文档介绍：Design Optimization of Fuzzy Logic Systems
Paolo Dadone
Dissertation submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
in
Electrical Engineering
Hugh F. VanLandingham, Chair
William T. Baumann
Subhash C. Sarin
Hanif D. Sherali
Dusan Teodorovic
May 18, 2001
Blacksburg, Virginia
Keywords: Fuzzy logic systems, Supervised learning, Optimization,
Non-differentiable optimization
Copyright 2001. Paolo Dadone
Design Optimization of Fuzzy Logic Systems
Paolo Dadone
(ABSTRACT)
Fuzzy logic systems are widely used for control, system identification, and pattern
recognition problems. In order to maximize their performance, it is often necessary to
undertake a design optimization process in which the adjustable parameters defining a
particular fuzzy system are tuned to maximize a given performance criterion. Some data
to approximate monly available and yield what is called the supervised learning
problem. In this problem we typically wish to minimize the sum of the squares of errors
in approximating the data.
We first introduce fuzzy logic systems and the supervised learning problem that, in
effect, is a nonlinear optimization problem that at times can be non-differentiable. We
review the existing approaches and discuss their weaknesses and the issues involved. We
then focus on one of these problems, ., non-differentiability of the objective function,
and show how current approaches that do not account for non-differentiability can
diverge. Moreover, we also show that non-differentiability may also have an adverse
practical impact on algorithmic performances.
We reformulate both the supervised learning problem and piecewise linear membership
functions in order to obtain a