A Novel Intuitionistic Fuzzy Vikor Method to Mcdm Based on Intuitionistic Fuzzy Β⋆-Covering Rough Set

Currently, the utilization of semi-overlap functions has become increasingly widespread in constructing fuzzy rough sets. However, the intuitionistic fuzzy rough set models, grounded in semi-overlap functions, and their applications have not been studied. Therefore, this paper introduces a novel intuitionistic fuzzy β⋆-covering rough set model that builds upon semi-overlap functions and applies it to address multi-criteria decision-making challenges. Initially, we present the concepts of intuitionistic fuzzy semi-overlap (semi-grouping) functions, and subsequently develop four intuitionistic fuzzy β⋆-neighborhood operators. Next, we propose some new intuitionistic fuzzy β⋆-covering rough set models by using intuitionistic fuzzy semi-overlap functions and intuitionistic fuzzy β⋆-neighborhood operators. In addition, by integrating the proposed new model with Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) method, we design an intuitionistic fuzzy VIKOR decision-making framework. We then apply this intuitionistic fuzzy VIKOR method to the pertinent issue of bone transplantation selection in medicine. Through a series of experiments and comparisons, we verify the stability, sensitivity and effectiveness of our method. The experimental results show that our method can rank nanomaterials well. Finally, we conduct experimental validation on a large data set, demonstrating that our method is also effective for large data. Furthermore, we design sequential similarity tests and hypothesis tests for compromise solutions, proving that our method is capable of generalization and exhibits good randomness.