Abstract
Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.
Highlights
Concept lattice, which is called Galois lattice, stems from the so-called formal concept analysis that was proposed by Wille in 1982 [1], which is oriented towards the discovery and design of concept hierarchies from relational databases
In paper [52], the discernibility matrix was proposed by using of the cuts of IF sets and established the method of the attribute reduction of IF concept lattice, but for the requirement of knowledge handling systems, combining IF set theory and formal concept analysis theory may result in a new hybrid mathematical structure from other views, such as [53]
The attribute reduction of IF generalized consistent decision formal context is introduced and we investigate the relation with the reduction based on the implication mappings
Summary
Concept lattice, which is called Galois lattice, stems from the so-called formal concept analysis that was proposed by Wille in 1982 [1], which is oriented towards the discovery and design of concept hierarchies from relational databases. In paper [52], the discernibility matrix was proposed by using of the cuts of IF sets and established the method of the attribute reduction of IF concept lattice, but for the requirement of knowledge handling systems, combining IF set theory and formal concept analysis theory may result in a new hybrid mathematical structure from other views, such as [53]. Attribute reduction is to find the minimum conditional attribute set that can keep the generalized consistence of the IF decision formal context Does it make the discovery of implicit knowledge easier and the representation simpler in data, but it extends the theory of concept lattice. The attribute reduction of IF generalized consistent decision formal context is introduced and we investigate the relation with the reduction based on the implication mappings.
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