Two-Universe Multi-granularity Probability Rough Sets Based on Intuitionistic Fuzzy Relations
HUANG Xinhong1,2, ZHANG Xianyong1,2, YANG Jilin2,3
1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066; 2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066; 3. College of Computer Science, Sichuan Normal University, Chengdu 610066
Abstract：In the complex uncertainty environment, extension factors are introduced into rough sets to enhance model robustness. Based on intuitionistic fuzzy relations, multi-granularity probability rough sets are investigated in two universes in this paper. Firstly, the intuitionistic fuzzy relations and two-universe background are utilized to model multi-granularity probabilistic rough sets, and four models and their integrated algorithms are acquired, including positive optimism, positive pessimism, inverse optimism and inverse pessimism. Then, mathematical properties of model lower and upper approximations are studied from the perspectives of set operation relation, probability parameter limitation and precision size comparison. Finally, the effectiveness and property correctness of the model are verified by a medical example, and the corresponding three-way decision making is provided. Regarding multi-granularity two-universe intuitionistic-fuzzy probability rough sets, systematicness, extension and applicability of the obtained models, algorithms and properties are confirmed in depth.
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2022, Vol. 35 
