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FUZZY ARITHMETIC BASED ON DIMENSION-ADAPTIVE SPARSE GRIDS: A CASE STUDY OF A LARGE-SCALE FINITE ELEMENT MODEL UNDER UNCERTAIN PARAMETERS

Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

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RONALDO F. NUNES

Department of Computational Mechanics, University of Campinas, 6122 Campinas, SP, Brazil

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, and

BARBARA I. WOHLMUTH

Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

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https://doi.org/10.1142/S0218488506004199Cited by:12 (Source: Crossref)

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 computing expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In many cases, not all uncertain input parameters carry equal weight, or the objective model exhibits separable structure. These characteristics can be exploited by dimension-adaptive algorithms. As a result, the treatment of even higher-dimensional problems becomes possible. This is demonstrated in this paper by a case study involving two large-scale finite element models in vibration engineering that are subjected to fuzzy-valued input data.

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