Structure identification of fuzzy model.

*(English)*Zbl 0652.93010A 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) |

##### Keywords:

multi-input single-output nonlinear systems; local fuzzy models; Structure identification; verification criteria
PDF
BibTeX
XML
Cite

\textit{M. Sugeno} and \textit{G. T. Kang}, Fuzzy Sets Syst. 28, No. 1, 15--33 (1988; Zbl 0652.93010)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Takagi, T; Sugeno, M, Fuzzy identification of systems and its applications to modelling and control, IEEE trans. systems man cybernet., 15, 116-132, (1985) · Zbl 0576.93021 |

[2] | Ivakhnenko, A.G; Vysotskiy, V.N; Ivakhnenko, N.A, Principal versions of the minimum bias criterion for a model and an investigation of their noise immunity, Soviet automat. control, 11, 27-45, (1978) |

[3] | Ivakhnenko, A.G; Todua, M.M, Prediction of random processes using self-organization of the prediction equation — part 1. problems of simple medium-term prediction, Soviet automat. control, 5, 35-51, (1972) |

[4] | Kondo, T, Revised GMDH algorithm estimating degree of the complete polynomial, Trans. soc. instrument and control engrs., 22, 928-934, (1986), (in Japanese) |

[5] | Akaike, H, A new look at the statistical model identification, IEEE trans. automat. control, 19, 716-723, (1974) · Zbl 0314.62039 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.