Fuzzy vectors via convex bodies

Cheng-Yong Du; Lili Shen

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arXiv · 1903.01607

Fuzzy vectors via convex bodies

Cheng-Yong Du·Lili Shen

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Abstract

In the most accessible terms this paper presents a convex-geometric approach to the study of fuzzy vectors. Motivated by several key results from the theory of convex bodies, we establish a representation theorem of fuzzy vectors through support functions, in which a necessary and sufficient condition for a function to be the support function of a fuzzy vector is provided. As applications, symmetric and skew fuzzy vectors are postulated, based on which a Mare\v{s} core of each fuzzy vector is constructed through convex bodies and support functions, and it is shown that every fuzzy vector over the $n$-dimensional Euclidean space has a unique Mare\v{s} core if, and only if, the dimension $n=1$.

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BibTeX RIS

Cheng-Yong Du, Lili Shen. 2019-03-05. Fuzzy vectors via convex bodies. https://arxiv.org/abs/1903.01607

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