Functional Analysis and T-S Fuzzy System Design
| Authors: | Qiu Renxi, MEC, Cardiff University, United Kingdom
Pham D.T., MEC, Cardiff University, United Kingdom |
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| Topic: | 5.1 Manufacturing Plant Control |
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| Session: | Advanced Manufacturing Applications |
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| Keywords: | Fuzzy hybrid systems, Fuzzy inference, Fuzzy logic, Fuzzy modelling, Function approximation, Transforms |
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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.
