Heavy OWA Operator of Trapezoidal Intuitionistic Fuzzy Numbers and its Application to Multi-Attribute Decision Making

Abstract

Heavy ordered weighted averaging (OWA) operator is important for characterizing the decision maker’s attitudinal character in multi-attribute decision making (MADM) problem with part or total ignorance. This paper develops a new method based on heavy OWA operator to solve the MADM problem in which the attributes are characterized by some trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFN, as a special kind of intuitionistic fuzzy set defined on the real numbers, is useful for characterizing the ill-known quantity in reality. Firstly, the operation laws and the cut sets concept for TrIFNs are introduced. Then the authors define the membership and non-membership average indexes. A new ranking method is developed on the basis of the two indexes. In the proposed decision model, the multi-attribute TrIFN values of the candidates are aggregated by the Heavy OWA operator, and ranked by their membership and non-membership average indexes. Lastly, the authors illustrate the proposed method by a numerical example which implies the practicality and effectiveness of the method.