A new theory of triangular intuitionistic fuzzy sets to solve the two-sided matching problem

Abstract

In view of the limitations of triangular intuitionistic fuzzy numbers (TIFNs) in value selection and application, the purpose of this paper is to redefine and demonstrate the algorithm, expectation function and distance measure of TIFNs, and to put forward a new theory of triangular intuitionistic fuzzy sets (TIFSs). The new theory of TIFSs is then applied to the field of two-sided matching decision-making. To solve the two-sided matching problem based on TIFSs, the agent behavior factors of both sides are calculated by this theory. On this basis, a multi-objective matching model under TIFS preference is constructed. Furthermore, the optimal matching scheme is obtained by transforming and solving the model according to the expected score, the linear weighting and the algorithm of “being as good as possible”. Finally, the practicability of the proposed two-sided matching method is verified by a transaction matching example. The novelty and key idea of the proposed method are as follows: (1) it combines the idea of closeness in TOPSIS method and the expected score in the new theory of TIFSs to measure the behavior factors of two-sided agents; (2) it builds a two-sided matching model considering the behavior factors under the preference of TIFSs; (3) according to the idea of “being as good as possible”, a novel algorithm for solving the two-sided matching model under TIFS preference is proposed. The major conclusion and advantage of this paper is that the obtained BM scheme using the proposed method can reflect agent behavior factors and maximize agents’ satisfaction as much as possible.