Concept lattices and order in fuzzy logic
Concept lattices and order in fuzzy logic
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DOI：
10.1016/j.apal.2003.01.001
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发表时间：
2004-08
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影响因子：
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通讯作者：
R. Belohlávek
中科院分区：
文献类型：
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作者：
R. Belohlávek
本文从模糊逻辑的观点探讨了概念格（Port-Royal学派意义上的概念层次结构）理论。偏序、格序和形式概念的概念被推广到模糊集。给出了一个刻画形式模糊概念层次结构的定理。此外，作为本方法的一个应用，Dedekind-MacNeille完成的部分模糊顺序进行了说明。该方法和结果为模糊数据的形式概念分析提供了基础：形式概念分析的输入数据命题“对象x具有属性y”也可以有中间真值，更符合实际。
The theory of concept lattices (i.e. hierarchical structures of concepts in the sense of Port-Royal school) is approached from the point of view of fuzzy logic. The notions of partial order, lattice order, and formal concept are generalized for fuzzy setting. Presented is a theorem characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context. Also, as an application of the present approach, Dedekind–MacNeille completion of a partial fuzzy order is described. The approach and results provide foundations for formal concept analysis of vague data—the propositions “object x has attribute y”, which form the input data to formal concept analysis, are now allowed to have also intermediate truth values, meeting reality better.