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FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS. 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. Illustrations of Situations.
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FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS Fuzzy Logic
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 Logic
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 Logic
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 Logic
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 Logic
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 Logic
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 Logic
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) Fuzzy Logic
CLASSIFICATION OF FUZZY FUNCTIONS where, 1>a1>a2>……>an-1>0 Fuzzy Logic
Relationship (9) is satisfied if and only if the variables(x,y,z) satisfy the following relations: Fuzzy Logic
2 Fuzzy Logic
……(17) Fuzzy Logic
……(18) Fuzzy Logic
Example: Fuzzy Logic