Multi-granular Intuitionistic Fuzzy Three-Way Decision Model Based on the Risk Preference Outranking Relation

As an important extension of decision-theoretic rough sets, three-way decision theory provides a new perspective for people to deal with uncertain problems. However, the traditional multi-granularity decision-theoretic rough sets model has limited ability in describing the risk preferences of decision-makers and the processing of intuitionistic fuzzy information. In addition, as far as we know, most of the risk loss functions in existing studies are based on utility theory. However, the complete compensability between attributes is not always true, and this fact may lead to inconsistencies between the final calculated results and the actual situation. We propose a multi-granular intuitionistic fuzzy three-way decision model based on the risk preference outranking relation. In this scenario, we first define the outranking relation on the intuitionistic fuzzy set and fuse it for the purpose of risk preference calculation. Next, starting from the single granularity, the relations between the membership outranking relation class, the nonmembership outranking relation class, and the rough approximation are analyzed, and the related properties are proven. Then, the single granularity is extended to construct the multi-granular intuitionistic fuzzy decision-theoretic rough sets and their corresponding three-way decision model. Furthermore, by systematically studying the decision loss costs of optimistic and pessimistic states, three-way decision rules are induced. The rationality and effectiveness of our proposed model are verified through a case study analysis and comparisons with existing methods. The results show that our proposed model can quantitatively analyze and calculate the uncertainty of decision-makers’ cognitive risk preferences, achieve global control of the decision-making process, and reduce the loss of decision-making costs.