Modelling Uncertainties in Multi-Criteria Decision Making using Distance Measure and TOPSIS for Hesitant Fuzzy Sets

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A notion for distance between hesitant fuzzy data is given. Using this new distance notion, we propose the technique for order preference by similarity to ideal solution for hesitant fuzzy sets and a new approach in modelling uncertainties. An illustrative example is constructed to show the feasibility and practicality of the new method.

[1] B. Ashtiani, F. Haghighirad, A. Makui and G. Montazer, Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets, Applied Soft Computing, 9(2), 2009, 457–461

[2] I. Beg and T. Rashid, Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS, OPSEARCH, 51(1), 2014, 98-129

[3] I. Beg and T. Rashid, TOPSIS for hesitant fuzzy linguistic term sets, International Journal of Intelligent Systems, 28, 2013, 1162–1171

[4] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management Science, 17(4), 1970, 141-164

[5] F. E. Boran, S. Gen, M. Kurt and D. Akay, A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications, 36, 2009, 11363–11368

[6] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems, 114, 2000) 1–9

[7] S. J. Chen and C. L. Hwang, Fuzzy multiple attribute decision making, Berlin: Springer, 1992)

[8] T.-C. Chu and Y.-C. Lin, An interval arithmetic based fuzzy TOPSIS model, Expert Systems with Applications, 36, 2009, 10870–10876

[9] D. Dubois, The role of fuzzy sets in decision sciences: Old techniques and new directions, Fuzzy Sets and Systems, 184, 2011, 3–28

[10] F. Herrera, E. Herrera-Viedma and L. Martinez, A fusion approach for managing multi-granularity linguistic term sets in decision making, Fuzzy Sets and Systems, 114, 2000, 43–58

[11] C. L. Hwang and K. Yoon, Multiple attributes decision making methods and applications, Berlin, Heidelberg: Springer, 1981)

[12] G. R. Jahanshahloo, H. F. Lotfi and M. Izadikhah, Extension of the TOPSIS method for decision-making problems with fuzzy data, Applied Mathematics and Computation, 181(2), 2006, 1544–1551

[13] J. Jiang, Y.-W. Chen, Y.-W. Chen, K.-W. Yang, TOPSIS with fuzzy belief structure for group belief multiple criteria decision making, Expert Systems with Applications, 38, 2011, 9400–9406

[14] T. Kaya and C. Kahraman, Multicriteria decision making in energy planning using a modified fuzzy TOPSIS methodology, Expert Systems with Applications, 38(6), 2011, 6577–6585

[15] G. Kim, C. Park and K. Yoon, Identifying investment opportunities for advanced manufacturing systems with comparative-integrated, International Journal of Production Economics, 50, 1997, 23-33

[16] M. S. Kuo, G. H. Tzeng and W. C. Huang, Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment, Mathematical and Computer Modelling, 45, 2007, 324–339

[17] I. Mahdavi, N. Mahdavi-Amiri, A. Heidarzade and R. Nourifar, Designing a model of fuzzy TOPSIS in multiple criteria decision making, Applied Mathematics and Computation, 206, 2008, 607–617

[18] D. S. Negi, Fuzzy analysis and optimization, PhD thesis. Department of Industrial Engineering, Kansas State University, 1989)

[19] J. Peng, J. Wang, J. Wang, L. Yang and X. Chen, An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Information Sciences, 307, 2015, 113–126

[20] T. Rashid, I. Beg and S. M. Husnine, Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS, Applied Soft Computing. Applied Soft Computing, 21, 2014, 462–468

[21] R. M. Rodriguez, L. Martinez and F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Transaction on fuzzy Systems 20(1), 2012, 109–118

[22] H. Shih, H. Shyur and E. Lee, An extension of TOPSIS for group decision making, Mathematical and Computer Modelling, 45, 2007, 801–813

[23] V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), 2010, 529–539

[24] T. C. Wang and T. H. Chang, Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment, Expert Systems with Applications, 33, 2007, 870–880

[25] J. H. Wang and J. Y. Hao, A new version of 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, 14(3), 2006, 435–445

[26] Y. J. Wang and H. S. Lee, Generalizing TOPSIS for fuzzy multiple-criteria group decision-making, Computers and Mathematics with Applications, 53, 2007, 1762–1772

[27] G. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems 31, 2012, 176-182

[28] M. Xia and Z. Xu, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning, 52, 2011, 395–407

[29] Z. Xu and M. Xia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems, 26, 2011, 410–425

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