Journal of Japan Industrial Management Association
Online ISSN : 2432-9983
Print ISSN : 0386-4812
Approximation of Multi-Dimensional Mapping by Bernstein Polinomial and Fuzzy ID 3
Hidetomo ICHIHASHITetsuya MIYOSHIKazunori NAGASAKATadashi SHIRAI
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1996 Volume 47 Issue 2 Pages 69-76

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Abstract
Selection of the variables and nonlinear terms of polinomials for approximating nonlinear multi-dimensional mappings has many difficulties, since it is a problem of a kind of combinatorial optimization. The group method of data handling (GMDH) is an algorithm for the nonlinear model identification from collected regression-type data. But, it needs the calculation of many combinations of polinomials which are called as the partial descriptions. The combinatorial algorithms are computationally intensive. This paper proposes a simple method of model identification using the fuzzy ID 3 and Bernstein polinomial, in which the B-spline is regarded as the membership function of fuzzy set. From a practical view point, an algorithm with less computational cost for selecting the terms of polinomial is discussed as well as links to rule extraction methds from numerical data. Since the obtained polinomial consists of the tensor product of B-splines, by regarding B-splines as the menber-ship functions of fuzzy sets, it can be represented as the fuzzy if-then rule type knowledges and fuzzy decision trees.
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© 1996 Japan Industrial Management Association
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