Advertisement

Multi-attribute decision making based on prioritized operators under probabilistic hesitant fuzzy environments

Methodologies and Application
  • 95 Downloads

Abstract

Probabilistic hesitant fuzzy sets (PHFSs) are currently attracting the attention of numerous scholars due to their efficiency in representing uncertain and fuzzy information. PHFSs are more convenient than hesitant fuzzy sets for decision makers to provide their preference information. However, several important issues in PHFSs utilization remain to be addressed. The shortcomings of the operations in PHFSs are discussed in this paper. Probabilistic hesitant fuzzy prioritized weighted average (PHFPWA) and probabilistic hesitant fuzzy prioritized weighted geometric (PHFPWG) operators are developed on the basis of idea of prioritized aggregation operators, and their properties are described. The relationship between PHFPWA and PHFPWG operators is investigated. A multi-attribute decision-making method based on the proposed operators is presented. Two practical examples are provided to illustrate the practicality and effectiveness of the proposed method. Comparison analysis and discussion with other aggregation operators based on the same examples are provided.

Keywords

Probabilistic hesitant fuzzy sets Multi-attribute decision making Prioritized aggregation operators PHFPWA operator PHFPWG operator 

Notes

Acknowledgements

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions that have led to this improved version of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefMATHGoogle Scholar
  2. Chen SM, Tsai WH (2016) Multiple attribute decision making based on novel interval-valued intuitionistic fuzzy geometric averaging operators. Inf Sci 367–368:1045–1065CrossRefGoogle Scholar
  3. Chen SQ, Wang YM, Shi H, Zhang MJ, Lin Y (2017) Alliance-based evidential reasoning approach with unknown evidence weights. Expert Syst Appl 78:193–207CrossRefGoogle Scholar
  4. Chen TY (2014) Multiple criteria decision analysis using a likelihood-based outranking method based on interval-valued intuitionistic fuzzy sets. Inf Sci 286:188–208CrossRefGoogle Scholar
  5. Fan ZP, Zhang X, Liu Y, Zhang Y (2013) A method for stochastic multiple attribute decision making based on concepts of ideal and anti-ideal points. Appl Math Comput 219:11438–11450MathSciNetMATHGoogle Scholar
  6. Gou XJ, Xu ZS (2016) Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci 372:407–427CrossRefGoogle Scholar
  7. Harsanyi JC (1976) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. In: Harsanyi JC (ed) Essays on ethics, social behavior, and scientific explanation. Springer, Dordrecht, pp 6–23CrossRefGoogle Scholar
  8. He YD, Chen HY, He Z, Wang GD, Zhou LG (2016) Scaled prioritized aggregation operators and their applications to decision making. Soft Comput 20:1021–1039CrossRefMATHGoogle Scholar
  9. He YG, He Z, Huang H (2017) Decision making with the generalized intuitionistic fuzzy power interaction averaging operators. Soft Comput 21:1129–1144CrossRefGoogle Scholar
  10. Jin FF, Ni ZW, Chen HY (2016) Note on "Hesitant fuzzy prioritized operators and their application to multiple attribute decision making". Knowl Based Syst 96:115–119CrossRefGoogle Scholar
  11. Li J, & Wang J Q (2017a) An extended QUALIFLEX method under probability hesitant fuzzy environment for selecting green suppliers. International Journal of Fuzzy Systems 19:1866–1879Google Scholar
  12. Li J, Wang JQ (2017b) Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cogn Comput 9:611–625CrossRefGoogle Scholar
  13. Li Y, Deng Y, Chan FTS, Liu J, Deng XY (2014) An improved method on group decision making based on interval-valued intuitionistic fuzzy prioritized operators. Appl Math Model 38:2689–2694MathSciNetCrossRefGoogle Scholar
  14. Liu JP, Liao XW, Yang JB (2015) A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty. Eur J Oper Res 246:858–873MathSciNetCrossRefMATHGoogle Scholar
  15. Liu PD (2017) Multiple attribute group decision making method based on interval-valued. Comput Ind Eng 108:119–212CrossRefGoogle Scholar
  16. Liu ZG, Dezert J, Pan Q, Mercier G (2011) Combination of sources of evidence with different discounting factors based on a new dissimilarity measure. Decis Support Syst 52:133–141CrossRefGoogle Scholar
  17. Mu ZM, Zeng SZ, Baležentis T (2015) A novel aggregation principle for hesitant fuzzy elements. Knowl Based Syst 84:134–143CrossRefGoogle Scholar
  18. Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143CrossRefGoogle Scholar
  19. Peng HG, Wang JQ (2017) Cloud decision model for selecting sustainable energy crop based on linguistic intuitionistic information. Int J Syst Sci 48:3316–3333CrossRefMATHGoogle Scholar
  20. Peng HG, Zhang HY, Wang JQ (2018) Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information. Int J Hosp Manag 68:124–138CrossRefGoogle Scholar
  21. Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47:2342–2358CrossRefMATHGoogle Scholar
  22. Tian ZP, Wang J, Wang JQ, Zhang HY (2016) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot 26:597–627CrossRefGoogle Scholar
  23. Tian ZP, Wang JQ, Wang J, Zhang HY (2018) A multi-phase QFD-based hybrid fuzzy MCDM approach for performance evaluation: a case of smart bike-sharing programs in Changsha. J Clean Prod 171:1068–1083CrossRefGoogle Scholar
  24. Torra V, & Narukawa Y (2009) On hesitant fuzzy sets and decision. In: IEEE international conference on fuzzy systems, 2009. Fuzz-Ieee, (pp 1378–1382)Google Scholar
  25. Verma R, Sharma BD (2014) Fuzzy generalized prioritized weighted average operator and its application to multiple attribute decision making. Int J Intell Syst 29:26–49CrossRefGoogle Scholar
  26. Vigier HP, Scherger V, Terceño A (2016) An application of OWA operators in fuzzy business diagnosis. Appl Soft Comput 54:440–448CrossRefGoogle Scholar
  27. Wang JQ, Cao YX, & Zhang HY (2017a) Multi-criteria decision-making method based on distance measure and choquet integral for linguistic Z-numbers. Cogn Comput 9:827–842Google Scholar
  28. Wang JQ, Peng JJ, Zhang HY, Chen XH (2017b) Outranking approach for multi-criteria decision-making problems with hesitant interval-valued fuzzy sets. Soft Comput.  https://doi.org/10.1007/s00500-00017-02791-00504 Google Scholar
  29. Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2014) Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf Sci 288:55–72MathSciNetCrossRefMATHGoogle Scholar
  30. Wang L, Shen QG, Zhu L (2016) Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making. Appl Soft Comput 38:23–50CrossRefGoogle Scholar
  31. Wang ZX, Li J (2017) Correlation coefficients of probabilistic hesitant fuzzy elements and their applications to evaluation of the alternatives. Symmetry. 9:259–377CrossRefGoogle Scholar
  32. Wei GW (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl Based Syst 31:176–182CrossRefGoogle Scholar
  33. 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 46:43–53CrossRefGoogle Scholar
  34. Wu ZB, Xu JP (2018a) A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf Fusion 41:217–231CrossRefGoogle Scholar
  35. Wu ZB, Xu JP (2018b) A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf Fusion 41:217–231CrossRefGoogle Scholar
  36. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407MathSciNetCrossRefMATHGoogle Scholar
  37. Xu ZS (2000) On consistency of the weighted geometric mean complex judgement matrix in AHP 1. Eur J Oper Res 126:683–687MathSciNetCrossRefMATHGoogle Scholar
  38. Xu ZS, Yu XH (2007) Prioritized intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  39. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190CrossRefMATHGoogle Scholar
  40. Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48:263–274MathSciNetCrossRefMATHGoogle Scholar
  41. Yu DJ (2013) Multi-criteria decision making based on generalized prioritized aggregation operators under intuitionistic fuzzy environment. Int J Fuzzy Syst 15:47–54MathSciNetGoogle Scholar
  42. Yu DJ, Wu YY, Lu T (2012) Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making. Knowl Based Syst 30:57–66CrossRefGoogle Scholar
  43. Yu DJ, Zhang WY, Xu YJ (2013) Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowl Based Syst 52:1–10CrossRefGoogle Scholar
  44. Yu SM, Wang J, Wang JQ, Li L (2017) A multi-criteria decision-making model for hotel selection with linguistic distribution assessments. Appl Soft Comput.  https://doi.org/10.1016/j.asoc.2017.1008.1009 Google Scholar
  45. Yu XH, Xu ZS (2013) Prioritized intuitionistic fuzzy aggregation operators. Inf Fusion 14:108–116CrossRefGoogle Scholar
  46. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  47. Zhang MJ, Wang YM, Li LH, Chen SQ, Slowinski R, Artalejo J, Billaut JC, Dyson R, Peccati L (2017) A general evidential reasoning algorithm for multi-attribute decision analysis under interval uncertainty. Eur J Oper Res 257:1005–1015MathSciNetCrossRefGoogle Scholar
  48. Zhang S, Xu ZS, He Y (2017) Operations and integrations of probabilistic hesitant fuzzy information in decision making. Inf Fusion 38:1–11CrossRefGoogle Scholar
  49. Zhang XY, Wang JQ (2017) Discussing incomplete 2-tuple fuzzy linguistic preference relations inmulti-granular linguistic MCGDM with unknown weight information. Soft Comput.  https://doi.org/10.1007/s00500-00017-02915-x
  50. Zhao XF, Lin R, Wei GW (2013) Fuzzy prioritized operators and their application to multiple attribute group decision making. Appl Math Model 37:4759–4770MathSciNetCrossRefGoogle Scholar
  51. Zhou H, Wang JQ, Zhang HY, Chen XH (2016) Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. Int J Syst Sci 47:314–327MathSciNetCrossRefMATHGoogle Scholar
  52. Zhou W, Xu ZS (2017a) Expected hesitant VaR for tail decision making under probabilistic hesitant fuzzy environment. Appl Soft Comput 60:297–311CrossRefGoogle Scholar
  53. Zhou W, Xu ZS (2017b) Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Trans Fuzzy Syst.  https://doi.org/10.1109/TFUZZ.2017.2723349
  54. Zhu B (2014) Decision method for research and application based on preference relation. Southeast University, NanjingGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of XingJian College of Science and Liberal ArtsGuangxi UniversityNanningPeople’s Republic of China
  2. 2.School of Mathematics and Information ScienceGuangxi UniversityNanningPeople’s Republic of China

Personalised recommendations