TOPSIS Multi-attribute Decision-making Method Based on Axiomatic Fuzzy Sets

Aiming at the multi-attribute decision-making problem where the attribute value is a linguistic value and the attribute weight is a real number, this paper proposes a TOPSIS multi-attribute decision-making method based on an axiomatic fuzzy set. Firstly, determine the language evaluation set and the corresponding Fuzzy division and the axiomatic fuzzy set generated by the fuzzy division to mathematically quantify the linguistic value in the process of multi-attribute decision-making into axiomatic fuzzy set processing. Then define the order relationship on the axiomatic fuzzy set, and based on the order relationship define the positive and negative ideal schemes. The Euclidean distance of the axiomatic fuzzy set is used to calculate the relative closeness between the alternative schemes and the positive and negative ideal schemes, and the comprehensive ranking index of the alternative schemes is obtained. Finally, an example is used to illustrate the effectiveness and practicability of the model.