Fuzzy Logic and its Applications

BySwaroop.M.R2SD07CS106

Under the Guidance ofTGS

Contents

1. Introduction to Fuzzy Logica. Definition , Description with example.b. Fuzzy Logic - Representation

2. Membership Functions : Examples3. Fuzzy Sets 4. Information Flow in Fuzzy Systems5. Applications 6. Benefits 7. Conclusion8. References

1.Introduction

• In this seminar the presentation includes the definition ,essence and application of Fuzzy Logic .

• Fuzzy logic is a main tool for designing a intelligent / ubiquitous /context aware systems.

• Fuzzy logic can represent multiple states of a given entity like temperature (low, medium, normal, high, very high, etc)

1a.Fuzzy Logic – A Definition

Fuzzy logic provides a method to formalize reasoning when dealing with vague terms. Traditional computing requires finite precision which is not always possible in real world scenarios. Not every decision is either true or false, or as with Boolean logic either 0 or 1. Fuzzy logic allows for membership functions, or degrees of truthfulness and falsehoods. Or as with Boolean logic, not only 0 and 1 but all the numbers that fall in between.

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.

1b. FUZZY LOGIC REPRESENTATION

For every problem must represent in terms of 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 Fastestfloat 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}else if ((speed >= 0.5)&&(speed < 0.75)) {

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

// speed is fastest}

Slow Fast

2.Membership Functions (MFs)

• Linguistic terms – Fuzzy Terms called as Linguistic Terms.

• Definition-These are the input or output variables of the system whose values are words or sentences from a natural language instead of numerical values.

• Characteristics of MFs:– Subjective measures– Not probability functions

Membership Functions

• Definition-Membership functions are used in the fuzzification and defuzzification steps of a given statement, to map the non-fuzzy input values to fuzzy linguistic terms and vice-versa.

• A membership function is used to qualify a linguistic term.

Types of Membership Functions

• Singleton Functions. – Only for 2 possibilityEx- inside , outside

• Trapezoidal Function.- More than 2 possibilityEx – Low , Medium ,High

3.Fuzzy Sets

• Formal definition:A fuzzy set A in X is expressed as a set of ordered

pairs:

A = {(x, Ma (x)) , x ϵ X }

A fuzzy set is totally characterized by amembership function (MF).

Fuzzy setMembership

function(MF)

Universe oruniverse of discourse

Fuzzy Set Operations

• Max – OR ( ex – Max (1 ,2) =2 )

• Min – AND ( ex – Min (1,2) = 1 )

• PROD – AND ( ex – PROD (1,2) = 1)

4.Information flow in Fuzzy System

Example

INPUT Fuzzification Rule Association Defuzzification

Temp = 10 C Temp = Low Temp = High Temp = 25

Fuzzy Sets

• Sets with fuzzy boundaries• A = Set of tall people

Crisp set A Fuzzy set AX

Y

X

Y

Membershipfunction1.0

5.10 Height Height

1.00.9

5.10 6.2

0.5

6.BENEFITS OF USING FUZZY LOGIC

FUZZY LOGIC IN OTHER FIELDS

Business

Hybrid Modelling

Expert Systems

How is Fuzzy Logic Used?

Fuzzy Mathematics

Fuzzy Numbers – almost 5, or more than 50

Fuzzy Geometry – Almost Straight Lines

Fuzzy Algebra – Not quite a parabola

Fuzzy Calculus

Fuzzy Graphs – based on fuzzy points

General Fuzzified Applications

• Quality Assurance

• Error Diagnostics

• Control Theory

• Pattern Recognition

Specific Fuzzified Applications

• Otis Elevators

• Vacuum Cleaners

• Hair Dryers

• Air Control in Soft Drink Production

• Noise Detection on Compact Disks

• Cranes

• Electric Razors

• Camcorders

• Television Sets

• Showers

Expert Fuzzified Systems

• Medical Diagnosis

• Legal

• Stock Market Analysis

• Mineral Prospecting

• Weather Forecasting

• Economics

• Politics

Common Objections to Fuzzy Logic

• Much of the opposition to fuzzy logic is based on the misconception

• Fuzzy logic invites the belief that the modeling process generates imprecise answers

Conclusion

• The exact directions and extent of future developments will be dictated by advancing technology and market forces

• Fuzzy logic is a tool and can only useful and powerful when combined with Analytical Methodologies and Machine Reasoning Techniques

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.

References

Fuzzy Logic. Fuzzy Logic - a powerful new technology.http://www.austinlinks.com/Fuzzy/

FuzzyNet On-line. Automatic Transmission http://www.aptronix.com/fuzzynet/applnote/transmis.htm

Garner, Martin. Weird Water and Fuzzy Logic: More notes of a Fringe Watcher.

Generation 5. An Introduction to Fuzzy Logic. http://www.generation5.org/fuzzyintro.shtml

Sowell, Thomas . FUZzy Logic For “Just Plain Folks” .