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Fuzzy Sets are used in artificial intelligence. Each

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 64E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 64E

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.

Step-by-Step Solution:

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}

Step 2 of 3

Chapter 2.2, Problem 64E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This full solution covers the following key subjects: fuzzy, element, set, membership, degree. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The full step-by-step solution to problem: 64E from chapter: 2.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Since the solution to 64E from 2.2 chapter was answered, more than 557 students have viewed the full step-by-step answer. The answer to “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.” is broken down into a number of easy to follow steps, and 220 words.

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