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.