Fuzzy logic provides a method to formalize reasoning involving vague concepts like temperature. It allows membership functions to represent degrees of truth rather than binary true/false. The document discusses fuzzy logic representation using membership functions, fuzzy sets and operations. It provides examples of fuzzy logic applications in areas like control systems, quality assurance, and expert systems. Fuzzy logic is a tool that can improve efficiency when combined with other techniques.

1. Fuzzy Logic and its ApplicationsBySwaroop.M.R2SD07CS106Under the Guidance ofTGS

2. ContentsIntroduction to Fuzzy LogicDefinition , Description with example. Fuzzy Logic - RepresentationMembership Functions : ExamplesFuzzy Sets Information Flow in Fuzzy SystemsApplications Benefits ConclusionReferences

3. 1.IntroductionIn 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)

4. 1a.Fuzzy Logic – A DefinitionFuzzy 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.

5. WHAT IS FUZZY LOGIC?Definition of fuzzy

6. Fuzzy – “not clear, distinct, or precise; blurred”

7. Definition of fuzzy logic

8. A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts. 1b. FUZZY LOGIC REPRESENTATIONSlowestFor every problem must represent in terms of fuzzy sets.[ 0.0 – 0.25 ]Slow[ 0.25 – 0.50 ]Fast[ 0.50 – 0.75 ]Fastest[ 0.75 – 1.00 ]

9. FUZZY LOGIC REPRESENTATION CONT.SlowestFastestSlowFastfloat 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}

10. 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 measuresNot probability functions

11. Membership FunctionsDefinition-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.

12. Types of Membership FunctionsSingleton Functions. – Only for 2 possibility Ex- inside , outsideTrapezoidal Function.- More than 2 possibility Ex – Low , Medium ,High

13. 3.Fuzzy SetsFormal definition:A fuzzy set A in X is expressed as a set of ordered pairs:A = {(x, Ma (x)) , x ϵX }Membershipfunction(MF)Universe oruniverse of discourseFuzzy setA fuzzy set is totally characterized by amembership function (MF).

14. Fuzzy Set OperationsMax – OR ( ex – Max (1 ,2) =2 )Min – AND ( ex – Min (1,2) = 1 )PROD – AND ( ex – PROD (1,2) = 1)

15. 4.Information flow in Fuzzy System

16. ExampleINPUTFuzzificationRule AssociationDefuzzificationTemp = 10 CTemp = LowTemp = HighTemp = 25

17. Fuzzy SetsSets with fuzzy boundariesA = Set of tall peopleXXFuzzy set ACrisp set AMembershipfunction1.01.00.90.5YY5.105.10HeightHeight6.2

18. 6.BENEFITS OF USING FUZZY LOGIC

19. FUZZY LOGIC IN OTHER FIELDS Business

20. Hybrid Modelling

21. Expert SystemsHow is Fuzzy Logic Used?Fuzzy MathematicsFuzzy Numbers – almost 5, or more than 50

22. Fuzzy Geometry – Almost Straight Lines

23. Fuzzy Algebra – Not quite a parabola

24. Fuzzy Calculus

25. Fuzzy Graphs – based on fuzzy pointsGeneralFuzzified ApplicationsQuality AssuranceError DiagnosticsControl TheoryPattern Recognition