Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute Group Decision Making with Incomplete Weight Information

Triangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on a real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The purpose of this paper is on developing a new ranking method of TIFNs and application to multiattribute group decision making (MAGDM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete. The weighted average operator of TIFNs is defined, the concepts of the possibility mean, variance of TIFNs as well as standard deviation are introduced. Hereby two new ranking indices considering the risk attitude of decision maker are developed to rank TIFNs. In the proposed group decision method, the collective overall attribute values of alternatives are obtained by using the weighted average operator of TIFNs We construct the multi-objective programming of maximizing the ranking indices of membership and non-membership functions on alternative’s collective overall attribute values, which is transformed into a single linear programming model by using the membership function based weighted sum approach. Thus, the ranking indices of membership and non-membership functions for the alternatives are derived, which are used to rank the alternatives. A personnel selection example is analyzed to demonstrate the applicability, universality and flexibility of the proposed models and method.