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FUZZY LOGIC (Logic Development (Convert crisp data into fuzzy data sets…
FUZZY LOGIC
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Application Areas
Consumer Electronic Goods: hi-fi systems, photocopiers, still and video cameras, television
Domestic Goods: microwave ovens, refigerators, vaccum cleaners, toasters, washing machines
Automotive Systems: automatic Gearboxes, four-wheel steering, vehicle environment control
Environment Control: air conditioners/dryers/heaters, humidifiers
System Architecture
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Defuzzification Module: transforms the fuzzy set obtained by the inference engine into a crisp value.
Inference Engine: simulates the human reasoning process by making fuzzy inference on the inputs and IF-THEN rules.
Fuzzification Module: transforms the system inputs, which are crisp numbers, into fuzzy sets.
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History
Jan Lukasiewicz proposed three-valued logic : True, False andPossible
Finally Lofti Zadeh published his paper on fuzzy logic-a part ofset theory that operated over the range [0.0-1.0]
Classical logic of Aristotle: Law of Bivalence "Every propositionis either True or False(no middle)"
Definition
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a superset of Boolean (conventional) logic that handles the concept of partial truth, which is truth values between
"completely true" and "completely false”.
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Fuzzy Sets
In fuzzy set theory elements have varying degrees of membership.A fuzzy set can be represented by:
A={{ x, A(x) }}
where, A(x) is the membership grade of a element x in fuzzy set.
Crisp Sets
Classical set theory enumerates all element using
A={a1,a2,a3,a4,…,an}
Set A can be represented by characteristic function
μ a(x)={ 1 if element x belongs to the set A
0 otherwise}
Membership function
Membership functions allow you to quantify linguistic term and represent a fuzzy set graphically. A membership function for a fuzzy set A on the universe of discourse X is defined as μA:X → [0,1].