Fuzzy Implicative Rules: A Unified Approach

Rule mining algorithms are one of the fundamental techniques in data mining for discovering significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rules to provide a solid theoretical framework for any fuzzy rule mining algorithm interested in capturing patterns in terms of logical conditionals rather than the co-occurrence of antecedent and consequent. In particular, we study which properties the fuzzy operators should satisfy to ensure a coherent behavior of different quality measures. As a consequence of this study, we introduce a new property of fuzzy implications related to a monotone behavior of the generalized modus ponens for which we provide several valid solutions. Also, we prove that our modeling generalizes other approaches if an adequate choice of the fuzzy implication is made, so it can be seen as an unifying framework. We test the applicability and relevance of our framework on different real datasets and with different fuzzy operators.