Transition Between TS Fuzzy Models and the Associated Convex Hulls by TS Fuzzy Model Transformation

Abstract

One of the primary objectives underlying the extensive 20-year development of the TS Fuzzy model transformation (originally known as TP model transformation) is to establish a framework capable of generating alternative Fuzzy rules for a given TS Fuzzy model, thereby manipulating the associated convex hull to enhance further design outcomes. The existing methods integrated into the TS Fuzzy model transformation offer limited capabilities in deriving only a few types of loose and tight convex hulls. In this article, we propose a radically new approach that enables the derivation of an infinite number of alternative Fuzzy rules and, hence, convex hulls in a systematic and tractable manner. The article encompasses the following key novelties. Firstly, we develop a Fuzzy rule interpolation method, based on the pseudo TS Fuzzy model transformation and the antecedent Fuzzy set rescheduling technique, that leads to a smooth transition between the Fuzzy rules and the corresponding convex hulls. Then, we extend the proposed concept with the antecedent Fuzzy set refinement and reinforcement technique to tackle large-scale problems characterized by a high number of inputs and Fuzzy rules. The paper also includes demonstrative examples to illustrate the theoretical key steps, and concludes with an examination of a real complex engineering problem to showcase the effectiveness and straightforward execution of the proposed convex hull manipulation approach.