T2RFIS: type-2 regression-based fuzzy inference system

Abstract

This article discusses a novel type-2 fuzzy inference system with multiple variables in which no fuzzy rules are explicitly defined. By using a rule-free system, we avoid the serious disadvantage of rule-based systems, which are burdened with the curse of dimensionality. In the proposed system, Gaussian membership functions are used for its inputs, and linearly parameterized system functions are used to obtain its output. To obtain the system parameters, a genetic algorithm with multi-objective function is applied. In the presented method, the genetic algorithm is combined with a feature selection method and a regularized ridge regression. The objective functions consist of a pair in which one function is defined as the number of active features and the other as the validation error for regression models or the accuracy for classification models. In this way, the models are selected from the Pareto front considering some compromise between their quality and simplification. Compared to the author’s previous work on the regression-based fuzzy inference system, a new inference scheme with type-2 fuzzy sets has been proposed, and the quality has been improved compared to the system based on type-1 fuzzy sets. Four experiments involving the approximation of a function, the prediction of fuel consumption, the classification of breast tissue, and the prediction of concrete compressive strength confirmed the efficacy of the presented method.