UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured fuzzy rules

Abstract

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules. Indeed, each rule should evaluate all input variables in its antecedent part. Thus, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Consequently, the FIS’s performance, generalizability, and interpretability are restricted by the aforementioned limitation. This study provides a neuro-fuzzy inference system that can create each fuzzy rule taking into account various sets of input variables in order to handle this problem. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, the consequent part of the Takagi–Sugeno–Kang FIS is properly changed to consider only the selected set of input variables. To learn the parameters of the proposed architecture, the Levenberg–Marquardt (LM) method is used for regression problems. For classification applications, a trust-region-based learning method (General quasi-Levenberg–Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification and regression problems. Based on these comparisons, the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy rules.