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FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

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

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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. Fuzzy Logic

  10. Fuzzy Logic

  11. CLASSIFICATION OF FUZZY FUNCTIONS where, 1>a1>a2>……>an-1>0 Fuzzy Logic

  12. Fuzzy Logic

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

  14. 2 Fuzzy Logic

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  22. Example: Fuzzy Logic

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