The fuzzy rule-base solution of differential equations

Armin Shmilovici; Oded Z. Maimon

doi:10.1016/0020-0255(96)00075-8

The fuzzy rule-base solution of differential equations

Research output: Contribution to journal › Article › peer-review

Abstract

The equivalence between differential equation models and fuzzy logic models is demonstrated for a certain family of fuzzy systems - those which use fuzzy spline wavelets as membership functions. The universal approximation property of fuzzy systems built with spline wavelets is exploited for replacing operational representations of differential equations with sparse matrix equations. The solution of the matrix equations has a direct interpretation as a set of fuzzy rules. The fuzzy rule base thus generated provides an approximate solution to the original differential equation while retaining the explanatory power of fuzzy systems. The proposed method enjoys the excellent numerical and computational characteristics of the fast wavelet transform.

Original language	English
Pages (from-to)	233-254
Number of pages	22
Journal	Information Sciences
Volume	92
Issue number	1-4
DOIs	https://doi.org/10.1016/0020-0255(96)00075-8
State	Published - 1 Jan 1996
Externally published	Yes

ASJC Scopus subject areas

Software
Control and Systems Engineering
Theoretical Computer Science
Computer Science Applications
Information Systems and Management
Artificial Intelligence

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10.1016/0020-0255(96)00075-8

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AB - The equivalence between differential equation models and fuzzy logic models is demonstrated for a certain family of fuzzy systems - those which use fuzzy spline wavelets as membership functions. The universal approximation property of fuzzy systems built with spline wavelets is exploited for replacing operational representations of differential equations with sparse matrix equations. The solution of the matrix equations has a direct interpretation as a set of fuzzy rules. The fuzzy rule base thus generated provides an approximate solution to the original differential equation while retaining the explanatory power of fuzzy systems. The proposed method enjoys the excellent numerical and computational characteristics of the fast wavelet transform.

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The fuzzy rule-base solution of differential equations

Abstract

ASJC Scopus subject areas

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