Improving a Fuzzy Association Rule-Based Classification Model by Granularity Learning based on Heuristic Measures over Multiple Granularities Michela Fazzolari and Rafael Alcal´ a Dept. of Computer Science and Artificial Intelligence University of Granada 18071 Granada, Spain Email: {fazzolari,alcala}@decsai.ugr.es Yusuke Nojima and Hisao Ishibuchi Dept. of Computer Science and Intelligent Systems Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai Osaka 599-8531, Japan Email: {nojima,hisaoi}@cs.osakafu-u.ac.jp Francisco Herrera Dept. of Computer Science and Artificial Intelligence University of Granada 18071 Granada, Spain Email: herrera@decsai.ugr.es Abstract—A multi-objective evolutionary fuzzy rule selection process extracts a subset of fuzzy rules from an initial set, by applying a multi-objective evolutionary algorithm. Two ap- proaches can be used to determine the number of terms (i.e. the granularity) associated with the linguistic variables that appear in the rules: a pre-established single granularity can be chosen, or a multiple granularities approach can be preferred. The latter favors a reduction in the number of extracted rules, but it also brings to a possible loss of interpretability. To prevent this problem, suitable granularities can be determined by applying automatic techniques before the initial rule generation process. In this contribution, we investigate how the application of a single granularity learning approach influences the performance of fuzzy associative rule-based classifiers. The aim is to reduce the complexity of the obtained models, trying to maintain a good classification ability. I. I NTRODUCTION A fuzzy rule-based system (FRBS) is composed of fuzzy rules. It has been frequently used in several fields and for a wide range of problems, such as classification, regression, modeling, control, etc. The fuzzy rules can be formulated by an expert or generated automatically considering numerical data that describe a certain phenomenon. To this aim, several techniques have been proposed in the past, but they usually aim to improve only the accuracy of the system, without considering the interpretability issue, which is one of the main advantages of FRBSs [1]. Among the proposed techniques, Evolutionary Algorithms (EAs) have been usefully applied, since they can generate automatically a fuzzy model by evolving its parameters in the evolutionary process. Initially, EAs only considered a single objective, but when the multi-objective problem was pointed out, they were extended to Multi-Objective Evolutionary Al- gorithms (MOEAs) [2], [3]. These algorithms can optimize multiple objectives and generate a group of solutions instead of a single one, in which each solution satisfies an objective with higher degree than the others. Therefore, MOEAs have been used to address the accuracy- interpretability trade-off in FRBSs [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. The hybridization between MOEAs and FRBSs is called Multi-Objective Evo- lutionary Fuzzy Systems (MOEFSs). In [10], [11], two of the most renowned works in the Evolutionary Multi-Objective Optimization (EMO) field, the authors have applied MOEAs to carry out a genetic fuzzy rule selection process, starting from an initial set of fuzzy rules. The aim is to obtain a set of Fuzzy Rule-Based Classifiers (FRBCs), considering two objectives at the same time: the classification accuracy and the number of rules. Then, in [13] a third objective was added to minimize the length of the rules. When performing evolutionary or genetic fuzzy rule se- lection, the appropriate number of Membership Functions (MFs) for each variable, i.e. the granularity, is not known beforehand. The two possibilities to address this problem are to previously fix a single granularity [10], [11] or to adopt multiple granularities [13]. The former approach is simpler, although the choice of the granularity is often performed by hand, and usually induces the generation of a high number of fuzzy rules. On the other hand, the multiple granularities approach is useful to reduce the number of rules in the obtained models, but the interpretability loss has often been pointed out. For this reason, in [17] the authors proposed a mechanism to identify appropriate single granularities while performing a multi-objective evolutionary fuzzy rule selection process, based on the proposal presented in [13]. The framework in- cludes four steps: a) first, a heuristic procedure is used to create a pre-specified number of promising fuzzy rules; b) then, for each attribute a single granularity is learnt, considering the frequency of used partitions and the importance of the rules extracted in the previous step; c) next, these granularities are used to extract again a pre-specified number of fuzzy rules; d) finally, a multi-objective evolutionary algorithm is used to perform the rule selection process. The present work proposes a method that combines the single granularity specification mechanism presented in [17] 44 978-1-4673-5899-6/13/$31.00 c 2013 IEEE