Lift, leverage, and conviction are three of the best commonly known interest measures for crisp association rules. All of them are based on a comparison of observed support and the support that is expected if the antecedent and consequent part of the rule were stochastically independent. The aim of this paper is to provide a correct definition of lift, leverage, and conviction measures for fuzzy association rules and to study some of their interesting mathematical properties. 1. Introduction Searching for association rules is a broadly discussed, developed, and accepted data mining technique [1, 2]. An association rule is an expression , where antecedent and consequent are conditions, the former usually in the form of elementary conjunction and the latter being usually atomic. Such rules are usually interpreted as the following implicational statement: “if is satisfied then is true very often too.” Naturally, analysts are interested only in such rules that are somehow interesting, unusual, or exceptional. To assess rule interestingness objectively, there have been developed many measures of rule interest or intensity. Among the most essential, support and confidence are traditionally considered. An objective of association rules mining is to find rules with support and confidence above some user-defined thresholds. Searching for association rules fits particularly well on binary or categorical data and many have been written on that topic [1–4]. For association analysis on numeric data, a prior discretization is proposed, for example, by Srikant and Agrawal [5]. Another alternative is to take an advantage of fuzzy logic [6]. The use of fuzzy logic in connection with association rules has been motivated by many authors (see e.g., [7] for recent overview). Fuzzy association rules are appealing also because of the use of vague linguistic terms such as “small” and “very big” [8–11]. In this paper, we focus on three measures of rule intensity that are all based on comparison between the observed support and the support that is expected under the assumption of independence of the rule’s antecedent and consequent. These measures are lift, leverage, and conviction. All of them were initially developed for nonfuzzy (i.e., “crisp”) association rules. Lift was firstly described in [12] under its original name “interest.” It was well studied for association rules on binary data in [13, 14]. Lift is defined as a ratio of observed support to the support that is expected under the assumption of independence of and . On the other hand, leverage [15] measures the
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