Abstract
In this chapter, based on the original idea of Wille of formal concept analysis and the AFS (Axiomatic Fuzzy Set) theory, we presents a rigorous mathematical treatment of fuzzy formal concept analysis referred to as an AFS Formal Concept Analysis (AFSFCA). It naturally augments the existing formal concepts to fuzzy formal concepts, with the aim of deriving their mathematical properties and applying them in the exploration and development of knowledge representation. Compared with other fuzzy formal concept approaches such as the L-concept [1,2] and the fuzzy concept [48], the main advantages of AFSFCA are twofold. One is that the original data and facts are the only ones required to generate AFSFCA lattices thus human interpretation is not required to define the fuzzy relation or the fuzzy set on G×M to describe the uncertainty dependencies between the objects in G and the attributes in M. Another advantage comes with the fact that is that AFSFCA is more expedient and practical to be directly applied to real world applications.
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