Fuzzy association rules: general model and applications

Abstract

Abstract-The theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data. In this paper, we are concerned with the development of a general model to discover association rules among items in a (crisp) set of fuzzy transactions. This general model can be particularized in several ways; each particular instance corresponds to a certain kind of pattern and/or repository of data. We describe some applications of this scheme, paying special attention to the discovery of fuzzy association rules in relational databases.

Agents that Learn How to Generate Arguments from Other Agents

“…Thus, the set of observed facts and the argument constitute a fuzzy transaction [8]. We will brie y describe the basic concepts about mining fuzzy generalized association rules below.…”

“…In our work, we assume a more general de nition of fuzzy transactions and fuzzy association rules that was presented by Delgado et al [8]. A fuzzy transaction is a nonempty fuzzy subset t ⊆ I.…”

“…For every i j ⊆ I, m ti (i j ) de nes the membership degree of i j in a fuzzy transaction t j , and m ti (I 0 ) is the degree of inclusion of an itemset I 0 ⊆ I in a fuzzy transaction t j , de ned as m ti (I 0 ) = min i j ∈ I 0 m ti (i j ). Then, let I be a set of items, D a set fuzzy transactions, A, C ⊆ I with A, C = ∅, and A ∩ C = ∅, a fuzzy association rule A → B holds in T i m ti (A) ≤ m ti (C) ∀t i ∈ D. This de nition preserves the meaning of association rules, due to the fact that if we assumed A ⊆ t i in some sense, we must assume C ⊆ t i given that m ti (A) ≤ m ti (C) [8].…”

“…In the context of our work, we see the facts observed in the negotiation context when an argument is generated as a fuzzy set, where each fact has a degree of membership as regards the semantic relation between the fact and the argument. Thus, these sets of observed facts and arguments constitute fuzzy transactions [8]. Consequently, uncertainty is taken into account during the mining process.…”

Fuzzy Frequent Pattern Mining in Spike Trains

“…We start by presenting a generalization of the standard frequent pattern mining problem based on what we call fuzzy transactions, which we refer to as the fuzzy frequent pattern mining problem-which however differs from other known fuzzy generalizations in the literature that receive the same name, such as e.g. that introduced in [15], based on the consideration of transactions with potentially missing items, or in [16], where fuzzy membership (to a transaction) is assigned to items.…”