A Mechanism to Improve the Interpretability of Linguistic Fuzzy Systems with Adaptive Defuzzification based on the use of a Multi-objective Evolutionary Algorithm

Abstract

This paper proposes a mechanism that helps improve the interpretability of linguistic fuzzy ruled based systems with common adaptive defuzzification methods. Adaptive defuzzification significantly improves the system accuracy, but introduces weights associated with each rule of the rule base, decreasing the system interpretability. The suggested mechanism is based on three goals: 1) reducing the number of total rules considering that rule weight close to zero can be removed; 2) reducing the rules with weights coupled because rules with weights close to one do not need the weight, and 3) reducing rules triggered jointly, all of them by using several metrics and a proposed interpretability index. This is performed using a multi-objective evolutionary algorithm, obtaining a set of solutions with different trade-offs between accuracy and interpretability. In addition, it is important to note that adaptive defuzzification and therefore the proposal developed in this work can be used together with other methodologies to improve system interpretability and accuracy, so it can be viewed as an interesting component.

An efficient multi-objective evolutionary adaptive conjunction for high dimensional problems in linguistic fuzzy modelling

“…Furthermore, we also adopt the Two Set Coverage [30] (CS) ratio as a tool to compare the Pareto fronts of different multi-objective approaches. We also used this ratio in [31]. CS considers X', X'' $ X' as two sets of phenotype decision vectors and a' and a'' are two points belong to sets X' and X'', respectively.…”

Handling Highly-Dimensional Classification Tasks With Hierarchical Genetic Fuzzy Rule-Based Classifiers

“…If these performances do not degrade and the rule's consequent does not change, we accept the chance. Moreover, since removing a feature results in a generalization of the rule, we must also assure that the overlapping between rules describing the same class label does not increase, a fact that would negate any merits achieved through the token mechanism and the respective definition of the coverage function (13). The similarity between two fuzzy rules k and ℓ , describing the same class label j C , is calculated through the matching degrees of the patterns they cover:…”

“…3.1. Therefore, it is possible that in later iterations FaIRLiC will not be able to produce rules for some well-covered class labels, due to the definition of the coverage criterion (13). This is acceptable and even desirable, since it speeds up FaIRLiC in later stages of the algorithm.…”

“…3.1. Effectively, if all training patterns of a class label have been covered by rules produced in previous iterations, subsequent iterations will produce only one rule for this class, which will be rejected due to the zero value of the modified coverage criterion (13). To that extent, later invocations of FaIRLiC are performed faster than the initial ones.…”

“…The high interpretational properties of fuzzy rule-based systems is considered to be their main virtue, with a number of contributions in the last few years devoted in defining and increasing the degree of their interpretability. [7][8][9][10][11][12][13] The main drawback of linguistic FRBCSs is a possible loss in accuracy when dealing with complex classification tasks, resulting from the inflexibility introduced by the discretization of the feature space into a fixed number of fuzzy sets with predefined membership functions.…”