Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems
Willner K, Wohlmuth BI, Klimke A (2004)
Publication Type: Journal article, Original article
Publication year: 2004
Journal
Publisher: World Scientific Publishing
Book Volume: 12
Pages Range: 745-759
Journal Issue: 6
DOI: 10.1142/S0218488504003181
Abstract
Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to compute expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In this paper, we illustrate the general applicability of this new method by computing two dynamic systems subjected to uncertain parameters as well as uncertain initial conditions. The first model consists of a system of delay differential equations simulating the periodic outbreak of a disease. In the second model, we consider a multibody mechanism described by an algebraic differential equation system. © World Scientific Publishing Company.
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Germany (DE)How to cite
APA:
Willner, K., Wohlmuth, B.I., & Klimke, A. (2004). Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 12(6), 745-759. https://dx.doi.org/10.1142/S0218488504003181
MLA:
Willner, Kai, B. I. Wohlmuth, and A. Klimke. "Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems." International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 12.6 (2004): 745-759.
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