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An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment

Authors:

Witold PedryczAuthors Info & Claims

Knowledge-Based Systems, Volume 86, Issue C

Pages 116 - 130

https://doi.org/10.1016/j.knosys.2015.05.025

Published: 01 September 2015 Publication History

Abstract

Interval type-2 fuzzy set (IT2FS) offers interesting avenue to handle high order information and uncertainty in decision support system (DSS) when dealing with both extrinsic and intrinsic aspects of uncertainty. Recently, multiple attribute decision making (MADM) problems with interval type-2 fuzzy information have received increasing attentions both from researchers and practitioners. As a result, a number of interval type-2 fuzzy MADM methods have been developed. In this paper, we extend the VIKOR (VlseKriterijumska Optimizacijia I Kompromisno Resenje, in Serbian) method based on the prospect theory to accommodate interval type-2 fuzzy circumstances. First, we propose a new distance measure for IT2FS, which is comes as a sound alternative when being compared with the existing interval type-2 fuzzy distance measures. Then, a decision model integrating VIKOR method and prospect theory is proposed. A case study concerning a high-tech risk evaluation is provided to illustrate the applicability of the proposed method. In addition, a comparative analysis with interval type-2 fuzzy TOPSIS method is also presented.

References

[1]

L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inf. Sci., 8 (1975) 199-249.

[2]

J.M. Mendel, R.B. John, Type-2 fuzzy sets made simple, IEEE Trans. Fuzzy Syst., 10 (2002) 117-127.

Digital Library

[3]

J.M. Mendel, R.I. John, F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE Trans. Fuzzy Syst., 14 (2006) 808-821.

Digital Library

[4]

D. Wu, J.M. Mendel, Uncertainty measures for interval type-2 fuzzy sets, Inf. Sci., 177 (2007) 5378-5393.

Digital Library

[5]

N.N. Karnik, J.M. Mendel, Centroid of a type-2 fuzzy set, Inf. Sci., 132 (2001) 195-220.

Digital Library

[6]

D. Wu, J.M. Mendel, A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets, Inf. Sci., 179 (2009) 1169-1192.

Digital Library

[7]

S. Greenfield, F. Chiclana, S. Coupland, R. John, The collapsing method of defuzzification for discretised interval type-2 fuzzy sets, Inf. Sci., 179 (2009) 2055-2069.

Digital Library

[8]

O. Castillo, P. Melin, A review on the design and optimization of interval type-2 fuzzy controllers, Appl. Soft Comput., 12 (2012) 1267-1278.

Digital Library

[9]

G. Deschrijver, Arithmetic operators in interval-valued fuzzy set theory, Inf. Sci., 177 (2007) 2906-2924.

Digital Library

[10]

H. Bustince, E. Barrenechea, M. Pagola, J. Fernández, Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst., 160 (2009) 1819-1840.

Digital Library

[11]

D. Wu, J.M. Mendel, Computing with words for hierarchical decision making applied to evaluating a weapon system, IEEE Trans. Fuzzy Syst., 18 (2010) 441-460.

Digital Library

[12]

J. Hu, Y. Zhang, X. Chen, Y. Liu, Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number, Knowl.-Based Syst., 43 (2013) 21-29.

Digital Library

[13]

T.-Y. Chen, C.-H. Chang, J.-f. Rachel Lu, The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making, Eur. J. Operat. Res., 226 (2013) 615-625.

[14]

S.-M. Chen, L.-W. Lee, Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets, Expert Syst. Appl., 37 (2010) 824-833.

Digital Library

[15]

W. Wang, X. Liu, Y. Qin, Multi-attribute group decision making models under interval type-2 fuzzy environment, Knowl.-Based Syst., 30 (2012) 121-128.

Digital Library

[16]

E. Celik, O.N. Bilisik, M. Erdogan, A.T. Gumus, H. Baracli, An integrated novel interval type-2 fuzzy MCDM method to improve customer satisfaction in public transportation for Istanbul, Transp. Res. Part E: Log. Transp. Rev., 58 (2013) 28-51.

[17]

J. Qin, X. Liu, Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment, Inf. Sci., 297 (2015) 293-315.

Digital Library

[18]

S.-M. Chen, L.-W. Lee, Fuzzy multiple criteria hierarchical group decision-making based on interval type-2 fuzzy sets, IEEE Trans. Syst. Man Cybernet. A, 40 (2010) 1120-1128.

Digital Library

[19]

C. Kahraman, B. Öztayşi, İ. Uçal Sarı, E. Turanoğlu, Fuzzy analytic hierarchy process with interval type-2 fuzzy sets, Knowl.-Based Syst., 59 (2014) 48-57.

Digital Library

[20]

L. Abdullah, L. Najib, A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process, Expert Syst. Appl., 41 (2014) 3297-3305.

Digital Library

[21]

S.-M. Chen, L.-W. Lee, Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method, Expert Syst. Appl., 37 (2010) 2790-2798.

Digital Library

[22]

T.-Y. Chen, A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets, Soft Comput., 18 (2014) 923-940.

Digital Library

[23]

T.-Y. Chen, An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets, Inf. Sci., 263 (2014) 1-21.

Digital Library

[24]

T.-Y. Chen, A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets, Appl. Soft Comput., 13 (2013) 2735-2748.

Digital Library

[25]

S.-M. Chen, L.-W. Lee, Fuzzy decision-making based on likelihood-based comparison relations, IEEE Trans. Fuzzy Syst., 18 (2010) 613-628.

Digital Library

[26]

J. Montero, D. Gómez, H. Bustince, On the relevance of some families of fuzzy sets, Fuzzy Sets Syst., 158 (2007) 2429-2442.

Digital Library

[27]

D. Bernardo, H. Hagras, E. Tsang, A genetic type-2 fuzzy logic based system for the generation of summarised linguistic predictive models for financial applications, Soft Comput., 17 (2013) 2185-2201.

Digital Library

[28]

Y. Gong, Fuzzy multi-attribute group decision making method based on interval type-2 fuzzy sets and applications to global supplier selection, Int. J. Fuzzy Syst., 15 (2013) 392-400.

[29]

T.-Y. Chen, An interactive method for multiple criteria group decision analysis based on interval type-2 fuzzy sets and its application to medical decision making, Fuzzy Optim. Dec. Mak., 12 (2013) 323-356.

[30]

J.-C. Wang, T.-Y. Chen, A closeness coefficient-based multiple criteria decision-making method using interval type-2 fuzzy sets and its application to watershed site selection, J. Indus. Prod. Eng., 31 (2014) 1-16.

[31]

S. Opricovic, Multicriteria optimization of civil engineering systems, Faculty Civil Eng. Belgrade, 2 (1998) 5-21.

[32]

S. Opricovic, G.H. Tzeng, Multicriteria planning of post - earthquake sustainable reconstruction, Comput. Aided Civil Infrastruct. Eng., 17 (2002) 211-220.

[33]

S. Opricovic, G.-H. Tzeng, Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS, Eur. J. Oper. Res., 156 (2004) 445-455.

[34]

S. Opricovic, G.-H. Tzeng, Extended VIKOR method in comparison with outranking methods, Eur. J. Oper. Res., 178 (2007) 514-529.

[35]

A. Sanayei, S. Farid Mousavi, A. Yazdankhah, Group decision making process for supplier selection with VIKOR under fuzzy environment, Expert Syst. Appl., 37 (2010) 24-30.

Digital Library

[36]

J.H. Park, H.J. Cho, Y.C. Kwun, Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information, Fuzzy Optim. Decis. Making, 10 (2011) 233-253.

Digital Library

[37]

H. Liao, Z. Xu, A VIKOR-based method for hesitant fuzzy multi-criteria decision making, Fuzzy Optim. Decis. Making, 12 (2013) 373-392.

Digital Library

[38]

T. Kaya, C. Kahraman, Fuzzy multiple criteria forestry decision making based on an integrated VIKOR and AHP approach, Expert Syst. Appl., 38 (2011) 7326-7333.

Digital Library

[39]

T. Kaya, C. Kahraman, Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: the case of Istanbul, Energy, 35 (2010) 2517-2527.

[40]

Y.-P. Ou Yang, H.-M. Shieh, G.-H. Tzeng, A VIKOR technique based on DEMATEL and ANP for information security risk control assessment, Inf. Sci., 232 (2013) 482-500.

Digital Library

[41]

N. Zhang, G. Wei, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Appl. Math. Modell., 37 (2013) 4938-4947.

[42]

H.-C. Liu, L.-X. Mao, Z.-Y. Zhang, P. Li, Induced aggregation operators in the VIKOR method and its application in material selection, Appl. Math. Modell., 37 (2013) 6325-6338.

[43]

S.-P. Wan, Q.-Y. Wang, J.-Y. Dong, The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers, Knowl.-Based Syst., 52 (2013) 65-77.

Digital Library

[44]

Y. Ju, A. Wang, Extension of VIKOR method for multi-criteria group decision making problem with linguistic information, Appl. Math. Modell., 37 (2013) 3112-3125.

[45]

D. Kahneman, A. Tversky, Prospect theory: an analysis of decision under risk, Econometrica, 47 (1979) 363-391.

[46]

A. Tversky, D. Kahneman, Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncert., 5 (1992) 297-323.

[47]

P. Wakker, A. Tversky, An axiomatization of cumulative prospect theory, J. Risk Uncert., 7 (1993) 147-175.

[48]

M. Abdellaoui, H. Bleichrodt, C. Paraschiv, Loss aversion under prospect theory: a parameter-free measurement, Manage. Sci., 53 (2007) 1659-1674.

Digital Library

[49]

U. Schmidt, H. Zank, Risk aversion in cumulative prospect theory, Manage. Sci., 54 (2008) 208-216.

Digital Library

[50]

H. Bleichrodt, U. Schmidt, H. Zank, Additive utility in prospect theory, Manage. Sci., 55 (2009) 863-873.

Digital Library

[51]

Y. Liu, Z.-P. Fan, Y. Zhang, Risk decision analysis in emergency response: a method based on cumulative prospect theory, Comput. Oper. Res., 42 (2014) 75-82.

Digital Library

[52]

P. Liu, F. Jin, X. Zhang, Y. Su, M. Wang, Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables, Knowl.-Based Syst., 24 (2011) 554-561.

Digital Library

[53]

X. Yuan, H. Li, J. Song, Interval-valued level cut sets, decomposition theorems and resentation theorems on interval-valued fuzzy sets, Fuzzy Syst. Math., 37 (2013) 3112-3125.

[54]

F. Chiclana, E. Herrera-Viedma, F. Herrera, S. Alonso, Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations, Eur. J. Oper. Res., 182 (2007) 383-399.

[55]

S. Massanet, J.V. Riera, J. Torrens, E. Herrera-Viedma, A new linguistic computational model based on discrete fuzzy numbers for computing with words, Inf. Sci., 258 (2014) 277-290.

Digital Library

[56]

F.J. Cabrerizo, E. Herrera-Viedma, W. Pedrycz, A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts, Eur. J. Oper. Res., 230 (2013) 624-633.

[57]

S. Greenfield, F. Chiclana, Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set, Int. J. Approx. Reason., 54 (2013) 1013-1033.

[58]

F. Chiclana, S.M. Zhou, Type-reduction of general type-2 fuzzy sets: the type-1 OWA approach, Int. J. Intell. Syst., 28 (2013) 505-522.

[59]

H.A. Hagras, A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots, IEEE Trans. Fuzzy Syst., 12 (2004) 524-539.

Digital Library

[60]

S. Coupland, R. John, Geometric type-1 and type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst., 15 (2007) 3-15.

[61]

.61 H. Bustince, J. Fernández, A. Kolesárová, R. Mesiar, Generation of linear orders for intervals by means of aggregation functions, Fuzzy Sets Syst., 220 (2013) 69-77.

Digital Library

[62]

Y. Gong, N. Hu, J. Zhang, G. Liu, J. Deng, Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers, Comput. Indus. Eng., 81 (2015) 167-176.

Digital Library

[63]

F.J. Cabrerizo, R. Urena, W. Pedrycz, E. Herrera-Viedma, Building consensus in group decision making with an allocation of information granularity, Fuzzy Sets Syst., 255 (2014) 115-127.

[64]

F.J. Cabrerizo, E. Herrera-Viedma, W. Pedrycz, A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts, Eur. J. Oper. Res., 230 (2013) 624-633.

[65]

W. Pedrycz, Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing, Eur. J. Oper. Res., 232 (2014) 137-145.

[66]

T.-H. Chang, Fuzzy VIKOR method: a case study of the hospital service evaluation in Taiwan, Inf. Sci., 271 (2014) 196-212.

[67]

H. Liao, Z. Xu, X.-J. Zeng, Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making, (2014) (in press), http://dx.doi.org/10.1109/TFUZZ.2014.2360556.

[68]

K.-Y. Shen, M.-R. Yan, G.-H. Tzeng, Combining VIKOR-DANP model for glamor stock selection and stock performance improvement, Knowl.-Based Syst., 58 (2014) 86-97.

Digital Library

[69]

P. Liu, X. Zhang, W. Liu, A risk evaluation method for the high-tech project investment based on uncertain linguistic variables, Technol. Forecast. Soc. Chang., 78 (2011) 40-50.

[70]

M. Pratama, S. Anavatti, J. Lu, Recurrent classifier based on an incremental meta-cognitive-based scaffolding algorithm, in: IEEE Trans. Fuzzy Syst. (2015) (in press), http://dx.doi.org/10.1109/TFUZZ.2015.2402683.

[71]

J. Lu, G. Zhang, F. Wu, Web-based Multi-Criteria Group Decision Support System with Linguistic Term Processing Function, IEEE Intell. Inf. Bull., 5 (2005) 34-43.

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cover image Knowledge-Based Systems

Knowledge-Based Systems Volume 86, Issue C

September 2015

299 pages

ISSN:0950-7051

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Copyright © Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 September 2015

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https://dl.acm.org/doi/10.1109/TFUZZ.2024.3451159
Dai XLi HZhou L(2024)A new approach to MADM problems with belief distributions based on weighted similarity measure and regret theoryExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.122831243:COnline publication date: 25-Jun-2024
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