Design Evaluation of Learning Type Fuzzy Inference Using Trapezoidal Membership Function

Abstract

Trapezoidal fuzzy inference is a general form of triangular fuzzy reasoning, that has proven to be effective at solving various types of inference problems. When used as a clustering method, fuzzy inference allows for adjusting cluster boundaries with each new datapoint. In trapezoidal fuzzy inference, both the membership function for the antecedent part and the singleton real value of the consequent part need to be learned. However, in typical applications of fuzzy inference, there is not much discussion of the appropriate way to construct fuzzy rules as a design problem. For example, when coding program, it is not clear how to determine the learning coefficients of the membership function and singleton, how to set their initial values, or how to schedule the learning sequence of the various parts of fuzzy rules. In this paper, we frame the problem of parameter adjustment for fuzzy rules not as a tuning problem but rather, as a design problem. We focus in particular on how to learn coefficients both for the membership functions of the antecedent part and the singletons of the consequent part, how to set initial values, and how to determine the learning sequence of consequent and antecedent parts. We start with a definition of trapezoidal fuzzy inference and introduce the steepest descent method for adjusting fuzzy rules. Next, we propose six new methods for initializing parameters, and five ways to schedule the learning sequence. We discuss the accuracy of the proposed design methods in light of quantitative evaluations performed on sample datasets.