Attribute reduction in intuitionistic fuzzy formal concepts

Abstract

Knowledge acquisition in intuitionistic fuzzy information systems is of importance because those fuzzy information systems are often encountered in many real-life problems. Formal concept analysis is a simple and effective tool for knowledge acquisition. However, there is still little work on introducing knowledge acquisition methods based on formal concept analysis into intuitionistic fuzzy information systems. This paper mainly extends the formal concept theory into intuitionistic fuzzy information systems. Firstly, two pairs of adjoint mappings are defined in intuitionistic fuzzy formal contexts. It is verified that both pairs of adjoint mappings form Galois connections. Secondly, two types of intuitionistic fuzzy concept lattices are constructed. After that, we also present the main theorems and propositions of the intuitionistic fuzzy concept lattices. Thirdly, we deeply discuss the attribute characteristics for type-1 generalized one-sided intuitionistic fuzzy concept lattice. Furthermore, a discernibility matrix-based algorithm is proposed for attribute reduction and the effectiveness of this algorithm is demonstrated by a practical example. The construction of intuitionistic fuzzy conceptS is meaningful for the complex and fuzzy information in real life.