An efficient adaptive fuzzy inference system for complex and high dimensional regression problems in linguistic fuzzy modelling

Abstract

The use of adaptive connectors as conjunction operators in adaptive fuzzy inference systems is one of the methodologies, also compatible with others, to improve the accuracy of fuzzy rule-based systems by means of local adaptation of the inference process to each rule of the rule base. However, when dealing with such currently challenging issues as high-dimensional regression problems, adapting their parameters becomes difficult due to the exponential rule explosion.

In this paper, we propose to address the problem by using a new adaptive conjunction operator. This operator provides considerable advantages in efficiency while maintaining the accuracy. Moreover, it is completed with a multi-objective evolutionary algorithm as a search method due to its efficiency in achieving different balances between complexity and accuracy in the learned fuzzy systems.

An in-depth experimental study is performed to show the advantages of the proposal presented, using 17 regression problems of different size and complexity, using different rule bases, analyzing the multi-objective algorithms and Pareto fronts obtained and performing statistical analyses. It confirms its effectiveness in terms of efficiency, but also in terms of accuracy and complexity of the obtained models.