Design optimization of fuzzy logic system

Design Optimization of Fuzzy Logic Systems Fuzzy logic systems are widely used for control, system identification, and patternrecognition problems. In order to maximize their performance, it is often necessary toundertake a design optimization process in which the adjustable parameters defining aparticular fuzzy system are tuned to maximize a given performance criterion. Some datato approximate are commonly available and yield what is called the supervised learningproblem. In this problem we typically wish to minimize the sum of the squares of errorsin approximating the data.We first introduce fuzzy logic systems and the supervised learning problem that, ineffect, is a nonlinear optimization problem that at times can be non-differentiable. Wereview the existing approaches and discuss their weaknesses and the issues involved. Wethen focus on one of these problems, i.e., non-differentiability of the objective function,and show how current approaches that do not account for non-differentiability candiverge. Moreover, we also show that non-differentiability may also have an adversepractical impact on algorithmic performances.We reformulate both the supervised learning problem and piecewise linear membershipfunctions in order to obtain a polynomial or factorable optimization problem. We proposethe application of a global nonconvex optimization approach, namely, a reformulationand linearization technique. The expanded problem dimensionality does not make thisapproach feasible at this time, even though this reformulation along with the proposed