The conventional set operations of fuzzy sets are based on the membership functions
using the max functions. In this paper, we shall consider the set operations of fuzzy
sets based on the concepts of gradual sets and gradual elements. When the fuzzy sets
can be formulated as consisting of gradual elements like the usual set consisting
of usual elements, the intersection and union of fuzzy sets can be defined as the
same way as the intersection and union of usual sets. In this case, the set operations
of fuzzy sets will be similar to the set operations of crisp sets.