2019/03/05 by Cheng-Yong Du, Du, Cheng-Yong, Lili Shen +1
Computer Science · Decision Sciences · Mathematics · #03E72 #26E50 #52A20 #FOS: Mathematics #Fuzzy Systems and Optimization #General Mathematics (math.GM) #Multi-Criteria Decision Making #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1903.01607
openalex publication_date 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Mareš 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 Mareš core if, and only if, the dimension n=1.