FRIwE: Fuzzy Rule Identification With Exceptions

Abstract

Abstract-In this paper, the FRIwE method is proposed to identify fuzzy models from examples. Such a method has been developed trying to achieve a double goal:accuracy and interpretability. In order to do that, maximal structure fuzzy rules are firstly obtained based on a method proposed by Castro et al. In a second stage, the conflicts generated by the maximal rules are solved, thus increasing the model accuracy. The resolution of conflicts are carried out by including exceptions in the rules. This strategy has been identified by psychologists with the learning mechanism employed by the human being, thus improving the model interpretability. Besides, in order to improve the interpretability even more, several methods are presented based on reducing and merging rules and exceptions in the model. The exhaustive use of the training examples gives the method a special suitability for problems with small training sets or high dimensionality. Finally, the method is applied to an example in order to analyze the achievement of the goals.

Specialization models for a general fuzzy set covering framework

“…Very few fuzzy rule learners use internally disjunctive description languages, and most fuzzy rule learners use purely conjunctive languages. An example of a fuzzy rule learner that uses internal disjunction is [2].…”

Sensitivity analysis of fuzzy rule-based classification systems by means of the Lipschitz condition

“…The first employs merging of simple fuzzy rules and the second searches over all possible rules. In the first approach (see Carmona et al 2004;Castro et al 1999;Pitambare and Kamde 2013), first simple fuzzy rules of the type (a) around individual (or small groups of) data points are derived and then these are merged into bigger rules. In the merging procedure, two (or more) adjacent fuzzy rules are merged together.…”

“…As this rule should replace the two original fuzzy rules, following Carmona et al (2004), Castro et al (1999) and Pitambare and Kamde (2013), for the new fuzzy set A = (A 1 or B 1 ), we get μ (A 1 or B 1 ) = min(1, μ A 1 + μ B 1 ), i.e., 'or' connective is modeled by the truncated addition. If A 1 and B 1 are two adjacent triangular fuzzy sets of granularity G, the fuzzy set A = (A 1 or B 1 ) will be a trapezoidal fuzzy set (see Fig.…”

“…For these cases in Carmona et al (2004), rules with exceptions were introduced. If we assume a fuzzy rule IF p 1 is (A 1 1 or .…”

A Fuzzy Inductive Algorithm for Modeling Dynamical Systems in a Comprehensible Way

“…The membership function of an interval is defined as where is a t-conorm (4) Assuming that each input variable takes a linguistic interval as value , the description of a dynamical system at an instant will be given by means of the set of intervals that each input variable takes at that instant, i.e., . In abstract, an instant description is an ordered set of intervals defined on variables .…”