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The fuzzy Riemann integral and its numerical integration

✍ Scribed by Hsien-Chung Wu

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 190 KB
Volume: 110
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(97)00353-9

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✦ Synopsis

The fuzzy Riemann integral and its numerical integration are proposed in this paper. The -level set of this fuzzy Riemann integral is a closed interval whose end points are the classical Riemann integrals, thus we provide a numerical method to approximate the fuzzy Riemann integral by invoking the Simpson's rule. We ÿt the end points (closed interval) of the -level set of the fuzzy Riemann integral as polynomials with variable in a least-squares sense. Finally, the membership function of the fuzzy Riemann integral can be transformed into nonlinear programming problem and can be solved by any current optimizer.

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