Granular fuzzy sets and three-way approximations of fuzzy sets

被引：14

作者：

Yao, Yiyu ^{[1
]}

Yang, Jilin ^{[2
]}

机构：

[1] Univ Regina, Dept Comp Sci, Regina, SK S4S 0A2, Canada

[2] Sichuan Normal Univ, Dept Comp Sci, Chengdu 610066, Sichuan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2023年 / 161卷

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Fuzzy set; Granular fuzzy set; Granular rough fuzzy set; Three-way approximation; Three-way decision; ROUGH SETS; DECISIONS;

D O I：

10.1016/j.ijar.2023.109003

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A Pawlak approximation space is a pair of a ground set/space and a quotient set/space, where the latter is induced by an equivalence relation on the former. With this two-space understanding, it is possible to lift any concepts and notions from the ground space to the quotient space. The results are granular versions that approximate the original concepts and notions. In this paper, we investigate the problem of lifting a fuzzy set in the ground space to granular fuzzy sets in the quotient space. By applying the principles of threeway decision, we introduce the idea of three-way granular approximations of fuzzy sets in terms of three granular fuzzy sets that represent the two extremes and one middle. The two extremes are given by granular rough fuzzy sets. We present several different ways to interpret and construct a middle.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：16

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