Abstract
The hesitant fuzzy set (HFS) can reflect the hesitation and uncertainty of decision-makers for the reason that it uses some possible values instead of a certain value. Considering that there is still no research on concept lattice or fuzzy formal concept analysis (FFCA) in a hesitant fuzzy environment, in this paper, we propose the definition and the related theory of hesitant fuzzy concept lattice. Firstly, we propose the hesitant fuzzy formal concept analysis theory and study the definition of hesitant fuzzy concept lattice. Secondly, we provide two effective reduction methods of hesitant fuzzy formal context and discuss the differences of them. Thirdly, we propose an incremental construction algorithm to construct the hesitant fuzzy concept lattice. After that, we study the similarity calculation method of hesitant fuzzy concepts. Finally, we design a practical application to validate the hesitant fuzzy concept lattice theory, which is proven to be correct and effective.
Highlights
Concept lattice was first proposed by Wille [1] in 1982, which is a mathematical tool for data analysis and knowledge processing
We mainly observe two principles: 1) In order to reduce the scale of the concept lattice and extract essential knowledge, the simplification process of the hesitant fuzzy formal context ought to be arranged before generating the concept lattice nodes
In this paper, the following innovative achievements have been achieved: Firstly, we introduced the hesitation fuzzy set theory into the formal context, and built the hesitant fuzzy formal context, and we studied the formal concept analysis theory with hesitant fuzzy information
Summary
Concept lattice was first proposed by Wille [1] in 1982, which is a mathematical tool for data analysis and knowledge processing. FFCA we give some related concepts of Fuzzy Concept Lattice theory, which are defined as follows: Definition 1 [17]: The triple K = (G, M , I = ψ (G × M )) is called a fuzzy formal context, where G and M represent a finite set of objects and a finite set of attributes respectively, I is a fuzzy relationship subset which is defined on G × M , and each fuzzy relationship (g, m) ∈ I has a corresponding membership v (g, m) ∈ [0, 1]. If X1 ∈ X2 and (X1, Y1) ≤ (X2, Y2), the complete lattice constructed by this partial order relation is called the fuzzy concept lattice of the fuzzy formal context K at the confidence threshold λ.
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