FUZZ-EQ: a data equalizer for boosting the discrimination power of fuzzy classifiers

Abstract

The definition of linguistic terms is a critical part of the construction of any fuzzy classifier. Fuzzy partitioning methods (FPMs) range from simple uniform partitioning to sophisticated optimization algorithms. In this paper we present FUZZ-EQ, a preprocessing algorithm that facilitates the construc-tion of meaningful fuzzy partitions regardless of the FPM used. The proposed approach is radically different from any existing FPM: instead of adjusting the fuzzy sets to the training data, FUZZ-EQ adjusts the training data to a hypothetical uniform partition before applying any FPM. To do so, the original data distribution is transformed into a uniform distribution by applying the probability integral transform. FUZZ-EQ allows FPMs to provide classifiers with more granularity on high density regions, increasing the overall discrimination capability. Additionally, we describe the procedure to reverse this transformation and recover the interpretability of linguistic terms. To assess the effectiveness of our proposal, we conducted an extensive empirical study consisting of 41 classification tasks and 9 fuzzy classifiers with different FPMs, rule induction algorithms, and rule structures. We also tested the scalability of FUZZ-EQ in Big Data classification problems such as HIGGS, with 11 million examples. Experimental results reveal that FUZZ-EQ significantly boosted the classification performance of those classifiers using the same linguistic terms for all rules, including state-of-the-art classifiers such as FARC-HD or IVTURS.