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AbstractThis 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.
CitationPham D, Qiu R (2005) 'Functional analysis and T-S fuzzy system design', 16th IFAC World Congress - Prague , Elsevier.
TypeConference papers, meetings and proceedings