Probability-hesitant fuzzy sets and the representation of preference relations
Abstract
Probability interpretations play an important role in understanding decision makers’ (DMs) behaviour in decision making. In this paper, we extend hesitant fuzzy sets to probability-hesitant fuzzy sets (P-HFSs) to enhance their modeling ability by taking DMs’ probabilistic preferences into consideration. Based on P-HFSs, we propose the concept of probability-hesitant fuzzy preference relation (P-HFPR) to collect the preferences. We then develop a consensus index to measure the consensus degrees of P-HFPR, and a stochastic method to improve the consensus degrees. All these results are essential for further research on P-HFSs.
Keyword : group decision making, fuzzy sets, preference relation, simulation
How to Cite
Zhu, B., & Xu, Z. (2018). Probability-hesitant fuzzy sets and the representation of preference relations. Technological and Economic Development of Economy, 24(3), 1029-1040. https://doi.org/10.3846/20294913.2016.1266529
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8: 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhu, B.; Xu, Z. 2013. Regression methods for hesitant fuzzy preference relations, Technological and Economic Development of Economy 19(Supl. 1): S214–S227. https://doi.org/10.3846/20294913.2014.881430
Zhu, B.; Xu, Z. 2014. Stochastic preference analysis in numerical preference relations, European Journal of Operational Research 237(2): 628–633. https://doi.org/10.1016/j.ejor.2014.01.068
Zhu, B.; Xu, Z. 2016. Extended hesitant fuzzy sets, Technological and Economic Development of Economy 22(1): 100–121. https://doi.org/10.3846/20294913.2014.981882
Zhu, B.; Xu, Z.; Xia, M. 2012. Hesitant fuzzy geometric Bonferroni means, Information Sciences 205(1): 72–85. https://doi.org/10.1016/j.ins.2012.01.048
Zhu, B.; Xu, Z.; Xu, J. 2014. Deriving a ranking from hesitant fuzzy preference relations under group decision making, IEEE Transactions on Cybernetics 44(8): 1328–1337. https://doi.org/10.1109/TCYB.2013.2283021
Diamond, P.; Kloeden, P. E. 1994. Metric spaces of fuzzy sets: theory and applications. World Scientific Publishing Company. https://doi.org/10.1142/2326
Dong, Y.; Zhang, G.; Hong, W.-C.; Xu, Y. 2010. Consensus models for AHP group decision making under row geometric mean prioritization method, Decision Support Systems 49(3): 281–289. https://doi.org/10.1016/j.dss.2010.03.003
Herrera-Viedma, E.; Alonso, S.; Chiclana, F.; Herrera, F. 2007. A consensus model for group decision making with incomplete fuzzy preference relations, Fuzzy Systems 15(5): 863–877. https://doi.org/10.1109/TFUZZ.2006.889952
Kacprzyk, J. 1997. Mu ltistage fuzzy control: a prescriptive approach. John Wiley & Sons, Inc.
Liao, H.; Xu, Z.; Xia, M. 2014. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, International Journal of Information Technology & Decision Making 13(01): 47–76. https://doi.org/10.1142/S0219622014500035
Orlovsky, S. 1978. Decision-making with a fuzzy preference relation, Fuzzy sets and systems 1(3): 155–167. https://doi.org/10.1016/0165-0114(78)90001-5
Torra, V. 2010. Hesitant fuzzy sets, International Journal of Intelligent Systems 25(1): 529–539. https://doi.org/10.1002/int.20418
Torra, V.; Narukawa, Y. 2009. On hesitant fuzzy sets and decision, in 2009 IEEE International Conference on Fuzzy Systems, 20–24 August 2009, 1378–1382. https://doi.org/10.1109/FUZZY.2009.5276884
Wang, J.; Wang, J.; Zhang, H.; Chen, X. 2016. Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information, International Journal of Fuzzy Systems 18(1): 81–97. https://doi.org/10.1007/s40815-015-0050-3
Xia, M.; Xu, Z. 2011a. Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning 52(3): 395–407. https://doi.org/10.1016/j.ijar.2010.09.002
Xia, M.; Xu, Z. 2011b. On consensus in group decision making based on fuzzy preference relations, in Consensual Processes, 267: 263–287. https://doi.org/10.1007/978-3-642-20533-0_15
Xu, Z. 2004. Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation, International Journal of Approximate Reasoning 36(3): 261–270. https://doi.org/10.1016/j.ijar.2003.10.011
Xu, Z. S.; Xia, M. M. 2011. Distance and similarity measures for hesitant fuzzy sets, Information Sciences 181(11): 2128–2138. https://doi.org/10.1016/j.ins.2011.01.028
Yu, D.; Zhang, W.; Huang, G. 2016. Dual hesitant fuzzy aggregation operators, Technological and Economic Development of Economy 22(2): 194–209. https://doi.org/10.3846/20294913.2015.1012657
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8: 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhu, B.; Xu, Z. 2013. Regression methods for hesitant fuzzy preference relations, Technological and Economic Development of Economy 19(Supl. 1): S214–S227. https://doi.org/10.3846/20294913.2014.881430
Zhu, B.; Xu, Z. 2014. Stochastic preference analysis in numerical preference relations, European Journal of Operational Research 237(2): 628–633. https://doi.org/10.1016/j.ejor.2014.01.068
Zhu, B.; Xu, Z. 2016. Extended hesitant fuzzy sets, Technological and Economic Development of Economy 22(1): 100–121. https://doi.org/10.3846/20294913.2014.981882
Zhu, B.; Xu, Z.; Xia, M. 2012. Hesitant fuzzy geometric Bonferroni means, Information Sciences 205(1): 72–85. https://doi.org/10.1016/j.ins.2012.01.048
Zhu, B.; Xu, Z.; Xu, J. 2014. Deriving a ranking from hesitant fuzzy preference relations under group decision making, IEEE Transactions on Cybernetics 44(8): 1328–1337. https://doi.org/10.1109/TCYB.2013.2283021