Structural optimization of fuzzy rule-based models: Towards efficient complexity management

Abstract

The primary aim of this study is concerned with the structural optimization of data-driven fuzzy rule-based systems (FRBS), with the intent of their complexity management. This is accomplished in two ways: the first one involves a structuralization of the antecedents and the second one deals with a structuralization of the consequents of the fuzzy rules. More specifically, this study contributes to the complexity management of fuzzy models by focusing on (i) the efficient arrangement (reduction) of the input spaces over which the antecedents of rules are formed and (ii) allocating the orders of local polynomial functions across the consequents of the rules. The originality of the study comes with the flexibility of FRBS that is endowed by admitting variability of input spaces standing in the antecedents of different rules as well as the variability of orders of polynomials (local functions) forming the consequents of the rules.Particle swarm optimization (PSO) is guided by the root mean squared error (RMSE) accuracy criterion to realize the efficient arrangement of input spaces and an allocation of the orders of the individual polynomials. In this optimization process, the Fuzzy C-Means (FCM) algorithm is employed to create fuzzy sets in the antecedents of the rules, while the standard Least Square Error (LSE) criterion is minimized to determine the coefficients of the polynomials in the consequents. The performance of the proposed model is quantified using some numeric data, including both synthetic and machine learning datasets.