一类推广的多粒度双量化决策粗糙模糊集

A Class of Generalized Rough Fuzzy Sets for Multigranularity Double-quantization Decision-theoretic

多粒度决策粗糙集作为一种特殊的概率粗糙集模型,其主要运用条件概率来表示相对量化信息,却忽略了等价类与经典集重叠部分的绝对量化信息,而绝对量化信息在程度多粒度粗糙集中被广泛讨论。因此,本文基于逻辑析取和合取算子将多粒度决策粗糙集和程度多粒度粗糙集相结合,同时引入模糊集和标量基数的思想,提出两对推广的多粒度决策粗糙模糊集∨∨-MGDTRFS和∧∧-MGDTRFS.随后,讨论了∨∨-MGDTRFS和∧∧-MGDTRFS的相关性质,并且给出两者之间的联系。

As a special probabilistic rough set model,the multigranularity decision-theoretic rough set mainly uses conditional probability to represent relative quantitative information,but ignores the absolute quantitative information of the overlap parts between equivalence class and the basic set.However,the graded multigranulation rough set considers the absolute quantitative information.Therefore,based on the logical disjunction and conjunction operators,this paper combines multigranularity decision-theoretic rough set and the graded multigranulation rough set with the idea of fuzzy sets and scalar cardinality,and then proposes two pairs of generalized multigranularity decision-theoretic rough fuzzy sets∨∨-MGDTRFS and∧∧-MGDTRFS.Subsequently,the related properties and connections between∨∨-MGDTRFS and∧∧-MGDTRFS are discussed.