Abstract
Interval-valued hesitant fuzzy preference relations (IVHFPRs) are powerful to express the judgments of decision makers (DMs) such as hesitancy and uncertainty. This paper continues to research decision making with IVHFPRs. To do this, it first defines a multiplicative consistency index for interval fuzzy preference relations (IFPRs). Then, it gives a new (acceptably) multiplicative consistency concept for IVHFPRs. After that, optimization models for judging the acceptably multiplicative consistency of IVHFPRs are built. When the multiplicative consistency is unacceptable, optimization models for improving the multiplicative consistency level and for minimizing the number of adjusted judgments are constructed, respectively. Based on the acceptably multiplicative consistency analysis, an algorithm for decision making with IVHFPRs is presented. Furthermore, formulae for determining the weights of the DMs and for measuring the consensus are offered. Based on the acceptably multiplicative consistency and consensus analysis, a new method for group decision making with IVHFPRs is proposed. Finally, an example about selecting the reservoir operation schemes is offered to show the efficiency of the new method and to compare with previous research.
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References
Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211
Krejčí J (2019) On extension of multiplicative consistency to interval fuzzy preference relations. Oper Res 19:783–815
Li CC, Dong YC, Xu YJ, Chiclana F, Herrera-Viedma E, Herrera F (2019) An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: taxonomy and future directions. Inf Fusion 52:43–156
Meng FY, An QX (2017) An approach for group decision making method with hesitant fuzzy preference relations. Knowl-Based Syst 127:1–15
Meng FY, Tan CQ, Chen XH (2017) Multiplicative consistency analysis for interval reciprocal preference relations: a comparative study. Omega 68:17–38
Tang J, Meng FY (2018) Ranking objects from group decision making with interval-valued hesitant fuzzy preference relations in view of additive consistency and consensus. Knowl-Based Syst 162:46–61
Tang J, An QX, Meng FY, Chen XH (2017) A natural method for ranking objects from hesitant fuzzy preference relations. Int J Inf Technol Decis Mak 16:611–1646
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539
Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407
Xu ZS (2001) A practical method for priority of interval number complementary judgment matrix. Oper Res Manag Sci 10:16–19
Xu YJ, Chen L, Rodríguez RM, Herrera F, Wang HM (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowl-Based Syst 99:71–78
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zhai YL, Xu ZS, Liao HC (2019) The stably multiplicative consistency of fuzzy preference relation and interval-valued hesitant fuzzy preference relation. IEEE Access 7:54929–54945
Zhang G, Dong Y, Xu Y (2012) Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations. Expert Syst Appl 39:2415–2420
Zhang ZM, Wang C, Tian XD (2015a) A decision support model for group decision making with hesitant fuzzy preference relations. Knowl-Based Syst 86:77–101
Zhang ZM, Wang C, Tian XD (2015b) Multi-criteria group decision making with incomplete hesitant fuzzy preference relations. Appl Soft Comput 36:1–23
Zhang YN, Tang J, Meng FY (2019) Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations. Appl Intell 49:837–857
Zhu B, Xu ZS, Xu JP (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44:328–1337
Acknowledgements
The authors first gratefully thank the Editor-in-Chief, the Associated Editor and two anonymous referees for their valuable and constructive comments which have much improved the paper. This work was supported by the National Natural Science Foundation of China (No. 71571192), the Beijing Intelligent Logistics System Collaborative Innovation Center (No. 2019KF-09) and the Major Project for National Natural Science Foundation of China (Nos. 91846301, 71790615).
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Tang, J., Meng, F. New method for interval-valued hesitant fuzzy decision making based on preference relations. Soft Comput 24, 13381–13399 (2020). https://doi.org/10.1007/s00500-020-04756-4
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DOI: https://doi.org/10.1007/s00500-020-04756-4