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Efficient fuzzy arithmetic for nonlinear functions of modest dimension using sparse grids

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2 Author(s)
Klimke, A. ; Inst. of Appl. Anal. & Numerical Simulation, Stuttgart Univ., Germany ; Wohlmuth, B.

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy extension of any objective function. We consider the difficult case of the objective function being an expensive to compute multivariate function of modest dimension (say d up to 16) where only real-valued evaluations of f are permitted. This often poses a difficult problem due to non-applicability of common fuzzy arithmetic algorithms, severe overestimation, or very high computational complexity. Our approach is composed of two parts: First, we compute a surrogate function using sparse grid interpolation. Second, we perform the fuzzy-valued evaluation of the surrogate function by a suitable implementation of the extension principle based on real or interval arithmetic. The new approach gives accurate results and requires only few function evaluations.

Published in:

Fuzzy Systems, 2004. Proceedings. 2004 IEEE International Conference on  (Volume:3 )

Date of Conference:

25-29 July 2004