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