Intersections and unions of fuzzy sets of operands

We investigate intersections and unions of sets with fuzzy sets of operands. These are natural generalizations of the corresponding operations which involve crisp sets of operands. It is shown that the resulting set is a fuzzy set of type-2 (T2FS). We prove several results which enable us to simplify constructing the type-2 membership functions for intersections and unions of fuzzy sets of operands. We check that de Morgan's laws hold for these two operations with fuzzy sets of operands. As far as the two operations on crisp sets are concerned, the resulting T2FS can be represented as two standard fuzzy sets of its sections. We provide some insight into how these sections are related.