Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory II

In part II of this paper, firstly, we study the relationship between the AFS (Axiomatic Fuzzy Zet) and FCA (Formal Concept Analysis, which has become a powerful theory for data analysis, information retrieval, and Knowledge discovery) and some algebraic homomorphisms between the AFS algebras and the concept lattices are established. Then, the numerical approaches to determining membership functions proposed in part I of this paper are used to study the fuzzy description and data clustering problems by mimicking human reasoning process. Finally, illustrative examples show that the framework of AFS theory offers a far more flexible and effective approach to artificial intelligence system analysis and design with applications to knowledge acquisition and representations in practice. (C) 2006 Elsevier Inc. All rights reserved.