In this paper, we propose an index that helps preserve the semantic interpretability of linguistic fuzzy models while a tuning of the membership functions (MFs) is performed. The proposed index is the aggregation of three metrics that preserve the original meanings of the MFs as much as possible while a tuning of their definition parameters is performed. Additionally, rule-selection mechanisms can be used to reduce the model complexity, which involves another important interpretability aspect. To this end, we propose a postprocessing multiobjective evolutionary algorithm that performs rule selection and tuning of fuzzy-rule-based systems with three objectives: accuracy, semantic interpretability maximization, and complexity minimization. We tested our approach on nine realworld regression datasets. In order to analyze the interaction between the fuzzy-rule-selection approach and the tuning approach, these are also individually proved in a multiobjective framework and compared with their respective single-objective counterparts. We compared the different approaches by applying nonparametric statistical tests for pairwise and multiple comparisons, taking into consideration three representative points from the obtained Pareto fronts in the case of the multiobjective-based approaches. Results confirm the effectiveness of our approach, and a wide range of solutions is obtained, which are not only more interpretable but are also more accurate.Index Terms-Fuzzy-rule-based systems (FRBSs), multiobjective evolutionary algorithms (MOEAs), rule selection, semantic interpretability index, tuning.
Recently, multi-objective evolutionary algorithms have been applied to improve the difficult tradeoff between interpretability and accuracy of fuzzy rule-based systems. It is known that both requirements are usually contradictory, however, these kinds of algorithms can obtain a set of solutions with different trade-offs. This contribution analyzes different application alternatives in order to attain the desired accuracy/interpr-etability balance by maintaining the improved accuracy that a tuning of membership functions could give but trying to obtain more compact models. In this way, we propose the use of multiobjective evolutionary algorithms as a tool to get almost one improved solution with respect to a classic single objective approach (a solution that could dominate the one obtained by such algorithm in terms of the system error and number of rules). To do that, this work presents and analyzes the application of six different multi-objective evolutionary algorithms to obtain simpler and still accurate linguistic fuzzy models by performing rule selection and a tuning of the membership functions. The results on two different scenarios show that the use of expert knowledge in the algorithm design process significantly improves the search ability of these algorithms and that they are able to improve both objectives together, obtaining more accurate and at the same time simpler models with respect to the single objective based approach.
This work proposes the application of Multi-Objective Genetic Algorithms to obtain Fuzzy Rule-Based Systems with a better trade-off between interpretability and accuracy in linguistic fuzzy modelling problems. To do that, we present a new post-processing method that by considering selection of rules together with tuning of membership functions gets solutions only in the Pareto zone with the highest accuracy, i.e., containing solutions with the least number of possible rules but still presenting high accuracy. This method is based on the well-known SPEA2 algorithm, applying appropriate genetic operators and including some modifications to concentrate the search in the desired Pareto zone.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.