594119895) 120587119860119894 sdot 120587(120594119895)) isthe weight of aggregation intuition fuzzy matrix

Step 5 (calculate the intuitionistic fuzzy positive ideal solutionand negative ideal solution) Determine the intuitionistic


fuzzy positive ideal solution 119860lowast and fuzzy positive negativeideal solution 119860minus they are defined as

119860lowast = (120583119860lowast119882 (120594119895) ]119860lowast119882 (120594119895))119860minus = (120583119860minus119882 (120594119895) ]119860minus119882 (120594119895)) (13)

1198691 collection is efficiency standards set and 1198692 collection iscost standards set

Under the condition

120583119860lowast119882 (120594119895) = ((max119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(min119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860lowast119882 (120594119895) = ((min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894

]119860119894sdot119882 (120594119895) | 119895 isin 1198692))120583119860minus119882 (120594119895) = ((min

119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860minus119882 (120594119895) = ((max119894

]119860119894sdot119882 (120594119895) | 119895 isin 1198691) (min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198692)) (14)

Step 6 (calculate the distance of the positive and negativeideal solution) 119878119894lowast is the distance between indicators and thepositive ideal solution 119878119894minus is the distance between indicatorsand the negative ideal solution Using Euclidean distance tocalculate 119878119894lowast and 119878119894minus it is concluded that

119878lowast = radic 12119899 119899sum119895=1 [(120583119860119895 sdot119908 (120594119895) minus 120583119860lowast119908 (120594119895))2 + (]119860119895sdot119908 (120594119895) minus ]119860lowast119908 (120594119895))2 + (120587119860119895 sdot119908 (120594119895) minus 120587119860lowast119908 (120594119895))2]119878minus = radic 12119899 119899sum119895=1 [(120583119860119894 sdot119908 (120594119895) minus 120583119860minus119908 (120594119895))2 + (]119860119894 sdot119908 (120594119895) minus ]119860minus119908 (120594119895))2 + (120587119860119894 sdot119908 (120594119895) minus 120587119860minus119908 (120594119895))2]

(15)

Step 7 (calculate the closeness coefficient)

119862lowast119894 = 119878119894minus119878119894lowast + 119878119894minus (16)

Under the condition 0 le 119862lowast119894 le 1Step 8 (rank alternatives) Rank all the alternatives from largeto small based on the closeness coefficient and select the bestone according to the value of 119862lowast119894 3 Illustrative Example

This article takes rural logistics center location selection ofDali in Yunnan province as an example to determine thefitting of the needs of the local rural logistics center locationThree experts (DM1 DM2 andDM3) comprehensively evalu-ate the rural logistics center locationThis paper uses primaryelection and precision selection for logistics center locationselection screening and optimizing work in order to makedecisions quickly and avoid the waste of time and resources

31 Primary Selection In the primary election stage firstdetermine the internal and external factors that influence thelogistics center choice in order to preliminarily measure andfilter logistics center location

Service RequirementThe logistics centermust be able tomeetthe basic needs of the rural distribution and has a certain

storage capacity [5] The logistics center has large scale andinformation technology capability to provide special serviceaccording to the characteristics and needs of customers

Service Quality The logistics center must be able to respondto the needs of customers and ensure complete distributionof goods on time [18] The logistics center has the ability toprovide flexible service to make the customer satisfied

Traffic Condition The logistics center location must haveconvenient transportation and meet the requirements ofoutput and input of a large number of goods and also canto a certain extent reduce the cost [5]

After collecting a large amount of logistics center locationinformation according to the basic demand of the rurallogistics center we finally confirm the five candidate logisticscenters (A1 A2 A3 A4 and A5) for subsequent selectionand evaluation based on the characteristics of the logisticsindustry

32 Precision Selection This paper simplifies the rural elec-tricity evaluation index system of logistics center locationselection in order to facilitate assessment The evaluationcriteria are as follows C1 traffic C2 economics C3 environ-ment C4 politics [1 4 7 18]

Step 1 (calculate the weight of the decision-makers) Wecalculate the importance of criterions according to Table 1


Table 1 The importance of criterions

Degree ScoreVery important (VI) (090 010)Important (I) (075 020)General (G) (050 045)Unimportant (U) (035 060)

Table 2 The weight of decision-maker important degree

DM1 DM2 DM3Degree VI G IWeight 0406 0238 0356

Calculate the weight of decision-makers by formula (7) asshown in Table 2

120582DM1= 0909 + (075 + 005 (075095)) + (050 + 005 (050095))= 0406120582DM2= 050 + 005 (050095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0238

Table 3 Degree of integration indicators

Degree ScoreEspecially good (EG) [100 000]Very very good (VVG) [090 010]Very good (VG) [080 010]Good (G) [070 020]Medium good (MG) [060 030]Medium (M) [050 040]Medium bad (MB) [040 050]Bad (B) [025 060]Very bad (VB) [010 075]Very very bad (VVB) [010 090]

120582DM3= 075 + 005 (075095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0356(17)

Step 2 (construct aggregation intuitionistic fuzzy matrixbased on the opinions of the decision-makers) We get a newlevel of indicators and score after integrating the opinions ofthe three policymakers as shown in Table 3

Aggregation index level is as shown in Table 4Construct intuitionistic fuzzy matrix after integrating the

opinions of the decision-makers

119877 =C1

A1A2A3A4A5

[[[[[[[[

(0728 0170 0012)(0596 0302 0102)(0849 0100 0051)(0663 0236 0101)(0562 0337 0101)

C2(0626 0272 0102)(0605 0292 0103)(0780 0118 0102)(0538 0361 0101)(0462 0438 0100)

C3(0780 0118 0102)(0664 0256 0100)(0769 0170 0061)(0746 0151 0103)(0668 0231 0101)

C4(0700 0200 0100)(0578 0321 0101)(0769 0128 0103)(0644 0254 0102)(0526 0374 0100)]]]]]]]] (18)

Step 3 (calculate the weight of the evaluation criteria) Theimportance of the evaluation criteria is as shown in Table 5

Calculate the weight of the evaluation criteria by formula(10)

1198821205941 1205942 1205943 1205944 = [[[[[(0861 0128 0011)(0750 0200 0050)(0680 0267 0053)(0576 0371 0053)

]]]]]119879

(19)

Step 4 (build weighted aggregation of intuitionistic fuzzydecision matrix) After calculating the weight of the evalu-ation criteria we build weighted aggregation of intuitionisticfuzzy decision matrix

1198771015840 =C1

A1A2A3A4A5

[[[[[[[[

(0627 0276 0097)(0513 0391 0096)(0731 0215 0054)(0571 0334 0095)(0484 0422 0094)

C2(0470 0418 0112)(0454 0434 0112)(0585 0294 0121)(0404 0489 0107)(0347 0550 0103)

C3(0530 0353 0117)(0438 0453 0109)(0523 0361 0116)(0507 0378 0115)(0454 0436 0110)

C4(0403 0497 0100)(0333 0573 0094)(0443 0452 0105)(0371 0531 0098)(0303 0606 0091)]]]]]]]] (20)


Table 4 Aggregation index level

Evaluation criteria Logistics center Decision-makerDM1 DM2 DM3

C1

A1 G VG GA2 MG G FA3 VVG VG VGA4 MG G GA5 F MG MG

C2

A1 MG G MGA2 F MG GA3 VG VG VGA4 F G MGA5 MB G F

C3

A1 VG G VGA2 G MG MGA3 VG VG GA4 VG G GA5 G G MG

C4

A1 G G GA2 MG M MGA3 VG VG GA4 G MG MGA5 M MG M

Table 5 The importance of the evaluation criteria

Evaluation criteria DM1 DM2 DM3C1 VI VI IC2 I I IC3 I I MC4 M I M

Step 5 (calculate the intuitionistic fuzzy positive ideal solu-tion and negative ideal solution) We have four evaluationcriteria C1 traffic C2 economics C3 environment C4 withpolitics efficiency standards set for 1198691 = C1C3C4 and costtype standards set for 1198692 = C2 We get the positive idealsolution and negative ideal solution by formula (13)

119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)

Step 6 According to formulae (15)-(16) we calculate thevalues 119878lowast 119878minus and 119862119894lowast Step 7 The alternatives can be ranked as A3 gt A1 gt A2 gtA4 gt A5 based on the value 119862119894 as shown in Table 6 A3 is acompromise solution as logistics center location selection

Table 6 The values of 119878lowast 119878minus and 119862119894lowast 119878lowast 119878minus 119862119894lowastA1 0092 0110 0546A2 0131 0082 0385A3 0074 0175 0702A4 0124 0075 0375A5 0174 0074 0300

4 Conclusions

This research establishes the rural logistics center locationdecision model based on the theory of intuitionistic fuzzyTOPSIS We integrate the information according to expertsrsquoscore based on the evaluation index system Then we usethe entropy weight method to determine the weight of eachevaluation index and rank the results by using intuitionisticfuzzy TOPSIS method This model helps decision-makersquickly find out the suitable rural logistics center location Inaddition it is applied in an illustrative example to prove thevalidity and practicability of the method

Our study contributes in three ways (1) Intuitionisticfuzzy set can effectively reduce the fuzziness and make theresults more realistic and accurate than fuzzy set The resultis more objective and reliable based on the raw date (2)Intuitionistic fuzzy improved TOPSIS can effectively dealwith uncertainty evaluation information Without addinga subjective condition this paper retains more decision-making information and makes the result more scientific (3)


According to the actual requirements of the rural logisticscenter we have established a more scientific and reasonableindex system and applied it to an illustrative example

This paper studies the rural logistics center locationdecisions based on incomplete information the decisionmethod fully applies to logistics center location under thecomplete information and it can be extended to other uncer-tain environments Although the usefulness of the approachhas been proven theoretically it still needs further validationTherefore the focus of the future is to validate the method byusing the mixed evaluation value of the multiple data typessubjective and objective

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thework described in this paper is supported by the AppliedBasic Research Science Foundation of Yunnan ProvincialDepartment of Science and Technology in China underProject no 2015FD028 theNational Natural Science Founda-tion of China under Project no 71502159 and the Science andTechnology Innovation Team Fund of Logistics Engineeringin Colleges and Universities of Yunnan Province China

References

[1] Y L Zhou W Q Shao D M Bai and L U Su-Mei ldquoStudy onthe modes for the development of rural logistics in the processof new urbanizationrdquo Logistics Sci-Tech vol 4 no 15 pp 23ndash322016

[2] T Avila A Corberan I Plana and J M Sanchis ldquoA branch-and-cut algorithm for the profitable windy rural postmanproblemrdquo European Journal of Operational Research vol 249no 3 pp 1092ndash1101 2016

[3] C G Sutcliffe J H van Dijk M Muleka J Munsanje P EThuma and W J Moss ldquoDelays in initiation of antiretroviraltherapy among HIV-infected children in rural Zambiardquo Pedi-atric InfectiousDisease Journal vol 35 no 4 pp e107ndashe112 2016

[4] S S SUN T LIU and H WANG ldquoStudy on establishment ofrural logistics service system from perspective of rural brokersrdquoJournal of Anhui Agricultural Sciences vol 5 no 53 pp 23ndash322015

[5] A Amini ldquoA multi-criteria group decision making approachfor rural industrial site selection using fuzzy TOPSIS in centralIranrdquo Journal of Climate vol 28 no 19 pp 7437ndash7456 2015

[6] C Rao M Goh Y Zhao and J Zheng ldquoLocation selectionof city logistics centers under sustainabilityrdquo TransportationResearch Part D Transport and Environment vol 36 pp 29ndash442015

[7] Y Li X Liu and Y Chen ldquoSelection of logistics center locationusing axiomatic fuzzy set and TOPSIS methodology in logisticsmanagementrdquo Expert Systems with Applications vol 38 no 6pp 7901ndash7908 2011

[8] S Liu Z Song and S Zhong ldquoPublic transportation hub loca-tion with stochastic demand an improved approach based onmultiple attribute group decision-makingrdquo Discrete Dynamics

in Nature and Society vol 2015 Article ID 430109 15 pages2015

[9] Y He Z He and H Chen ldquoExtensions of atanassovrsquos intuition-istic fuzzy interaction bonferroni means and their applicationto multiple-attribute decision makingrdquo IEEE Transactions onFuzzy Systems vol 24 no 3 pp 558ndash573 2016

[10] X M Bai ldquoBased on entropy TOPSIS agricultural logisticscenter location modelrdquo Journal of Anhui Agricultural Sciencesvol 4 no 12 pp 34ndash45 2011

[11] E Celik M Erdogan and A T Gumus ldquoAn extended fuzzyTOPSISndashGRA method based on different separation measuresfor green logistics service provider selectionrdquo InternationalJournal of Environmental Science and Technology vol 13 no 5pp 1377ndash1392 2016

[12] G Luo Y Liu and X Mo ldquoFactor analysis model based onthe theory of the TOPSIS in the application researchrdquo DiscreteDynamics in Nature and Society vol 2017 Article ID 9173460 8pages 2017

[13] Y H HE L B WANG Z Z HE and M XIE ldquoA fuzzyTOPSIS and rough set based approach for mechanism analysisof product infant failurerdquo Engineering Applications of ArtificialIntelligence vol 47 no C pp 25ndash37 2016

[14] Y Wang and T T Chen ldquoRural logistics development speedprediction simulation researchrdquo Computer Simulation vol 4no 23 pp 44ndash52 2016

[15] Z Xu ldquoChoquet integrals of weighted intuitionistic fuzzyinformationrdquo Information Sciences An International Journalvol 180 no 5 pp 726ndash736 2010

[16] H S Le and N T Thong ldquoIntuitionistic fuzzy recommendersystems an effective tool for medical diagnosisrdquo Knowledge-Based Systems vol 74 no 1 pp 133ndash150 2015

[17] Li Jin-ming C Li and SOManagement ldquoPartner selection forSDN enterprises based on intuitionistic fuzzy TOPSISmethodrdquoLogistics Sci-Tech vol 3 no 23 pp 23ndash32 2015

[18] D M Bai W Q Shao Y L Zhou Y Chen and H G TaoldquoResearch on collaborative development of E-commerce andrural logistics in the rsquointernet plusrsquo Erardquo Logistics Sci-Tech vol5 no 34 pp 34ndash44 2016

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Stochastic AnalysisInternational Journal of


researchesmake conclusion unreasonable by using processeddata Compared with these methods intuitionistic fuzzinesscan effectively reduce the fuzziness andmake the resultsmorerealistic and accurate by using raw date [11ndash13] Intuitionisticfuzzy improved TOPSIS can effectively deal with uncertaintyevaluation information

In the rural logistics center location of the existingresearch most theoretical models and algorithms focus ona single project model where application value is not highand model accuracy and science degrees are not perfectAnd part of the studies also stay on a level that onlyconsiders a single objective and aims at cost or benefit [210 14] They considered other indicators as a constraint andthe establishment of the evaluation index system is not tocarry out the green circulation and sustainable developmentconcept

This paper studies rural logistics center location selectionbased on the theory of intuitionistic fuzzy TOPSIS Basedon the existing theories and empirical studies this paperestablishes the evaluation index system of logistics centerlocation standing in the rural demand angle that combineslogistics center location of the relevant theories and the char-acteristics of the rural logistics Based on the rural electricityunder the incomplete information logistics center locationselection problem this paper establishes the rural electricbusiness logistics center location decision model using thetheory of intuitionistic fuzzy sets and TOPSIS decision-making This model calculates the weight with intuitionisticfuzzy weight and uses TOPSIS decision-making method fora final decision This method is easy to operate and can helpdecision-makers quickly find out the suitable criteria for thedevelopment of the rural logistics center location Finallywe give an illustrative example that proves the validity andfeasibility of evaluation methods

2 The Proposed Method

21 Intuitionistic Fuzzy Set The intuitionistic fuzzy set isrelative to the expansion of the traditional fuzzy sets Intu-itionistic fuzzy sets take into account the membership degreeand information such as the degree of membership andhesitation [15] Therefore the intuitionistic fuzzy set is moreflexible than traditional fuzzy sets and practical in dealingwith vagueness and uncertainty Compared with fuzzy setsthe intuitionistic fuzzy collective shows the fuzziness anduncertainty in the real world and it can better deal withthe uncertain information in the decision-making process[7 9 15ndash17] This method has good performance in terms oftheory and application At present the intuitionistic fuzzyset applies to decision-making medical diagnosis logic pro-gramming pattern recognition machine learning marketprediction and so forth [16]

Definition 1 Set 119883 is a nonempty set then the theory ofdomain 119883 on intuitionistic fuzzy sets can be represented as119860

119860 = ⟨120594 120583119860 (120594) ]119860 (120594)⟩ | 120594 isin 119883 (1)

Among them 120583119860 is the membership degree for 119860 ]119860 isthe nonmembership degree for 119860 and 120583119860(120594) and ]119860(120594) arefor the 119883 element that belongs to 119860 membership and thenonmembership degree120583119860 119883 997888rarr [0 1] 120594 isin 119883 997888rarr 120583119860 (120594) isin [0 1]

]119860 119883 997888rarr [0 1] 120594 isin 119883 997888rarr ]119860 (120594) isin [0 1] (2)

They meet the condition0 le 120583119860 (120594) + ]119860 (120594) le 1 (3)

For the theory of domain intuitionistic fuzzy set 119860 of119883120587119860 = 1 minus 120583119860 (120594) minus ]119860 (120594) (4)

The element in 120594 belongs to 119860 degree of hesitation oruncertainty

Obviously for any 120594 isin 119883 we have 0 lt 120587119860(120594) lt 1In particular any fuzzy set 119860 in the theory of domain 119883

can be established in the following equation120587119860 (120594) = 1 minus 120583119860 (120594) minus ]119860 (120594) (5)

Sets 119860 and 119861 are two fuzzy sets in the theory field 119883multiplication is defined as119860 otimes 119861 = 120583119860 (120594) sdot 120583119861 (120594) ]119860 (120594) + ]119861 (120594) minus ]119860 (120594)

sdot ]119861 (120594) | 120594 isin 119883 (6)

22TheProposedAlgorithm Unlike traditional TOPSIS deci-sion the elements of the decision matrix are intuitionisticfuzzy numbers under the environment of intuitionistic fuzzyTOPSIS multiple attribute decision-making method Wecalculated each scheme and the distance between the idealsolution and the negative ideal solution with intuition fuzzynumber related calculation formulas First experts integrateassessment information according to the evaluation indexsystem Then entropy weight method is used to determinethe weight of each evaluation index Finally we determinethe decision scheme of sorting by intuitionistic fuzzy TOPSISmethod for logistics center

The specific decision-making steps are as follows

Step 1 (determine theweight of decision-makers) We assumethat the decision-making group has 119894 The data of decision-maker is represented by intuitionistic fuzzy numbers119863119896 = [120583119896 ]119896 120587119896] is the rating fuzzy number directly ofDM119896 The weight of DM119896 is as follows

120582119896 = (120583119896 + 120587119896 (120583119896 (120583119896 + ]119896)))sum119897119896=1 (120583119896 + 120587119896 (120583119896 (120583119896 + ]119896))) (7)

Under the conditionsum119897119896=1 120582119896 = 1Step 2 (construct intuitionistic fuzzy matrix) Intuitionisticfuzzy decision matrix is 119877(119896) = (119877(119896)119894119895 )119898times119899 The weight of each



119877(119896) = (119877(119896)119894119895 )119898times119899119877119894119895 = IFWA120582 (119903(1)119894119895 119903(2)119894119895 119903(119897)119894119895 ) = 1205821119903(1)119894119895 oplus 1205822119903(2)119894119895


(1 minus 120583(119896)119894119895 )120582119896 119897prod119896=1

(](119896)119894119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119894119895 )120582119896 minus 119897prod119896=1

(](119896)119894119895 )120582119896] (8)




(9)




119896=1

(1 minus 120583(119896)119895 )120582119896 119897prod119896=1

(](119896)119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119895 )120582119896 minus 119897prod119896=1

(](119896)119895 )120582119896]119882 = [119882111988221198823 119882119895]

(10)




(11)




(12)







Under the condition


(min119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860lowast119882 (120594119895) = ((min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894


119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860minus119882 (120594119895) = ((max119894

]119860119894sdot119882 (120594119895) | 119895 isin 1198691) (min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198692)) (14)



(15)



















120582DM1= 0909 + (075 + 005 (075095)) + (050 + 005 (050095))= 0406120582DM2= 050 + 005 (050095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0238



120582DM3= 075 + 005 (075095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0356(17)




119877 =C1

A1A2A3A4A5

[[[[[[[[

(0728 0170 0012)(0596 0302 0102)(0849 0100 0051)(0663 0236 0101)(0562 0337 0101)

C2(0626 0272 0102)(0605 0292 0103)(0780 0118 0102)(0538 0361 0101)(0462 0438 0100)

C3(0780 0118 0102)(0664 0256 0100)(0769 0170 0061)(0746 0151 0103)(0668 0231 0101)

C4(0700 0200 0100)(0578 0321 0101)(0769 0128 0103)(0644 0254 0102)(0526 0374 0100)]]]]]]]] (18)



1198821205941 1205942 1205943 1205944 = [[[[[(0861 0128 0011)(0750 0200 0050)(0680 0267 0053)(0576 0371 0053)

]]]]]119879

(19)


1198771015840 =C1

A1A2A3A4A5

[[[[[[[[

(0627 0276 0097)(0513 0391 0096)(0731 0215 0054)(0571 0334 0095)(0484 0422 0094)

C2(0470 0418 0112)(0454 0434 0112)(0585 0294 0121)(0404 0489 0107)(0347 0550 0103)

C3(0530 0353 0117)(0438 0453 0109)(0523 0361 0116)(0507 0378 0115)(0454 0436 0110)

C4(0403 0497 0100)(0333 0573 0094)(0443 0452 0105)(0371 0531 0098)(0303 0606 0091)]]]]]]]] (20)




C1


C2


C3


C4





119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)



4 Conclusions








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






119877(119896) = (119877(119896)119894119895 )119898times119899119877119894119895 = IFWA120582 (119903(1)119894119895 119903(2)119894119895 119903(119897)119894119895 ) = 1205821119903(1)119894119895 oplus 1205822119903(2)119894119895


(1 minus 120583(119896)119894119895 )120582119896 119897prod119896=1

(](119896)119894119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119894119895 )120582119896 minus 119897prod119896=1

(](119896)119894119895 )120582119896] (8)




(9)




119896=1

(1 minus 120583(119896)119895 )120582119896 119897prod119896=1

(](119896)119895 )120582119896 119897prod119896=1

(1 minus 120583(119896)119895 )120582119896 minus 119897prod119896=1

(](119896)119895 )120582119896]119882 = [119882111988221198823 119882119895]

(10)




(11)




(12)







Under the condition


(min119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860lowast119882 (120594119895) = ((min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894


119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860minus119882 (120594119895) = ((max119894

]119860119894sdot119882 (120594119895) | 119895 isin 1198691) (min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198692)) (14)



(15)



















120582DM1= 0909 + (075 + 005 (075095)) + (050 + 005 (050095))= 0406120582DM2= 050 + 005 (050095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0238



120582DM3= 075 + 005 (075095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0356(17)




119877 =C1

A1A2A3A4A5

[[[[[[[[

(0728 0170 0012)(0596 0302 0102)(0849 0100 0051)(0663 0236 0101)(0562 0337 0101)

C2(0626 0272 0102)(0605 0292 0103)(0780 0118 0102)(0538 0361 0101)(0462 0438 0100)

C3(0780 0118 0102)(0664 0256 0100)(0769 0170 0061)(0746 0151 0103)(0668 0231 0101)

C4(0700 0200 0100)(0578 0321 0101)(0769 0128 0103)(0644 0254 0102)(0526 0374 0100)]]]]]]]] (18)



1198821205941 1205942 1205943 1205944 = [[[[[(0861 0128 0011)(0750 0200 0050)(0680 0267 0053)(0576 0371 0053)

]]]]]119879

(19)


1198771015840 =C1

A1A2A3A4A5

[[[[[[[[

(0627 0276 0097)(0513 0391 0096)(0731 0215 0054)(0571 0334 0095)(0484 0422 0094)

C2(0470 0418 0112)(0454 0434 0112)(0585 0294 0121)(0404 0489 0107)(0347 0550 0103)

C3(0530 0353 0117)(0438 0453 0109)(0523 0361 0116)(0507 0378 0115)(0454 0436 0110)

C4(0403 0497 0100)(0333 0573 0094)(0443 0452 0105)(0371 0531 0098)(0303 0606 0091)]]]]]]]] (20)




C1


C2


C3


C4





119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)



4 Conclusions








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of








Under the condition


(min119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860lowast119882 (120594119895) = ((min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894


119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198691)

(max119894120583119860119894 sdot119882 (120594119895) | 119895 isin 1198692))

]119860minus119882 (120594119895) = ((max119894

]119860119894sdot119882 (120594119895) | 119895 isin 1198691) (min119894

]119860119894 sdot119882 (120594119895) | 119895 isin 1198692)) (14)



(15)



















120582DM1= 0909 + (075 + 005 (075095)) + (050 + 005 (050095))= 0406120582DM2= 050 + 005 (050095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0238



120582DM3= 075 + 005 (075095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0356(17)




119877 =C1

A1A2A3A4A5

[[[[[[[[

(0728 0170 0012)(0596 0302 0102)(0849 0100 0051)(0663 0236 0101)(0562 0337 0101)

C2(0626 0272 0102)(0605 0292 0103)(0780 0118 0102)(0538 0361 0101)(0462 0438 0100)

C3(0780 0118 0102)(0664 0256 0100)(0769 0170 0061)(0746 0151 0103)(0668 0231 0101)

C4(0700 0200 0100)(0578 0321 0101)(0769 0128 0103)(0644 0254 0102)(0526 0374 0100)]]]]]]]] (18)



1198821205941 1205942 1205943 1205944 = [[[[[(0861 0128 0011)(0750 0200 0050)(0680 0267 0053)(0576 0371 0053)

]]]]]119879

(19)


1198771015840 =C1

A1A2A3A4A5

[[[[[[[[

(0627 0276 0097)(0513 0391 0096)(0731 0215 0054)(0571 0334 0095)(0484 0422 0094)

C2(0470 0418 0112)(0454 0434 0112)(0585 0294 0121)(0404 0489 0107)(0347 0550 0103)

C3(0530 0353 0117)(0438 0453 0109)(0523 0361 0116)(0507 0378 0115)(0454 0436 0110)

C4(0403 0497 0100)(0333 0573 0094)(0443 0452 0105)(0371 0531 0098)(0303 0606 0091)]]]]]]]] (20)




C1


C2


C3


C4





119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)



4 Conclusions








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of










120582DM1= 0909 + (075 + 005 (075095)) + (050 + 005 (050095))= 0406120582DM2= 050 + 005 (050095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0238



120582DM3= 075 + 005 (075095)09 + (050 + 005 (050095)) + (075 + 005 (075095))= 0356(17)




119877 =C1

A1A2A3A4A5

[[[[[[[[

(0728 0170 0012)(0596 0302 0102)(0849 0100 0051)(0663 0236 0101)(0562 0337 0101)

C2(0626 0272 0102)(0605 0292 0103)(0780 0118 0102)(0538 0361 0101)(0462 0438 0100)

C3(0780 0118 0102)(0664 0256 0100)(0769 0170 0061)(0746 0151 0103)(0668 0231 0101)

C4(0700 0200 0100)(0578 0321 0101)(0769 0128 0103)(0644 0254 0102)(0526 0374 0100)]]]]]]]] (18)



1198821205941 1205942 1205943 1205944 = [[[[[(0861 0128 0011)(0750 0200 0050)(0680 0267 0053)(0576 0371 0053)

]]]]]119879

(19)


1198771015840 =C1

A1A2A3A4A5

[[[[[[[[

(0627 0276 0097)(0513 0391 0096)(0731 0215 0054)(0571 0334 0095)(0484 0422 0094)

C2(0470 0418 0112)(0454 0434 0112)(0585 0294 0121)(0404 0489 0107)(0347 0550 0103)

C3(0530 0353 0117)(0438 0453 0109)(0523 0361 0116)(0507 0378 0115)(0454 0436 0110)

C4(0403 0497 0100)(0333 0573 0094)(0443 0452 0105)(0371 0531 0098)(0303 0606 0091)]]]]]]]] (20)




C1


C2


C3


C4





119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)



4 Conclusions








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







C1


C2


C3


C4





119860lowast = (0731 0251 0054) (0585 0294 0121) (0530 0353 0117) (0303 0606 0091)119860minus = (0484 0422 0094) (0347 0550 0103) (0438 0453 0109) (0443 0452 0105) (21)



4 Conclusions








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of









Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




a study of rural logistics center location based on...

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