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 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
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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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