Fuzzy LogicIntelligent Technique

Qamar Wajid Ali

OVERVIEW

Where did it begin? What is Fuzzy Logic? Fuzzy Logic in Control Systems Fuzzy Logic in Other Fields Fuzzy Logic vs. Neural Networks Fuzzy Logic Benefits

Fuzzy Logic began 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.

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.

What is Fuzzy Logic? Contd.

Fuzzy logic is a form of many-valued logic In contrast with traditional logic theory, where binary sets

have two-valued logic: true or false, completely true or completely false 0 or 1

WHY FUZZY LOGIC

The reason for the most successful of today's technologies which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human

decision making It fills an important gap in engineering design methods left vacant by

purely mathematical approaches (e.g. linear control design), and purely logic-based approaches (e.g. expert systems) in system design.

WHY FUZZY CONTROL?

The reasoning in fuzzy logic is similar to human reasoning It allows for approximate values and inferences as well as

incomplete or ambiguous data (binary yes/no choices) Fuzzy logic is able to process incomplete data and provide

approximate solutions to problems

Fuzzy Control Procedure

Fuzzy control, which directly uses fuzzy rules is the most important application in fuzzy theory.

Using a procedure originated by Ebrahim Mamdani in the late 70s, three steps are taken to create a fuzzy controlled machine: Fuzzification(Using membership functions to graphically describe a

situation) Rule evaluation(Application of fuzzy rules)  DE-fuzzification(Obtaining the crisp or actual results) 

Degrees of Truth

Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. For example, let a 100  ml glass contain 30 ml of water. Then we may consider two concepts: Empty and Full. The meaning of each of them can be represented by a certain fuzzy set.

Then one might define the glass as being 0.7 empty and 0.3 full

Applying the Values

In this image, the meaning of the expressions cold, warm, and hot is represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions.

Fig. below illustrates bivalent sets to characterize the temperature of a room

Example

Traditional Representation of Logic

Slow FastSpeed = 0 Speed = 1

bool speed; get the speed if ( speed == 0) {

// speed is slow} else {

// speed is fast}

Fuzzy Logic Representation For every problem must represent in terms of

fuzzy sets What are fuzzy sets?

Slowest

Fastest

Slow Fast

[ 0.0 – 0.25 ] [ 0.25 – 0.50 ]

[ 0.50 – 0.75 ]

[ 0.75 – 1.00 ]

Fuzzy Logic Representation Cont.

Slowest Fastest

float speed; get the speed if ((speed >= 0.0)&&(speed < 0.25)) {

// speed is slowest} else if ((speed >= 0.25)&&(speed < 0.5)) {

// speed is slow}

Slow Fast

else if ((speed >= 0.5)&&(speed < 0.75)) {

// speed is fast}else // speed >= 0.75 && speed < 1.0 {

// speed is fastest}

How do fuzzy sets differ from classical sets?

In classical set theory we assume that all sets rare well-defined (or crisp), that is given any object in our universe we can always say that object either is or is not the member of a particular set.

CLASSICAL SETS The set of people that can run a mile in 4 minutes or less. The set of children under age seven that weigh more than 1oo pounds.

FUZZY SETS The set of fast runners The set of overweight children

Applications

ABS Brakes Expert Systems Control Units Bullet train between Tokyo and Osaka Video Cameras Automatic Transmissions Washing Machines

Fuzzy Controllers

• Used to control a physical system

TEMPERATURE CONTROLLER A temperature control system has four settings

Cold, Cool, Warm, and Hot

Change the speed of a heater fan, based off the room temperature and humidity.

Anti Lock Break System ( ABS )

Inputs for Intel Fuzzy ABS are derived from Brake 4 WD Feedback Wheel speed Ignition

Outputs Pulsewidth Error lamp

Fuzzy Inference (Expert) Systems

Input_1 Fuzzy IF-

THENRules

OutputInput_2

Input_3

Service Time

Fuzzy IF-THEN

RulesTip Level

Ambiance

Food Quality

Fuzzy Inference (Expert) Systems

Fuzzify: Apply MF on

input

Generalized Modus Ponens with specified aggregation operations

Defuzzify: Method of Centroid,

Maximum, ...

Suggested Fuzzy Inference System

Want to OrderPizza

RecognizeShop

Service Time

Tip LevelFood Quality

Ambiance

Output Fuzzy MF for each Phoneme

Assign a Fuzzy Value for each Phoneme, Output Highest N Values to a

Linguistic model

Image ProcessingBinaryGray LevelColor (RGB,HSV etc.)

Can we give a crisp definition to light blue?

FUZZY LOGIC VS NEURAL NETWORKS

How does a Neural Network work? Both model the human brain.

Fuzzy Logic Neural Networks

Both used to create behavioural systems.

BENEFITS OF USING FUZZY LOGIC

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