新型多粒度变精度(*,·)-模糊粗糙集

doi:10.6040/j.issn.1671-9352.0.2024.187

摘要/Abstract

摘要： 引入一种新型变精度(*,·)-模糊粗糙集,结合多粒度思想,提出了包含乐观、悲观和折中3个基本模型的多粒度变精度(*,·)-模糊粗糙集,研究了模型的代数性质和拓扑性质,证明了模型满足包含性、幂等性、对偶性等性质,并且能诱导模糊拓扑、模糊余拓扑结构。

关键词: 模糊粗糙集, 变精度, 多粒度, 三角模

Abstract: A novel variable precision(*,·)-fuzzy rough set is introduced. Combined with the idea of multi-granularity, a multi-granularity variable precision(*,·)-fuzzy rough set is further proposed, which includes three basic models, optimism, pessimism and compromise. The algebraic and topological properties of the model are investigated, and it is proved that the model satisfies the properties of inclusion, idempotency and duality, and can induce fuzzy topology and fuzzy cotopology structure.

Key words: fuzzy rough set, variable precision, multi-granularity, triangular norm

中图分类号:

TP181

李心如,李令强,贾成昭. 新型多粒度变精度(*,·)-模糊粗糙集[J]. 《山东大学学报(理学版)》, 2025, 60(7): 131-142.

LI Xinru, LI Lingqiang, JIA Chengzhao. Novel multi-granularity variable precision(*,·)-fuzzy rough set[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(7): 131-142.

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