On The Reduction Of Concept Lattice In Fuzzy Context

This paper studies the reduction of fuzzy concept lattices in fuzzy contexts.Firstly, we discuss the exact reduction and the approximate reduction in a concept lattice by means of the similarity relation. Beholavek studied the similarity relations between two fuzzy concept lattices L(U,A,I₁) and L(U,A,I₂). Inspired by his discussion, this paper studies the similarity relation between the fuzzy context (U, A, I) and its subcontext (U,D,I_D). Two new concepts of the extendable subcontext and unextend-able subcontext are introduced, and the similarity relations between the fuzzy context (U,A,I) and its subcontext(U, D, I_d) are defined respectively in the two cases. Then we propose the concepts of the exact reduction and the approximate reduction in fuzzy concept lattices. The exact reduction is the minimal attributes set such that L(U, A, I) and L(U,D,I_d) are isomorphic. In other words, the similarity between L(U,A,I) and L(U, D,I_D) equal to 1. The approximate reduction is the minimal attributes set such that the similarity between L(U, A, I) and L(U, D, I_d) is not less than a given value.Secondly, we studies the reduction of a fuzzy concept lattice in a fuzzy context by employing the variable precision concept under various precisions. The cut-context is studied. It is proved that the variable precision concept is isomorphic to the concept lattice induced by the cut-context in the same precision. Thus, we can convert the reduction of a variable precision concept into the reduction of the concept lattice induced by the cut-context in the same precision. Then we can use the method of attribute reduction proposed by [30] to obtain all of the reducts in the fuzzy concept lattices.