| AFS (Axiomatic Fuzzy Sets) theory was proposed by Professor Liu Xiaodong in 1995. It can be applied to study the law of human thinking and is easily operated by computers. It is a mathematical abstract of the mechanisms of decompose and compose of human conceptions. And it preferably opened out both the essential mechanism that human describe complex fuzzy conceptions depending on experiences and intuitions and the essential mechanism that human choosing the corresponded membership functions. AFS theory applies topological molecular lattices to human conceptions. In the framework of AFS theory, operations are more objective, rigor and unity.Fuzzy cognitive map (FCM) offers a far more flexible and powerful framework for representing human knowledge and for reasoning. In FCM, it is able to represent all types of concepts and express the arcs (edges) connecting these concepts in terms of symbols or numeric values. As a new crossed field of multiple applied subjects, data mining absorbed nutrition from many subjects and played a more and more important role in variety activities of designs-making. How to make use of the rich data to serve human being effectively has already become one of the focuses of all the information fields.This paper introduces the AFS theory systemic from five aspects: AFS algebra, AFS structure, AFS fuzzy logic system, the basic ideas and the engineering meaning also presents a brief review of the developments and applications about Fuzzy Cognitive Maps, data mining and AFS theory. It also analyses the problems existing in the Fuzzy Cognitive Maps and points out there is advantage using AFS theory to study Fuzzy Cognitive Maps. A set of rigorous, systemic and unitize analytic and design method about Fuzzy Cognitive maps have been studied. This paper also discusses the significance, the main problems the foreground about the study of Fuzzy Cognitive Maps based on AFS theory and its application on data mining.
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