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Functional analysis and T-S fuzzy system design

By Duc Truong Pham and Renxi Qiu

Abstract

This paper introduces the idea of viewing fuzzy modelling and fuzzy system design from a functional analysis perspective. Fuzzy transforms, which are based on the generalised Fourier transform in functional analysis, are proposed. It is demonstrated that, mathematically, a T-S fuzzy model is equivalent to a fuzzy transform. Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function. The functional point of view leads to an insight into the behaviour of a fuzzy system. It provides a theoretical basis for exploring improvements to the efficiency of T-S fuzzy modelling

Topics: TA
Publisher: International Federation of Automatic Control
Year: 2005
DOI identifier: 10.3182/20050703-6-cz-1902.01473
OAI identifier: oai:http://orca.cf.ac.uk:36193
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