A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers

Abstract

TODIM (an acronym in Portuguese of interactive and multicriteria decision making), which can capture the decision-makers’ (DMs) psychological behavior, is a recently developed multiple criteria decision making (MCDM) method. The classical TODIM method is introduced to handle information in the form of crisp numbers, but it has no capability to deal with fuzzy information such as triangular intuitionistic fuzzy numbers (TIFNs), which are flexible in reflecting the uncertainty and hesitation associated with the DMs’ opinions. In this paper, an extended TODIM method is proposed to solve multi-criteria group decision making (MCGDM) problems in a triangular intuitionistic fuzzy environment where weights of both DMs and criteria are completely unknown. First, the definition and characteristics of the classical TODIM and the comparative TIFNs are introduced. Then, novel operation laws considering the interaction between membership and non-membership values of different intuitionistic fuzzy sets are defined, and a weighted arithmetic interaction averaging operator of TIFNs is derived. In addition, an improved distance measure of TIFNs is proposed. From the perspective of similarity, we can obtain the weight of the evaluation value provided by each decision-maker, and aggregate individual decision matrices into a group decision matrix. The classical TODIM method is extended to deal with MCGDM problems with TIFNs, and detailed decision steps are given. Finally, a decision making problem to select renewable energy alternatives is applied to illustrate the validity and practicality of the proposed method.