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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.
Fuzzy Systems, 2004. Proceedings. 2004 IEEE International Conference on (Volume:3 )
Date of Conference: 25-29 July 2004