基于直觉模糊关系的双论域多粒度概率粗糙集

Two-Universe Multi-granularity Probability Rough Sets Based on Intuitionistic Fuzzy Relations

在复杂的不确定性环境中,粗糙集引入拓展要素,可增强模型强健性,因此,文中基于直觉模糊关系,在双论域上研究多粒度概率粗糙集.首先,利用直觉模糊关系与双论域背景,进行多粒度概率粗糙集建模,得到正向乐观、正向悲观、逆向乐观、逆向悲观4种模型及相关集成算法.然后,研究模型下上近似的数学性质,包括集合运算关系、概率参数极限、精度大小对比3方面.最后,采用医疗实例验证模型有效性与性质正确性,提供三支决策制定方案,并验证关于多粒度双论域直觉模糊概率粗糙集所得模型、算法、性质都具有深入的系统性、扩张性、应用性.

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.