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FUZZY LOGIC
PRESENTED BY:
K S S SANTOSH KUMAR
13MT07IND015
WHAT IS FUZZY LOGIC?
Definition of fuzzy
Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
A form of knowledge representation suitable for notions that
cannot be defined precisely, but which depend upon their
contexts.
TRADITIONAL REPRESENTATION OF LOGIC
Slow FastSpeed = 0 Speed = 1
FUZZY LOGIC REPRESENTATION
For every problem must represent in terms of fuzzy sets.
Slowest
Fastest
Slow
Fast
FUZZY LOGIC REPRESENTATION
Slowest FastestSlow Fast
ORIGINS OF FUZZY LOGIC
Traces back to Ancient Greece
Lotfi Asker Zadeh ( 1965 )
First to publish ideas of fuzzy logic.
Professor Toshire Terano ( 1972 )
Organized the world's first working group on fuzzy systems.
F.L. Smidth & Co. ( 1980 )
First to market fuzzy expert systems.
Fuzzy Sets
Extension of Classical Sets
Not just a membership value of in the set and out the set,
1 and 0 but partial membership value, between 1 and 0
Example: Height
Tall people: say taller than or equal to 1.8m 1.8m , 2m, 3m etc member of this set
1.0 m, 1.5m or even 1.79999m not a member
e.g. Tall(x) = {1 if x >= 1.9m , 0 if x <= 1.7m
else ( x - 1.7 ) / 0.2 }
Fuzzy Short
Short(x) = {0 if x >= 1.9m ,
1 if x <= 1.7m
else ( 1.9 - x ) / 0.2 }
Fuzzy Set Operators
Fuzzy Set: Union
Intersection
Complement
Many possible definitions we introduce one possibility
Fuzzy Set Union
Union ( fA(x) and fB(x) ) =
max (fA(x) , fB(x) )
Union ( Tall(x) and Short(x) )
Fuzzy Set Intersection
Intersection ( fA(x) and fB(x) ) =
min (fA(x) , fB(x) )
Intersection ( Tall(x) and Short(x) )
Fuzzy Set Complement
Complement( fA(x) ) = 1 - fA(x)
Not ( Tall(x) )
Fuzzy Logic Operators
Fuzzy Logic: NOT (A) = 1 - A
A AND B = min( A, B)
A OR B = max( A, B)
Fuzzy Logic NOT
17
Fuzzy Logic AND
18
Fuzzy Logic OR
How fuzzy logic is applied
IF/THEN rules
For example, an extremely simple temperature regulator
that uses a fan might look like this:
IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain level
IF temperature IS hot THEN speed up fan
Design of a FLC for heater
)(x
eTemperatur0
Very Cold Cold Normal
35 10050 80
)(x
%
Heater0
MaxMedOff
35 10050 80
R1: If temp is Very Cold Then Heater is Max
R2: If temp is Cold Then Heater is Med
R3: If temp is Normal Then Heater is Off
FUZZY LOGIC IN CONTROL SYSTEMS
Fuzzy Logic provides a more efficient and resourceful
way to solve Control Systems.
Some Examples
Temperature Controller
In Automotive Systems
Anti – Lock Break System ( ABS )
TEMPERATURE CONTROLLER
The problem Change the speed of a heater fan, based off the room
temperature and humidity. A temperature control system has four settings
Cold, Cool, Warm, and Hot Humidity can be defined by:
Low, Medium, and High Using this we can define
the fuzzy set.
In Automotive Systems
ANTI LOCK BREAK SYSTEM ( ABS )
Nonlinear and dynamic in nature Inputs for Intel Fuzzy ABS are derived from
Brake 4 WD Feedback Wheel speed Ignition
Outputs Pulsewidth Error lamp
Washing Machine Video Camera
Video Games
Example: Dinner for Two
Golden rules for tipping:
1. IF the service is poor OR the food is rancid
THEN tip is cheap (5%).
2. IF the service is good
THEN tip is average (15%).
3. IF the service is excellent OR the food is delicious
THEN tip is generous (25%).
CONCLUSION
Fuzzy logic provides an alternative way to represent
linguistic and subjective attributes of the real world in
computing.
It is able to be applied to control systems and other
applications in order to improve the efficiency and
simplicity of the design process.