Intersection and union of type-2 fuzzy sets and connection to (1, 2)-double cuts

Abstract

It is known that the standard intersection and union of type-1 fuzzy sets (i.e., the intersection and union under the minimum t-norm and maximum tconorm) are the only cutworthy operations for type1 fuzzy sets. The aim of this paper is to show that similar property holds also for type-2 fuzzy sets, with respect to some special cutting. As was already demonstrated, the intersection and union of type-2 fuzzy sets are not preserved in α-planes. Thus, we study another kind of cutting, so-called double cuts, and show that the intersection and union of type-2 fuzzy sets are preserved in these double cuts.