Three-Way Decision Models Based on Multi-granulation Rough Intuitionistic Hesitant Fuzzy Sets

In practice, people may hesitate to evaluate uncertain things. As an extension of fuzzy sets, intuitionistic hesitant fuzzy sets use multiple membership and non-membership degrees to express uncertain evaluations. Multi-granulation rough set theory is utilized to deal with information in an intuitionistic hesitant fuzzy decision information system, and three-way decision models are established to make decisions. First, rough intuitionistic hesitant fuzzy sets and four multi-granulation rough intuitionistic hesitant fuzzy set models are proposed, and their properties are discussed. Second, we define the combination formula for the upper and lower approximations of multi-granulation rough intuitionistic hesitant fuzzy sets, and present a new intuitionistic hesitant fuzzy cross-entropy. Then, the conditional probabilities under four cases are calculated by the TOPSIS approach. Third, the thresholds in intuitionistic hesitant fuzzy decision-theoretic rough sets are calculated, and corresponding three-way decision rules are given. Finally, four kinds of three-way decision models based on the proposed multi-granulation rough intuitionistic hesitant fuzzy sets are constructed. Furthermore, the decision rule extraction algorithm is designed. The example proved that the four kinds of three-way decision models can evaluate objects with different attitudes and provide decision-making solutions, which demonstrates the feasibility and effectiveness of the proposed algorithm.