Matrix game-based approach for MADM with probabilistic triangular intuitionistic hesitant fuzzy information and its application

Abstract

This paper develops a zero-sum matrix game-based methodology for multi-attribute decision making (MADM) problems, where the attribute information is described by the probabilistic triangular intuitionistic hesitant fuzzy set (PTIHFS), and their weights are unknown. Firstly, we propose a new comprehensive rank method to measure PTIHFSs based on the concepts of the centroid value and the ambiguity value. Then, in order to obtain the rational attribute weights strategies (solutions) with DM's preferences/parameters, the transformed parameterized PTIHFS bilinear programming models are proposed for the zero-sum matrix. Next, the alternatives are sorted by the aggregation scores of each alternative with different parameters. Finally, we apply the zero-sum matrix game-based models and approach in a carrying capacity evaluation, the feasibility and superiority are demonstrated by comparing them with other methods. The proposed simple measure method of PTIHFSs, and it is used for interactive decision-making, which can much significantly promote the application of MADM.