Fuzzy Logic1 FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS.

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Presentation transcript:

Fuzzy Logic1 FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

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

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

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

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

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

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)

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

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

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Fuzzy Logic22 Example:

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