Computation of the output of a function with fuzzy inputs based on a low-rank tensor approximation

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• 作者：Samuel Corveleyn ; ^{scorveleyn@gmail.com} ; Stefan Vandewalle ; ^{stefan.vandewalle@kuleuven.be}
• 关键词：Fuzzy numbers ; Zadeh's extension principle ; α-cut approach ; Global optimization ; Grid search ; Low-rank tensors
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：74-89
• 全文大小：3237 K
• 卷排序：310

文摘

We apply a derivative-free optimization method based on novel low-rank tensor methods to the problem of propagating fuzzy uncertainty through a continuous real-valued function. Adhering to Zadeh's extension principle, such a problem can be reformulated as a sequence of optimization problems over nested search spaces. The optimization method we use is based on a low-rank tensor approximation of the function sampled on a grid and a search for the minimal and maximal entries in this low-rank tensor. In contrast to classical fuzzy uncertainty propagation methods, such as the vertex method and the transformation method, the method we propose does not exhibit an inherent exponential scaling for increasing dimension of the search space. Obviously, no derivative-free optimization algorithm can exist which shows sub-exponential scaling with the dimension for all possible continuous functions. The algorithm that we present here, however, can exploit a specific type of structure and regularity (beyond continuity) that is often present in real-world optimization problems. We illustrate this with some high-dimensional numerical examples where the presented method clearly outperforms some established derivative-free optimization codes.