Axiomatic approaches of fuzzy concept operators

Xiaoxue Song, Xia Wang, Wenxiu Zhang
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引用次数: 1

Abstract

In formal concept analysis, various fuzzy generalizations of formal concepts have been made. The fuzzy concept operators defined under the condition that the truth values (degrees) coming from a complete residuated lattice satisfy many interesting properties. Conversely, fuzzy concept operators can be characterized in terms of their properties. In this paper, the axiomatic approaches in the theory of fuzzy formal concept analysis based on a complete residuated lattice are presented. In the axiomatic approach, the fuzzy conceptual knowledge system is defined, and axiom sets satisfied by the fuzzy conceptual knowledge system are stated. It is proved that axioms of the fuzzy conceptual knowledge system guarantee the existence of certain types of binary fuzzy relations producing the same fuzzy formal concepts. The independence of axiom sets characterizing the fuzzy conceptual knowledge system is examined.
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模糊概念算子的公理化方法
在形式概念分析中,对形式概念进行了各种模糊推广。模糊概念算子是在来自完全剩馀格的真值(度)满足许多有趣性质的条件下定义的。相反,模糊概念算子可以根据其性质来表征。本文给出了基于完全剩馀格的模糊形式概念分析理论中的公理化方法。在公理化方法中,定义了模糊概念知识系统,给出了模糊概念知识系统所满足的公理集。证明了模糊概念知识系统的公理保证了产生相同模糊形式概念的某些类型的二元模糊关系的存在。研究了表征模糊概念知识系统的公理集的独立性。
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