Abstract
Interval-valued intuitionistic preference relation (IV-IPR) is a new type of preference structure used to describe uncertain evaluation information in decision making process. In this paper, we first define the concept of IV-IPR with multiplicative transitivity, and then give a procedure to construct an IV-IPR with multiplicative transitivity from an incomplete IV-IPR with only known off-diagonal elements. We also extend this procedure to deal with more general cases with much more known evaluation information. Moreover, we develop an approach to group decision making with incomplete IV-IPRs, and finally give an actual application of our approach and compare it with the other approach in the existing literature.
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References
Alonso S, Cabrerizo FJ, Chiclana F, Herrera F, Herrera-Viedma E (2009) Group decision-making with incomplete fuzzy linguistic preference relations. Int J Intell Syst 24:201–222
Alonso S, Herrera-Viedma E, Chiclana F, Herrera F (2010) A web based consensus support system for group decision making problems and incomplete preferences. Inf Sci 180:4477–4495
Chen TY, Wang HP, Lu YY (2011) A multi-criteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst Appl 38:7647–7658
Chiclana F, Herrera-Viedma E, Alonso S (2009) A note on two methods for estimating missing pairwise preference values. IEEE Trans Syst Man Cybern.-Part B: Cybern. 39:1628–1633
Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2009) Cardinal consistency of reciprocal preference relation: a characterization of multiplicative transitivity. IEEE Trans. Fuzzy Syst. 17:14–23
Deschrijver G, Kerre EE (2003) On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst 136:333–361
Deschrijver G, Kerre EE (2008) Aggregation operators in interval-valued fuzzy and Atanassov’s intuitionistic fuzzy set theory. In: Bustince H, Herrera F, Montero J (eds) Fuzzy sets and their extensions: representation, aggregation and models. Springer, Heidelberg, pp 183–203
Fedrizzi M, Giove S (2007) Incomplete pairwise comparison and consistency optimization. Eur J Oper Res 183:303–313
Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394–4402
Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern-Part B: Cybern 37:176–189
Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, Berlin
Liao HC, Xu ZS, Xia MM (2013) Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int J Inf Technol Decis Mak. doi:10.1142/S0219622014500035
Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155–167
Porcel C, Herrera-Viedma E (2010) Dealing with incomplete information in a fuzzy linguistic recommender system to disseminate information in university digital libraries. Knowl-Based Syst 23:32–39
Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1037–1053
Szmidt E, Kacprzyk J (2003) A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst 18:837–852
Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12:117–131
Wang ZJ, Wang LF, Li KW, Luo J (2010) Linear programming models for deriving priority weights from interval-valued intuitionistic preference relations with multiplicative transitivity. In: Proceedings of 7th international conference on service systems and service management, pp 28–30, June, Tokyo, Japan, doi:10.1109/ICASSP.2010.5530259
Wang ZJ (2013) Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations. Appl Math Model 37:6377–6388
Xu ZS, Chen J (2007). On geometric aggregation over interval-valued intuitionistic fuzzy information. In: The 4th international conference on fuzzy systems and knowledge discovery (FSKD’07), vol. 2, Haikou, China, pp. 466–471
Xu ZS, Liao HC (2013) Intuitionistic fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2013.2272585
Xu (2012) Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decis Negot. doi:10.1007/s10726-011-9278-y
Xu ZS (2007a) A survey of preference relations. Int J Gen Syst 36:179–203
Xu ZS (2007b) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379
Xu ZS, Cai XQ (2009) Incomplete interval-valued intuitionistic preference relations. Int J Gen Syst 38:871–886
Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139
Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int J Intell Syst 26:787–813
Acknowledgments
The work was supported in part by the National Natural Science Foundation of China (No. 61273209), the Research Grants Council of Hong Kong (No. 410213), and the State Key Lab for Manufacturing Systems Engineering Foundation, sklms2011010, Xi’an Jiaotong University.
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Xu, Z., Cai, X. Group Decision Making with Incomplete Interval-Valued Intuitionistic Preference Relations. Group Decis Negot 24, 193–215 (2015). https://doi.org/10.1007/s10726-014-9386-6
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DOI: https://doi.org/10.1007/s10726-014-9386-6