Improving interpretability in approximative fuzzy models via multiobjective evolutionary algorithms

Abstract

Current research lines in fuzzy modeling mostly tackle improving the accuracy in descriptive models and improving of the interpretability in approximative models. This article deals with the second issue, approaching the problem by means of multiobjective optimization in which accuracy and interpretability criteria are simultaneously considered. Evolutionary algorithms are especially appropriated for multiobjective optimization because they can capture multiple Pareto solutions in a single run of the algorithm. We propose a multiobjective evolutionary algorithm to find multiple Pareto solutions~fuzzy models! showing a trade-off between accuracy and interpretability. Additionally, neural-network-based techniques in combination with ad hoc techniques for improving interpretability are incorporated into the multiobjective evolutionary algorithm to improve the efficiency of the algorithm.

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

“…For high-dimensional problems in a continuous input-output domain where precise numerical prediction is required, such models require a significant number of fuzzy rules, which can potentially exponentially increase when the dimensionality of the problem is increased. Some applications of multi-objective optimisation techniques have also been discussed in the literature [26][27][28][29] to study the trade-off between accuracy and interpretability of Takagi-Sugeno (TS) fuzzy models [10]. Compared with Mamdani fuzzy systems, TS fuzzy systems are relatively less transparent, since they replace the linguistic consequent parts of the Mamdani fuzzy systems with mathematical (deterministic) functions.…”

GP-COACH: Genetic Programming-based learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems

“…Carse and Pipe's special issue [13] includes papers focused on the multiobjective evolutionary learning [37], boosting [63] and evolutionary adaptive inference systems [5]. Casillas et al's special issue [19] is focused on the trade-off between interpretability and accuracy, collecting papers that proposed different GFSs for tackling this problem: with multiobjective approaches [47,39], and optimizing the definition for the linguistic variables [4,11].…”

Finite satisfiability of propositional interval logic formulas with multi-objective evolutionary algorithms

“…Three multi-objective Pareto-based evolutionary approaches have been used to solve F SAT A , namely, Preselection with niches (PSN), ENORA and NSGA-II; they differ from each other in the selection mechanism. PNS was initially developed in [14] for function approximation and dynamic modeling with TSK fuzzy models. ENORA was proposed in [20] for multi-objective constrained real parameter optimization.…”