Abstract: To address the issue of hesitation degree redistribution in similarity measurement of intuitionistic fuzzy sets, researchers typically rely on fixed formulas yielding constant results, which deviate from practical situations. To resolve this, a novel similarity measurement method for intuitionistic fuzzy sets is proposed. This method innovatively introduces a random function to perform fine-grained redistribution of hesitation degrees into membership and non-membership degrees, while preserving the remaining hesitation degree. This approach significantly enhances the discrimination ability and computational efficiency of the measurement while maintaining information integrity, fulfilling the core requirements of similarity measurement. Furthermore, the possible value range of the similarity between two intuitionistic fuzzy numbers is thoroughly discussed, enhancing the applicability of the similarity measure. The application of this method in the selection of cutting slope schemes verifies its rationality, practicality, and innovation, demonstrating promising application prospects.

Key words: intuitionistic fuzzy sets, similarity, road cut slope, scheme evaluation