Implication-Based Fuzzy Association Rules

Abstract

Abstract. Fuzzy association rules provide a data mining tool which is especially interesting from a knowledge-representational point of view since fuzzy attribute values allow for expressing rules in terms of natural language. In this paper, we show that fuzzy associations can be interpreted in different ways and that the interpretation has a strong influence on their assessment and, hence, on the process of rule mining. We motivate the use of multiple-valued implication operators in order to model fuzzy association rules and propose quality measures suitable for this type of rule. Moreover, we introduce a semantic model of fuzzy association rules which suggests to consider them as a convex combination of simple association rules. This model provides a sound theoretical basis and gives an explicit meaning to fuzzy associations. Particularly, the aforementioned quality measures can be justified within this framework.

Fuzzy sets in machine learning and data mining

“…For example, the existence of different types of fuzzy rules [24] suggests that fuzzy associations can be interpreted in different ways and, hence, that the evaluation of an association cannot be independent of its interpretation. In particular, one can raise the question which generalized logical operators can reasonably be applied in order to evaluate fuzzy associations, e.g., whether the antecedent part and the consequent part should be combined in a conjunctive way (à la Mamdani rules) or by means of a generalized implication (as in implication-based fuzzy rules) [29]. Moreover, since standard evaluation measures for association rules can be generalized in many ways, it is interesting to investigate properties of particular generalizations and to look for an axiomatic basis that supports the choice of specific measures [22].…”

“…Formally, this leads to using different types of support and confidence measures for evaluating the quality (interestingness) of an association [29,20]. Consequently, it may happen that a data set supports a fuzzy association A B quite well in one sense, i.e., according to a particular semantics, but not according to another one.…”

A systematic approach to the assessment of fuzzy association rules

“…For example, since an implication is true if its antecedent is false, an object x with A(x) = 0 would fully support of a rule A B. As proposed in [21], a possible way out is to combine the implication A(x) B(x) conjunctively with the relevance of an object x for the rule, Rel A,B (x), thereby expressing that x supports A B if…”

Mining Fuzzy Association Rules in the Framework of AFS Theory

“…In [6], the algorithm proposed by Srikant and Agrawal proceeded by partitioning attribute domains into several intervals and transforming quantitative values into binary ones in order to apply the classical mining algorithm.Fuzzy set technology are applied to knowledge discovery by such as fuzzy extensions of association rules and approximate dependencies base on fuzzy sets, fuzzy logic operators, fuzzy implication operators and fuzzy similarity relations [7][8][9][10][11][12]. Other fuzzy extensions of association rules include, weighted association rules [13] and different fuzziness-related interestingness measures [14]. The mining results based on the above mentioned approaches for a data systems are all strongly dependent on the options of fuzzy logic operators, fuzzy implication operator, the membership functions defined for the fuzzy sets and the fuzzy similarity relation given in advance.…”