基于二型模糊预序的模糊粗糙集模型

Fuzzy rough set model based on type-2 fuzzy preorders

摘要

以二型模糊预序为基本结构研究了模糊粗糙集,定义一对模糊上下近似算子,并研究它们的性质和相互关系,证明上可定义集和下可定义集是等价的,上可定义集和下可定义集构成一个满层的 Alexandrov 模糊拓扑。

Abstract

Based on the fundamental structure of type-2 fuzzy preorders, fuzzy rough sets are investigated, and a pair of fuzzy upper and lower approximation operators are defined. Furthermore, their properties and interrelations are explored. It is shown that upper definable sets and lower definable sets are equivalent. Definable sets form a stratified Alexandrov fuzzy topology such that the upper and lower approximation operators are the related closure and interior operators respectively.

关键词

二型模糊预序 / 模糊粗糙集 / 模糊近似算子 / 可定义集 / Alexandrov 模糊拓扑

Key words

type-2 fuzzy preorder / fuzzy rough set / fuzzy upper/ lower approximation operator / definable set / Alexandrov fuzzy topology

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基金资助

国家自然科学基金资助项目(12371462)

国家自然科学基金资助项目(12231007)

南京工程学院引进人才科研启动基金资助项目(YKJ202351)

江苏省双创人才计划(JSSCRC2021521)

黑龙江省自然科学基金联合基金重点项目(ZL2024A001)