Different representations of fuzzy vectors

Abstract

Fuzzy vectors were introduced as a description of imprecise quantities whose uncertainty originates from vagueness, not from a probabilistic model. Support functions are a classical tool for representation and computation with compact convex sets. The combination of these two techniques-support functions of fuzzy vectors-has been proposed by Puri and Ralescu. Independently, Bobylev proposed another type of support functions which allows a more economical representation. However, the form of the functions is not very intuitive. We suggest a new type of support functions which combines the advantages of both preceding approaches. We characterize the functions which are support functions of fuzzy vectors in the new sense. © 2009 Springer Berlin Heidelberg.