A regret-based three-way decision with novel intuitionistic fuzzy similarity in intuitionistic fuzzy information system

Three-way decision is a strategic approach that utilizes fuzzy set theory to divide the decision-making space into three regions to handle uncertainty information. Considering the various difficulties researchers encounter in dealing with uncertainty, the intuitionistic fuzzy set, as a type of fuzzy set, can effectively handle this uncertainty. The regret-joy function furnishes a supplementary viewpoint for the limitations of rational choice theory under uncertain conditions. This paper introduces a novel three-way decision method developed within the framework of intuitionistic fuzzy information systems, using the regret-joy function. Specifically, first, we introduce a novel intuitionistic fuzzy similarity degree to define the fuzzy similarity relationship between two alternatives. Second, in the intuitionistic fuzzy similarity class, we explore a method for calculating conditional probability using objective weights. Then, by integrating the relative loss function derived from the regret-joy function with conditional probability, we propose a novel three-way decision method within the framework of intuitionistic fuzzy information systems. Ultimately, the efficacy and reasonableness of the presented method are confirmed through case studies and comparisons. We conduct a sensitivity analysis on the parameters to determine their optimal range, showcasing the superiority of our proposed method.