Fuzzy Sets are used in artificial intelligence. Each elememt in the universal set U has a degree of membership, which is a real number bertween 0 to 1 (including 0 and 1), in a fuzzy set S. The fuzzy set S is denoted by listing the elements with their degrees of membership (elements with 0 degree of mebership are not listed). For instance, we write {0.6 Alice, 0.9 Brian, 0.4 Fred, 0.1 Oscar, 0.5 Rita} for the set F (of famous people) to indicate that Alice has 0.6 degree of membership in F, Brian has 0.9 degree of membership in F, Fred has 0.4 degree of membership in F, Oscar has 0.1 degree of membership in F, and Rita has 0.5 degree of membership in F (so that Brian is the most famous and Oscar is the least famous of these people. Also, Suppose that R is a set of rich people with R = {0.4 Alice, 0.8 Brian, 0.2 Fred, 0.9 Oscar, 0.7 Rita}.

The union of two fuzzy sets S and T is the fuzzy set S ∪ T. where the degree of membership of an element in S ∪ T is the maximum of the degrees of membership of this element in S and in T. Find the fuzzy set F ∪ R of rich or famous people.

Solution:

Step 1:

We have two sets

F-for (famous people)-{0.6 Alice, 0.9 Brian, 0.4 Fred, 0.1 Oscar, 0.5 Rita}

R-for (rich people)={0.4 Alice, 0.8 Brian, 0.2 Fred, 0.9 Oscar, 0.7 Rita}