
134 Chapter 5 Fuzzy LogiC
5.5 OPERATIONS ON FUZZY SETS
On the crisp sets, operations like intersection, union, and complement are
well defined. Such operations are possible on fuzzy sets as well. Zadeh (1965)
suggested the minimum operator for the intersection between two fuzzy sets
and the maximum operator for the union of two fuzzy sets. These opera-
tors coincide with crisp unification and intersection only if we consider the
membership degrees 0 and 1.
5.5.1 Intersection of Fuzzy Sets
The intersection of A and B is defined as (A ∩ B)(x) = min{A(x),B(x)} =
A(x) ∩ B(x), for ∀ x ∈ X, as demonstrated in Figure 5.5.
Figure 5.5
Intersection ...