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

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Abstract

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.

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Funding

This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 62076089 and 61772176, the Scientific and Technological Project of Henan Province of China under Grant Nos. 182102210078 and 182102210362, and the Plan for Scientific Innovation of Henan Province of China under Grant No. 18410051003.

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Authors and Affiliations

  1. College of Computer and Information Engineering, Henan Normal University, Xinxiang, 453007, China

    Zhanao Xue, Bingxin Sun, Haodong Hou, Wenli Pang & Yanna Zhang

  2. Engineering Lab of Intelligence Business and Internet of Things, Henan Province, Xinxiang, 453007, China

    Zhanao Xue, Bingxin Sun, Haodong Hou, Wenli Pang & Yanna Zhang

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  1. Zhanao Xue
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Xue, Z., Sun, B., Hou, H. et al. Three-Way Decision Models Based on Multi-granulation Rough Intuitionistic Hesitant Fuzzy Sets. Cogn Comput 14, 1859–1880 (2022). https://doi.org/10.1007/s12559-021-09956-0

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