1. Fuzzy Logic and its Applications By Swaroop.M.R 2SD07CS106 Under the Guidance of TGS

2. Contents Introduction to Fuzzy Logic Definition , Description with example. Fuzzy Logic - Representation Membership Functions : Examples Fuzzy Sets Information Flow in Fuzzy Systems Applications Benefits Conclusion References

3. 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)

4. 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.

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

7. Definition of fuzzy logic

9. FUZZY LOGIC REPRESENTATION CONT. Slowest Fastest Slow Fast 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 } 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 measures Not probability functions

11. 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.

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

13. 3.Fuzzy Sets Formal definition: A fuzzy set A in X is expressed as a set of ordered pairs: A = {(x, Ma (x)) , x ϵX } Membership function (MF) Universe or universe of discourse Fuzzy set A fuzzy set is totally characterized by a membership function (MF).

14. Fuzzy Set Operations Max – 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. Example INPUT Fuzzification Rule Association Defuzzification Temp = 10 C Temp = Low Temp = High Temp = 25

17. Fuzzy Sets Sets with fuzzy boundaries A = Set of tall people X X Fuzzy set A Crisp set A Membership function 1.0 1.0 0.9 0.5 Y Y 5.10 5.10 Height Height 6.2

18. 6.BENEFITS OF USING FUZZY LOGIC

20. Hybrid Modelling

22. Fuzzy Geometry – Almost Straight Lines

23. Fuzzy Algebra – Not quite a parabola

24. Fuzzy Calculus

26. 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

27. Expert Fuzzified Systems Medical Diagnosis Legal Stock Market Analysis Mineral Prospecting Weather Forecasting Economics Politics

28. 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

29. 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