Computing expensive multivariate functions of fuzzy numbers using sparse grids
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. Computing expensive multivariate functions of fuzzy numbers, however, often poses a difficult problem due to non-applicability of common fuzzy arithmetic algorithms, severe overestimation, or very high computational complexity. This paper proposes a new approach based on sparse grids, consisting 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. (c) 2005 Elsevier B.V. All rights reserved.
sparse grids fuzzy arithmetic interval analysis uncertainty modeling