Research on the Interval–Valued Intuitionistic Fuzzy Multi–Attribute Decision–Making Model Based on TOPSIS Extended by Projection Measure

As the social and economic environments continue to evolve, decision-making environments are characterized by ambiguity and uncertainty, which has led researchers to have a growing preference for interval intuitionistic fuzzy numbers (IVIFN) as decision-making information. This paper focuses on the IVIF multi-attribute decision-making (MADM) model. In this model, determining the weights of decision attributes and measuring the similarity of two decision vectors are crucial steps. Based on these steps, the paper proposed a comprehensive normalized projection measure that extended the technique of order preference by similarity to an ideal solution (TOPSIS) method to establish the IVIF-MADM model. The main contributions of this study are as follows: (1) the development of a new generalized normalized projection measure formulation, which comprehensively measures the similarity of two IVIF number vectors; (2) a kind of optimization model is constructed to ascertain the weights of the evaluation attributes, taking the maximization of the distinguishability of the projection values between all alternative schemes and the positive and negative ideal solutions as the objective; and (3) a dynamic testing method is innovatively proposed to demonstrate the model’s superiority. The feasibility and effectiveness of the model proposed in this paper are investigated by comparing static and dynamic experiments. The results confirm that the model proposed in this paper is practical and can produce a stable ranking of alternatives, and it can produce the same ranking of alternatives in all dynamic experimental cases. The dynamic testing method also shows that the model in this paper has better stability and robustness.