四种截集形式粗糙模糊集扩展原理的交表示

楚雄师范学院学报 ›› 2023, Vol. 38 ›› Issue (3): 96-102.

四种截集形式粗糙模糊集扩展原理的交表示

何天荣

丽江师范高等专科学校数学与信息技术学院,云南丽江 674199

收稿日期:2021-06-15 出版日期:2023-05-20 发布日期:2023-08-07
作者简介:何天荣（1979–）,男,教授,研究方向为模糊数学及粗糙集理论。E-mail：hetianrong3421@163.com,Tel：13888812207
基金资助:
云南省教育厅科学研究基金项目（No. 2019J0384）

Intersection Representation of Four Cut Sets of Rough Fuzzy Set Extension Principle

HE Tianrong

Colldge of Mathematics and Information Technology, Lijiang Teachers' College, Lijiang, Yunnan Province 674199

Received:2021-06-15 Online:2023-05-20 Published:2023-08-07

摘要/Abstract

摘要： 关于粗糙模糊集扩展原理的研究,现有的研究结论都是基于粗糙模糊子集并的表示形式下得出的.本文引入了粗糙模糊集的 $λ$ —上截集, $λ$ —下截集, $λ$ —下重截集和 $λ$ —上重截集、粗糙模糊子集交的表示及基于交的表示的对应四种截集的分解定理,给出了交的表示下基于四种截集形式的粗糙模糊变换的定义及粗糙模糊集的扩展原理、并给出详细的理论证明。

关键词: 粗糙模糊集, 截集, 交的表示, 分解定理, 扩展原理

Abstract: The existing research conclusions on the principle of rough fuzzy set extension are based on the representation of fuzzy subset union. In this paper, we introduce the decomposition theorems for the representation of upper cut set, lower cut set, lower heavy cut set and upper heavy cut set, and the corresponding four cut sets based on the representation of intersection, give the extension principle of the rough fuzzy set based on the four cut sets with theoretical proof in detail.

Key words: rough fuzzy set, cut set, representation of intersection, decomposition theorem, extension principle

中图分类号:

O159

何天荣. 四种截集形式粗糙模糊集扩展原理的交表示[J]. 楚雄师范学院学报, 2023, 38(3): 96-102.

HE Tianrong. Intersection Representation of Four Cut Sets of Rough Fuzzy Set Extension Principle[J]. Journal of Chuxiong Normal University, 2023, 38(3): 96-102.

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