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

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  • Fuzzy Logic*FUZZY LOGIC AND ITS APPLICATION TO SWITCHING SYSTEMS

    Fuzzy Logic

  • IntroductionThe first step in this direction was made by Zadeh who proposed a so called Fuzzy Set theory dealing with events and situations having subjectively ascribed attributes

    Fuzzy Logic

  • Illustrations of SituationsThe 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 SetsLet 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

  • 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

  • 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

  • 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

  • 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

  • Fuzzy Logic

  • Fuzzy Logic

  • CLASSIFICATION OF FUZZY FUNCTIONSwhere, 1>a1>a2>>an-1>0

    Fuzzy Logic

  • Fuzzy Logic

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

    Fuzzy Logic

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  • Example:

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  • Questions?

    Fuzzy Logic

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