An approach to Atanassov’s interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory | International Journal of Computational Intelligence Systems
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An approach to Atanassov’s interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory

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  • Published: 01 June 2015
  • Volume 8, pages 591–605, (2015)
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An approach to Atanassov’s interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory
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  • Fanyong Meng1,2,
  • Chunqiao Tan1 &
  • Xiaohong Chen1 

  • 45 Accesses

  • 23 Citations

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Abstract

Prospect theory is a very effective method to express behavioral decision making under uncertainty. This paper attempts to develop a method to multi-attribute decision making with Atanassov’s interval-valued intuitionistic fuzzy information using prospect theory. This method first transforms Atanassov’s interval-valued intuitionistic fuzzy variables into the prospect values using the value function in prospect theory. Based on the aspiration levels, Atanassov’s intuitionistic fuzzy prospect gain and loss matrices are obtained. Then, using the Atanassov’s interval-valued intuitionistic hybrid weight averaging (IVIHWA) operator or the Atanassov’s interval-valued intuitionistic hybrid Shapley weight averaging (IVIHSWA) operator, the comprehensive Atanassov’s interval-valued intuitionistic fuzzy prospect value of each alternative is calculated. According to the comprehensive Atanassov’s interval-valued intuitionistic fuzzy prospect values, a ranking method of alternatives is presented. Finally, two illustrative examples are selected to show the feasibility and availability of the proposed method.

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References

  1. I. Chamodrakas, I. Leftheriotis and D. Martakos, In-depth analysis and simulation study of an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS, Appl. Soft Comput. 11(1) (2011) 900–907.

    Google Scholar 

  2. Y. W. Chen and M. Larbani, Two-person zero-sum game approach for fuzzy multiple attribute decision making problems, Fuzzy Set. Syst. 157(1) (2006) 34–51.

    Google Scholar 

  3. Z. P. Fan, G. F. Hu and S. H. Xiao, A method for multiple attribute decision-making with the fuzzy preference relation on alternatives, Comput. Ind. Eng. 46(2) (2004) 321–327.

    Google Scholar 

  4. Z. P. Fan and B. Feng, A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment, Inform. Sci. 179(20) (2009) 3603–3618.

    Google Scholar 

  5. X. B. Gu and Q. X. Zhu, Fuzzy multi-attribute decision-making method based on eigenvector of fuzzy attribute evaluation space, Decision Supp. Syst. 41(2) (2006) 400–410.

    Google Scholar 

  6. C. Kahraman and S. Çebí, A new multi-attribute decision making method: Hierarchical fuzzy axiomatic design, Expert Syst. Appl. 36(3) (2009) 4848–4861.

    Google Scholar 

  7. Z. Pei, Simplification of fuzzy multiple attribute decision making in production line evaluation, Knowl-Based Syst. 47 (2013) 23–34.

    Google Scholar 

  8. K. T. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst. 31(2) (1989) 343–349.

    Google Scholar 

  9. K. T. Atanassov, Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst. 64 (1994) 159–174.

    Google Scholar 

  10. F.Y. Meng, C. Q. Tan and Q. Zhang, The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making, Knowl-Based Syst. 42 (2013) 9–19.

    Google Scholar 

  11. C. Q. Tan, A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS, Expert Syst. Appl. 38(4) (2011) 3023–3033.

    Google Scholar 

  12. G. W. Wei and X. R. Wang, Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making, in : The CIS, Harbin, China, 2007, pp.495–499.

  13. Z. S. Xu and J. Chen, Approach to group decision making based on interval-valued intuitionistic judgment matrices, Syst. Eng. - Theory and Practice 27(1) (2007) 126–133.

    Google Scholar 

  14. Z. S. Xu, Choquet integrals of weighted intuitionistic fuzzy information. Inform. Sci. 180(5) (2010) 726– 736.

  15. D. J. Yu, Y. Y. Wu and T. Lu, Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making, Knowl-Based Syst. 30 (2012) 57–66.

  16. G. Beliakov, H. Bustince, D. P. Goswami, U. K. Mukherjee and N. R. Pal, On averaging operators for intuitionistic fuzzy sets, Inform. Sci. 181(6) (2011) 1116–1124.

    Google Scholar 

  17. Z. S. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control De. 22(2) (2007) 215– 219.

  18. Z. S. Xu and J. Chen, On geometric aggregation over interval-valued intuitionistic fuzzy information, in: The 4 FSKD 07, Haikou, China, 2007, pp. 466–471.

  19. T. Y. Chen, H. P. Wang and Y. Y Lu, A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective, Expert Syst. Appl. 38(6) (2011) 7647–7658.

    Google Scholar 

  20. S. M. Chen, M. W. Yang, S. W. Yang, T. W. Sheu and C. J. Liau, Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets, Expert Syst. Appl. 39(15) (2012) 12085–12091.

    Google Scholar 

  21. Z. J. Wang and K. W. Li, An interval-valued intuitionistic fuzzy multi-attribute group decision making framework with incomplete preference over alternatives, Expert Syst. Appl. 39(18) (2012) 13509– 13516.

  22. Z. L. Yue and Y Y. Jia, An application of soft computing technique in group decision making under interval-valued intuitionistic fuzzy environment, Appl. Soft Comput. 13(5) (2013) 2490–2503.

    Google Scholar 

  23. Y J. Zhang, P. J. Ma, X. H. Su and C. P. Zhang, Multi-attribute group decision making under interval-valued intuitionistic fuzzy environment, Acta Autom. Sin. 38(2) (2012) 220–227.

    Google Scholar 

  24. J. Y Chai, J. N. K. Liu and Z. S. Xu, A rule-based group decision model for warehouse evaluation under interval-valued intuitionistic fuzzy environments, Expert Syst. Appl. 40(6) (2013) 1959–1970.

    Google Scholar 

  25. S. M. Chen and T. S. Li, Evaluating students’ answerscripts based on interval-valued intuitionistic fuzzy sets, Inform. Sci. 235 (2013) 308–322.

    Google Scholar 

  26. G. İntepe, E. Bozdag, T. Koc, The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach, Comput. Ind. Eng. 65(2) (2013) 277–285.

    Google Scholar 

  27. K. Xu, J. Z. Zhou, R. Gu and H. Qin, Approach for aggregating interval-valued intuitionistic fuzzy information and its application to reservoir operation, Expert Syst. Appl. 38(7) (2011) 9032–9035.

    Google Scholar 

  28. Z. H. Zhang, J. Y Yang, Y P. Ye, Y Hu and Q. S. Zhang, A type of score function on intuitionistic fuzzy sets with double parameters and its application to pattern recognition and medical diagnosis, Procedia Eng. 29 (2012) 4336–4342.

    Google Scholar 

  29. D. Kahneman, A. Tversky Prospect theory: an analysis of decision under risk, Econometrica 47(2) (1979) 263–292.

    Google Scholar 

  30. R. A. Krohling and T. T. M. de Souza, Combining prospect theory and fuzzy numbers to multi-criteria decision making, Expert Syst. Appl. 39 (2012) 11487–11493.

    Google Scholar 

  31. S. Dhami and A. Al-Nowaihi, Why do people pay taxes? Prospect theory versus expected utility theory, J. Econ. Behav Organization 64(1) (2007) 171–192.

    Google Scholar 

  32. Z. P. Fan, X. Zhang, F. D. Chen and Y Liu, Multiple attribute decision making considering aspiration-levels: A method based on prospect theory, Comput. Ind. Eng. 65(2) (2013) 341–350.

    Google Scholar 

  33. G Gurevich, D. Kliger and O. Levy, Decision-making under uncertainty - A field study of cumulative prospect theory, J. Bank. Fin. 33(7) (2009) 1221–1229.

    Google Scholar 

  34. L. F. A. M. Gomes and M. M. P. P. Lima, TODIM: Basics and application to multicriteria ranking of projects with environmental impacts, Foundations Comput. Dec. Sci. 16(4) (1992) 113–127.

    Google Scholar 

  35. V. Lotfi and T. J. Stewart, An aspiration-level interactive model for multiple criteria decision making, Comput. Ind. Eng. 19(7) (1992) 671–687.

    Google Scholar 

  36. K. T. Atanassov, intuitionistic fuzzy sets, Fuzzy Set. Syst. 20(1) (1986) 87–96.

    Google Scholar 

  37. S. K. De, R. Biswas and A. R. Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Set. Syst. 114(3) (2000) 477–484.

    Google Scholar 

  38. M. Abdellaoui, Parameter-free elicitation of utility and probability weighting functions, Manage. Sci. 46(11) (2000) 1497–1512

  39. H. T. Banks and M. Q. Jacobs, A differential calculus for multifunctions, J. Math. Anal. Appl. 29(2) (1970) 46–272.

    Google Scholar 

  40. L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Set. Syst. 161(11) (2010) 1564–1584.

    Google Scholar 

  41. Z. S. Xu and X. Q. Cai, Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information, Int. J. Intell. Sys. 25(6) (2010) 489–513.

    Google Scholar 

  42. F. Y. Meng, C. Q. Tan and Q. Zhang, The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making, Knowl-Based Syst. 42 (2013) 9–19.

    Google Scholar 

  43. X. M. Zhang, Z. S. Xu and X. H. Yu, Shapley value and Choquet integral-based operators for aggregating correlated intuitionistic fuzzy information, Information-TOYOKO 14(5) (2011) 1847–1858.

    Google Scholar 

  44. L. S. Shapley, A value for n-person game, Princeton University Press, Princeton, 1953.

  45. M. Sugeno, Theory of fuzzy integral and its application, Doctorial Dissertation, Tokyo Institute of Technology, 1974.

  46. C. Q. Tan and X. H. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making, Expert Syst. Appl. 37(1) (2010) 149–157.

    Google Scholar 

  47. J. Ye, Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Syst. Appl. 36(3) (2009) 6899–6902.

    Google Scholar 

  48. F. Y. Meng and J. Tang, Interval-valued intuitionistic fuzzy multi-criteria group decision making based on cross entropy and Choquet integral, Int. J. Intell. Syst. 28(12) (2013) 1172–1195.

    Google Scholar 

  49. H. Bustince, M. Galar, B. Bedregal, A. Kolesárová and R. Mesiar, A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy sets applications, IEEE Tran. Fuzzy Syst. 21(6) (2013) 1150–1162.

    Google Scholar 

  50. H. Bustince, J. Fernández, A. Kolesárová and R Mesiar, Generation of linear orders for intervals by means of aggregation functions, Fuzzy Sets Syst. 220(1) (2013) 69–77.

    Google Scholar 

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Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Fanyong Meng, Chunqiao Tan & Xiaohong Chen

  2. School of Management, Qingdao Technological University, Qingdao, 266520, China

    Fanyong Meng

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  1. Fanyong Meng
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Correspondence to Fanyong Meng.

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Meng, F., Tan, C. & Chen, X. An approach to Atanassov’s interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory. Int J Comput Intell Syst 8, 591–605 (2015). https://doi.org/10.1080/18756891.2015.1036224

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  • Received: 03 June 2014

  • Accepted: 10 March 2015

  • Published: 01 June 2015

  • Issue Date: January 2015

  • DOI: https://doi.org/10.1080/18756891.2015.1036224

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Keywords

  • multi-attribute decision making
  • prospect theory
  • Atanassov’s interval-valued intuitionistic fuzzy set
  • Atanassov’s interval-valued intuitionistic fuzzy prospect value
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