1. Fuzzy Logic1 FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

2. Fuzzy Logic2 Introduction The first step in this direction was made by Zadeh who propsed a so called “Fuzzy Set” theory dealing with events and situations having subjectively ascribed attributes

3. Fuzzy Logic3 Illustrations of Situations The set of all real numbers much greater than 100 (Is 125 a member of this set?) The set of all intelligent humans.(Do I belong to this set?) The set of all poor people.(Am I a member of this set?) Obviously, all the above sets are very fuzzily defined and their members do not possess sharply defined attributes

4. Fuzzy Logic4 Fuzzy Sets Let X and Y be two fuzzy sets, and x and y be the membership grades of an object with respect to sets X and Y, respectively Definition 1: Two fuzzy sets X and Y are equal (X=Y) if, and only if, for every object -i one has that its membership grade Xi in X is equal to its membership grade Yi in Y

5. Fuzzy Logic5 Definition 2: A fuzzy set is the complement of another fuzzy set X and is denoted by X’ if and only if, for every object-i one has that its member-ship grade Xi’ in X’ is equal to 1-Xi, where Xi is the member ship grade of the object -i in X

6. Fuzzy Logic6 Definition 3: A fuzzy set X is contained in another fuzzy set Y if and only if for every object i one has that Xi <= Yi

7. Fuzzy Logic7 Definition 4: Two fuzzy sets X and Y form a union, denoted by Z = X + Y if and only if, for every object i one has that Zi = max(Xi,Yi)

8. Fuzzy Logic8 Definition 5: Two fuzzy sets X and Y form an intersection, denoted by Z = X.Y, if and only if for every object i one has that Zi = min(Xi,Yi)

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11. Fuzzy Logic11 CLASSIFICATION OF FUZZY FUNCTIONS where, 1>a1>a2>……>a n-1 >0

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13. Fuzzy Logic13 Relationship (9) is satisfied if and only if the variables(x,y,z) satisfy the following relations:

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19. Fuzzy Logic19 ……(17)

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21. Fuzzy Logic21 ……(18)

22. Fuzzy Logic22 Example:

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