Mining Fuzzy Association Rules in the Framework of AFS Theory

In this paper, firstly we study the representations and fuzzy logic operations for the fuzzy concepts in real data systems. Secondly, we propose a new fuzzy association rule mining algorithm in the framework of AFS (Axiomatic Fuzzy Sets) theory. Compared with the current algorithms, the advantage of proposed algorithm has two advantages. One is that the membership functions of the fuzzy sets representing the extracted rules and the fuzzy logic operations applied to extract fuzzy rules are determined by the distribution of the data, instead of the fuzzy sets defined by some special functions, t-norm, t-conorm, negation operator, implication operator and fuzzy similarity relation given in advance. The extracted fuzzy rules are interpretable and similar to human intuition. Another is that its simplicity in implementation and mathematical beauty in fuzzy theory, and can be directly applied to extract fuzzy association rules in real data systems. Finally, a well-known example Iris dataset is used to illustrate the effectiveness of the new algorithm based on the proposed degrees of implication. We obtained reclassification accuracy 98 %.