Examples, counterexamples, and measuring fuzzy associations

This paper examines the measurement of the degree to which tuples in a database support a relation among attributes based on a comparison of the number of examples and counterexamples of the relation. In particular, we are concerned with associations that represent imprecise constraints placed upon the value of one attribute by those of other attributes. Associations of this form may be described by fuzzy rules and the analysis requires an assessment of the degree to which a tuple satisfies the imprecise constraint specified by the rule. Standard measures of rule validity are extended to fuzzy associations based on the degree that the tuples are examples, counterexamples, or irrelevant to imprecise relations. A scaling of the relevance of a tuple is proposed to minimize the impact of the accumulation of small membership values on the confidence-based validity measures.