Possibility mean and variance based method for multi-attribute decision making with triangular intuitionistic fuzzy numbers

Abstract

Triangular intuitionistic fuzzy numbers (TIFNs) are useful to deal with ill-known quantities in decision making problems. The focus of this paper is on multi-attribute decision making (MADM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete, which are solved by developing a new decision method based on possibility mean and variance of TIFNs. The notions of possibility mean and variance for TIFNs are introduced as well as the possibility standard deviation. A new ranking approach for TIFNs is developed according to the ratio of the possibility mean to the possibility standard deviation. Hereby we construct a bi-objective programming model, which maximizes the ratios of the possibility mean to the possibility standard deviation for membership and non-membership functions on alternative's overall attribute values. Using the lexicographic approach, the bi-objective programming model is transformed into two non-linear programming models, which are further transformed into the linear programming models by using the variable transformation. Thus, we can obtain the maximum ratios of the possibility mean to the possibility standard deviation, s are used to rank the alternatives. A numerical example is examined to demonstrate applicability and implementation process of the proposed method.