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Structure identification of fuzzy model. (English) Zbl 0652.93010
A main idea of a class of models studied in this paper concerns a representation of a model of multi-input single-output nonlinear systems by means of a family of local fuzzy models. They make use of fuzzy implication statements; for the i-th model we get: if $$X_ 1$$ is $$A^ i_ 1$$ and $$X_ 2$$ is $$A^ i_ 2$$ and... and $$X_ p$$ is $$A^ i_ p$$ then $$y^ i=c_ 0+\sum^{p}_{j=1}c^ i_ j,x_ j$$, $$i=1,2,...,N$$ where $$A^ i_ 1,A^ i_ 2,...,A^ i_ p$$ are fuzzy sets describing linguistic labels for successive input variables refering to the i-th model while $$y^ i$$ results from a linear dependence between input and output variables. This type of dependence holds, however, only for a certain range of the values of the input variable. Then for any value of input variables $$x^ 0_ j,j=1,2,...,p$$, a truth value of the condition part is derived as a product of all components, namely, $$w^ i=\prod^{p}_{j=1}A^ i_ j(x^ 0_ j)$$ and the output y is calculated as $y=\sum^{N}_{i=1}w^ iy^ i/\sum^{N}_{i=1}w^ i.$ Structure identification for this class of models is introduced and relevant verification criteria are studied. Moreover, assuming a piecewise linear character of membership functions of fuzzy sets standing in the rules $$(A^ j_ i)$$, an algorithm of the adjustment of their parameters is provided.
Reviewer: W.Pedrycz

##### MSC:
 93B30 System identification 93C10 Nonlinear systems in control theory 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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##### References:
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