Set-fuzzy-set-norm Variation of Set-fuzzy-set Multifunctions

Abstract

In this paper, we introduce F(R p ), the collection of all finite sets of fuzzy subsets in F bc (R p ), which is the class of the upper semicontinuous fuzzy subsets of R p 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.