Several hybrid aggregation operators for triangular intuitionistic fuzzy set and their application in multi-criteria decision making

Abstract

In this paper, on the basis of analyzing some existing limitations in the operational laws defined for triangular intuitionistic fuzzy numbers (TIFNs), we first proposed some improved operational laws for TIFNs. Then, based on new operational laws, we developed some aggregation operators for TIFNs, such as triangular intuitionistic fuzzy-weighted averaging operator, triangular intuitionistic fuzzy geometric operator, triangular intuitionistic fuzzy-ordered-weighted averaging operator, triangular intuitionistic fuzzy-ordered-weighted geometric operator, triangular intuitionistic fuzzy hybrid averaging operator, and triangular intuitionistic fuzzy hybrid geometric operators, and discussed some desirable properties of these operators. Furthermore, based on these aggregation operators, we developed a multi-criteria decision-making (MCDM) method in which the criteria values were represented by TIFNs. Finally, a numerical example was used to show the practicality and effectiveness of the proposed MCDM method by comparing the proposed method with the existing methods.