Compatibility analysis is an efficient and important tool used to measure the consensus of opinions within a given group of individuals. In this paper, we give a compatibility measure between intuitionistic preference values and a compatibility measure between intuitionistic preference relations, respectively, and study their properties. It is shown that each individual intuitionistic preference relation and the collective intuitionistic preference relation is perfectly compatible if and only if all the individual intuitionistic preference relations are perfectly compatible. Based on the compatibility measures, a consensus reaching procedure in group decision making with intuitionistic preference relations is developed, and a method for comparing intuitionistic fuzzy values is pointed out, by which the considered objects are ranked and selected. In addition, we extend the developed measures, procedure and method to accommodate group decision making situations with interval-valued intuitionistic preference relations. Numerical analysis on our results through an illustrative example is also carried out.
Group decision making Intuitionistic preference relations Interval-valued intuitionistic preference relations Compatibility measure
This is a preview of subscription content, log in to check access.
Xu ZS, Cai XQ (2010) Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim Decis Mak 9: 359–381CrossRefGoogle Scholar
Xu ZS, Cai XQ (2011) Uncertain power average operators for aggregating interval fuzzy preference relations. Group Decis Negotiat. doi:10.1007/s10726-010-9213-7
Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int J Intell Syst 21: 787–813CrossRefGoogle Scholar
Xu ZS, Chen J (2007) Approach to group decision making based on interval-valued intuitionistic judgment matrices. Syst Eng Theory Pract 27: 126–133CrossRefGoogle Scholar
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35: 417–433CrossRefGoogle Scholar
Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8: 123–139CrossRefGoogle Scholar
Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18: 183–190CrossRefGoogle Scholar