Notes on the lattice of fuzzy rough sets with crisp reference sets

被引：3

作者：

Gegeny, David ^{[1
]}

Kovacs, Laszlo ^{[2
]}

Radeleczki, Sandor ^{[1
]}

机构：

[1] Univ Miskolc, Inst Math, H-3515 Miskolc, Hungary

[2] Univ Miskolc, Dept Informat Technol, H-3515 Miskolc, Hungary

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2020年 / 126卷

关键词：

Fuzzy rough set; Lower and upper approximation; Fuzzy equivalence; Uncertain knowledge; Regular double Stone lattice; Dually well-ordered set;

D O I：

10.1016/j.ijar.2020.08.007

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Since the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine one of these approaches, namely fuzzy rough sets with crisp reference sets, from a lattice-theoretic point of view. We connect the lower and upper approximations of a fuzzy relation R to the approximations of the core and support of R. We also show that the lattice of fuzzy rough sets corresponding to a fuzzy equivalence relation R and the crisp subsets of its universe is isomorphic to the lattice of rough sets for the (crisp) equivalence relation E, where E is the core of R. We establish a connection between the exact (fuzzy) sets of R and the exact (crisp) sets of the support of R. (C) 2020 The Authors. Published by Elsevier Inc.

引用

页码：124 / 132

页数：9

共 26 条

[1]

[Anonymous], 1997, Rough Sets and Data Mining, DOI DOI 10.1007/978-1-4613-1461-5_15

[2]

[Anonymous], 1993, ALGEB METHODS LOGIC, DOI DOI 10.4064/-28-1-117-124

[3]

[Anonymous], 1988, Bull. Polish Acad. Sci. Math.

[4]

[Anonymous], 1992, Bull. Pol. Acad. Sci., Math.