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Multi-attribute group decision making under probabilistic hesitant fuzzy environment with application to evaluate the transformation efficiency

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Abstract

Hesitant fuzzy sets were introduced by Torra to efficiently address situations in which the membership degree of an element in a set is expressed by several different values. However, there is a large shortcoming in hesitant fuzzy sets—the serious loss of information. Therefore, in this paper, we improve upon hesitant fuzzy sets by implementing a probabilistic hesitant fuzzy set (PHFS). Then, we introduce some new basic operations on the probabilistic hesitant fuzzy elements (PHFEs) using the Frank t-conorm and t-norm. Based on these proposed operations, we further develop probabilistic hesitant fuzzy weighted arithmetic and geometric aggregation operators. The desired properties and the relationships among them are investigated in detail. In addition, an approach to multi-attribute group decision making (MAGDM) is investigated on the basis of the new operators. Finally, a numerical example of public company efficiency evaluation is provided to illustrate the application and validity of the proposed approach.

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References

  1. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  Google Scholar 

  2. Atanassov K (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–46

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov K (2000) Two theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst 110:267–269

    Article  MathSciNet  MATH  Google Scholar 

  4. Song Y, Wang X, Lei L et al (2015) A novel similarity measure on intuitionistic fuzzy sets with its applications. Appl Intell 42(2):252–261

    Article  Google Scholar 

  5. Chen N, Xu ZS, Xia (2015) The electric multi-criteria decision-making method based on hesitant fuzzy sets. Int J Inf Technol Decis Mak 14(03):621–657

    Article  Google Scholar 

  6. TY Chen (2011) A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings. Inf Sci 181:3652–3676

    Article  Google Scholar 

  7. Chen TY (2012) Comparative analysis of SAW and TOPSIS based on interval-valued fuzzy sets: discussions on score functions and weight constraints. Expert Syst Appl 39:1848–1861

    Article  Google Scholar 

  8. Du XQ (2008) Probability and mathematical statistics. Springer

  9. Deschrijver G, Kerra EE (2002) A generalization of operators on intuitionistic fuzzy sets using triangular norms and conforms. Intuitionistic Fuzzy Sets 8(1):19–27

    Google Scholar 

  10. Deschrijver G, Cornelis C, Kerre EE (2004) On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans Fuzzy Syst 12:45–61

    Article  MATH  Google Scholar 

  11. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  12. Farhadinia B (2014) A series of score functions for hesitant fuzzy sets. Inf Sci 277:102–110

    Article  MathSciNet  MATH  Google Scholar 

  13. Gu X, Wang Y, Yang B (2011) A method for hesitant fuzzy multiple attribute decision making and its application to risk investment. J Converg Inf Technol 6(6):282–287

    Google Scholar 

  14. Zeng SZ, Li W, Merigo JM (2013) Extended induced ordered weighted averaging distance operators and their application to group decision-making. Int J Inf Technol Decis Mak 12(04):789–811

    Article  Google Scholar 

  15. Klement EP, Mesiar R, Pap E (2004) Triangular norms position paper I: basic analytical and algebraic properties. Fuzzy Sets Syst 143(1):5–26

    Article  MathSciNet  MATH  Google Scholar 

  16. Li DF (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets. J Comput Syst Sci 70(1):73–85

    Article  MathSciNet  MATH  Google Scholar 

  17. Liao HC, Xu ZS, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142

    Article  MathSciNet  MATH  Google Scholar 

  18. Miyamoto S (2000) Multisets and fuzzy multisets. In: Liu ZQ, Miyamoto S (eds) Soft computing and human-centered machines. Springer, Berlin, pp 9–33

    Chapter  Google Scholar 

  19. Miyamoto S (2005) Remarks on basics of fuzzy sets and fuzzy multisets. Fuzzy Sets Syst 156(3):427–431

    Article  MathSciNet  MATH  Google Scholar 

  20. Papakostas GA, Hatzimichailidis AG, Kaburlasos VG (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recogn Lett 34:1609–1622

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. Peng DH, Gao CY, Gao ZF (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37:5837–5850

    Article  MathSciNet  MATH  Google Scholar 

  23. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  24. Turksen LB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 80:191–210

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang JQ, Li JJ (2011) Multi-criteria fuzzy decision-making method based on cross entropy and score functions. Expert Syst Appl 38:1032–1038

    Article  Google Scholar 

  26. Wang JQ, Li KJ, Zhang HY (2012) Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function. Knowl-Based Syst 27:119–125

    Article  Google Scholar 

  27. Das SK, Mandal T, Edalatpanah SA (2017) A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Appl Intell 46(3):509–519

    Article  Google Scholar 

  28. Wei GW, Zhao XF (2013) Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 24:789–803

    MathSciNet  MATH  Google Scholar 

  29. Wei GW, Zhao XF, Lin R (2013) Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl-Based Syst 46:43–53

    Article  Google Scholar 

  30. Wei GW, Zhao XF, Wang HJ (2013) Hesitant fuzzy choquet integral aggregation operators and their applications to multiple attribute decision making. Information-an International Interdisciplinary Journal 37:357–365

    Google Scholar 

  31. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407

    Article  MathSciNet  MATH  Google Scholar 

  32. Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl-Based Syst 31:78–88

    Article  Google Scholar 

  33. Xu ZS (2004) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30

    Article  MathSciNet  MATH  Google Scholar 

  34. Xu ZS (2004) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184

    Article  MATH  Google Scholar 

  35. Xu ZS (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180:181–190

    Article  MATH  Google Scholar 

  36. Ali F, Kim EK, Kim YG (2015) Type-2 fuzzy ontology-based opinion mining and information extraction: a proposal to automate the hotel reservation system. Appl Intell 42(3):481–500

    Article  Google Scholar 

  37. Chen TY (2014) An interactive signed distance approach for multiple criteria group decision-making based on simple additive weighting method with incomplete preference information defined by interval type-2 fuzzy sets. Int J Inf Technol Decis Mak 13(05):979–1012

    Article  Google Scholar 

  38. Yu DJ, Zhang WY, Xu YJ (2013) Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowl-Based Syst 52:1–10

    Article  Google Scholar 

  39. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  40. Zhang ZM (2009) An interval-valued intuitionistic fuzzy rough set model. Fundamenta Informaticae 97 (4):471–498

    MathSciNet  MATH  Google Scholar 

  41. Zhang ZM (2013) Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf Sci 234:150–181

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhou W (2014) An accurate method for determining hesitant fuzzy aggregation operator weights and its application to project investment. Int J Intell Syst 29(7):668–686

    Article  Google Scholar 

  43. Zhang S, Xu ZS, He Y (2017) Operations and integrations of probabilistic hesitant fuzzy information in decision making. Information Fusion 38:1–11

    Article  Google Scholar 

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Acknowledgments

The work was supported by Guizhou Province Department of Education Fund (Nos. KY[2015]34, KY[2016]088), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 16KJB520001). The authors are thankful to the anonymous reviewers and the editor for their valuable comments and constructive suggestions that have led to an improved version of this paper.

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Authors and Affiliations

  1. School of Management, Wuhan University of Technology, Wuhan, Hubei, 430070, China

    Fangju Jiang

  2. Changzhou University Huaide College, Taizhou, Jiangsu, 214500, China

    Qinggong Ma

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  1. Fangju Jiang
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  2. Qinggong Ma
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Correspondence to Fangju Jiang.

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Jiang, F., Ma, Q. Multi-attribute group decision making under probabilistic hesitant fuzzy environment with application to evaluate the transformation efficiency. Appl Intell 48, 953–965 (2018). https://doi.org/10.1007/s10489-017-1041-x

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