Question

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.

Short answer

A fuzzy set of reach or famous is \( = \left\{ {\left( {0.6,Alice} \right),\left( {0.9,Brian} \right),\left( {0.4,Fred} \right),\left( {0.9,Oscar} \right),\left( {0.9,Rita} \right)} \right\}\)

Step-by-step solution

1Explanation

Given in the question,

F = Set of all famous people.

\(F = \left\{ {\left( {0.6,Alice} \right),\left( {0.9,Brian} \right),\left( {0.4,Fred} \right),\left( {0.1,Oscar} \right),\left( {0.9,Rita} \right)} \right\}\)

R = Set of all reach people.

\(R = \left\{ {\left( {0.4,Alice} \right),\left( {0.8,Brian} \right),\left( {0.2,Fred} \right),\left( {0.9,Oscar} \right),\left( {0.7,Rita} \right)} \right\}\)

concept

We know that the multiset union definition,

Allow A and B to be multiple sets. multi-set union A and B multiple sets where the multiplication of an object is the maximum of its multiplication in A and B

solution

Here we solve our question,

\(\begin{aligned}{l}F \cup R = \left\{ {\left( {0.6,Alice} \right),\left( {0.9,Brian} \right),\left( {0.4,Fred} \right),\left( {0.1,Oscar} \right),\left( {0.9,Rita} \right)} \right\} \cup \\\left\{ {\left( {0.4,Alice} \right),\left( {0.8,Brian} \right),\left( {0.2,Fred} \right),\left( {0.9,Oscar} \right),\left( {0.7,Rita} \right)} \right\}\end{aligned}\)

\( = \left\{ {\left( {0.6,Alice} \right),\left( {0.9,Brian} \right),\left( {0.4,Fred} \right),\left( {0.9,Oscar} \right),\left( {0.9,Rita} \right)} \right\}\)

Hence, a fuzzy set of reach or famous is \( = \left\{ {\left( {0.6,Alice} \right),\left( {0.9,Brian} \right),\left( {0.4,Fred} \right),\left( {0.9,Oscar} \right),\left( {0.9,Rita} \right)} \right\}\)