2015/09/02 by Huan Huang, Huang, Huan, Congxin Wu +1
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #General Mathematics (math.GM) #Multi-Criteria Decision Making #Optimization and Mathematical Programming
paper · pdf · doi:10.48550/arxiv.1509.01456
openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.