Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory

被引：155

作者：

Lai, Hongliang ^{[1
]}

Zhang, Dexue ^{[1
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2009年 / 50卷 / 05期

关键词：

Formal concept analysis; Rough set theory; Concept lattice; Complete residuated lattice; Fuzzy closure system; Fuzzy opening system; The law of double negation; ORDER;

D O I：

10.1016/j.ijar.2008.12.002

中图分类号：

TP18 [人工智能理论];

学科分类号：

140502 [人工智能];

摘要：

This paper presents a comparative study of concept lattices of fuzzy contexts based on formal concept analysis and rough set theory. It is known that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on formal concept analysis [R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277-298]. This paper shows that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on rough set theory if and only if the residuated lattice (L, *, 1) satisfies the law of double negation. Thus, the expressive power of concept lattices based on rough set theory is weaker than that of concept lattices based on formal concept analysis. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：695 / 707

页数：13

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