Abstract

In this paper, we introduce F(Rp), the collection of all finite sets of fuzzy subsets in Fbc(Rp), which is the class of the upper semicontinuous fuzzy subsets of Rp with bounded convex compact closure of the supports. Then we define set-fuzzyset multifunctions and discuss various kinds of them such as monotone, fuzzy measure, subadditive, null-additive, null-nulladditive, multisubmeasure and null-continuous. We introduce the set-fuzzy-set-norm variation of a set-fuzzy-set multifunction and present some properties between a set-fuzzy-set multifunction and its variations such as fuzzyness, continuity from below, null-additivity, and null-null-additivity.