形式模糊背景中单边模糊概念格的属性约简

Attribute reduction of single-sided fuzzy concept lattice in formal fuzzy contexts

形式概念分析是一种有效的知识表示和知识发现的方法,形式背景和形式概念是形式概念分析中的两个基本概念.形式背景描述了对象集和属性集间的一个二元经典关系,隐含其中的知识通过概念格的形式表示出来.形式模糊背景是形式背景在模糊集理论下的自然推广,建立在其上的模糊概念格在实际应用中面临许多困难,为此,多种形式的模糊概念格的改进形式应运而生.单边模糊概念格就是一种具有较好应用前景的改进模糊概念格.主要研究基于经典-模糊概念格的形式模糊背景的属性约简问题,这里属性约简的概念具有保持相应的概念格整体结构不变的含义.关于属性约简,给出了多种形式的属性约简判定定理,针对属性约简,将所有属性分为三类,探究了不同类型属性的特征刻画.最后,通过引入模糊概念间的辨识属性集的概念,得到了基于辨识属性矩阵的属性约简方法,并通过示例验证了属性约简方法的可行性.

Formal concept analysis is an effective method of knowledge representation and knowledge discovery,in which formal context and formal concept are two basic concepts.A formal context is just a binary classical relation between an object set and an attribute set,and the knowledge hidden in which is represented by a concept lattice.Formal fuzzy context is a natural extension of formal context in fuzzy set theory,the fuzzy concept lattice based on formal fuzzy context meets many difficulties in practical application,so that some modified fuzzy concept lattice are proposed.One-sided fuzzy concept lattice is just a kind of modified fuzzy concept lattices with better application prospect.This paper mainly focus on the study of attribute reduction of formal fuzzy contexts based on the classic-fuzzy concept lattices,where,notion of attribute reduction means keeping the whole structure of the corresponding concept lattices unchanged.With respect to the attribute reducts,a variety of judgement theorems for the attribute reducts are given.Based on the attribute reducts,all attributes are divided into three classes,and different types of attributes are characterized by different features.Finally,by introducing a notion of discernible attribute set between concepts,a method of attribute reduction is established,and the feasibility of the attribute reduction method is verified by an example.