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  1. 1. Fuzzy Logic and its Applications<br />By<br />Swaroop.M.R<br />2SD07CS106<br />Under the Guidance of<br />TGS<br />
  2. 2. Contents<br />Introduction to Fuzzy Logic<br />Definition , Description with example.<br /> Fuzzy Logic - Representation<br />Membership Functions : Examples<br />Fuzzy Sets <br />Information Flow in Fuzzy Systems<br />Applications <br />Benefits <br />Conclusion<br />References<br />
  3. 3. 1.Introduction<br />In this seminar the presentation includes the definition ,essence and application of Fuzzy Logic .<br />Fuzzy logic is a main tool for designing a intelligent / ubiquitous /context aware systems.<br />Fuzzy logic can represent multiple states of a given entity like temperature (low, medium, normal, high, very high, etc)<br />
  4. 4. 1a.Fuzzy Logic – A Definition<br />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. <br />
  5. 5. WHAT IS FUZZY LOGIC?<br /><ul><li>Definition of fuzzy
  6. 6. Fuzzy – “not clear, distinct, or precise; blurred”
  7. 7. Definition of fuzzy logic
  8. 8. A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts.</li></li></ul><li> 1b. FUZZY LOGIC REPRESENTATION<br />Slowest<br /><ul><li>For every problem must represent in terms of fuzzy sets.</li></ul>[ 0.0 – 0.25 ]<br />Slow<br />[ 0.25 – 0.50 ]<br />Fast<br />[ 0.50 – 0.75 ]<br />Fastest<br />[ 0.75 – 1.00 ]<br />
  9. 9. FUZZY LOGIC REPRESENTATION CONT.<br />Slowest<br />Fastest<br />Slow<br />Fast<br />float speed; <br />get the speed <br />if ((speed >= 0.0)&&(speed < 0.25)) {<br /> // speed is slowest<br />} <br />else if ((speed >= 0.25)&&(speed < 0.5)) <br />{<br /> // speed is slow<br />}<br />else if ((speed >= 0.5)&&(speed < 0.75)) <br />{<br /> // speed is fast<br />}<br />else // speed >= 0.75 && speed < 1.0 <br />{<br /> // speed is fastest<br />}<br />
  10. 10. 2.Membership Functions (MFs)<br />Linguistic terms – Fuzzy Terms called as Linguistic Terms.<br />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.<br />Characteristics of MFs:<br />Subjective measures<br />Not probability functions<br />
  11. 11. Membership Functions<br />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.<br />A membership function is used to qualify a linguistic term.<br />
  12. 12. Types of Membership Functions<br />Singleton Functions. – Only for 2 possibility<br /> Ex- inside , outside<br />Trapezoidal Function.- More than 2 possibility<br /> Ex – Low , Medium ,High<br />
  13. 13. 3.Fuzzy Sets<br />Formal definition:<br />A fuzzy set A in X is expressed as a set of ordered pairs:<br />A = {(x, Ma (x)) , x ϵX }<br />Membership<br />function<br />(MF)<br />Universe or<br />universe of discourse<br />Fuzzy set<br />A fuzzy set is totally characterized by a<br />membership function (MF).<br />
  14. 14. Fuzzy Set Operations<br />Max – OR ( ex – Max (1 ,2) =2 )<br />Min – AND ( ex – Min (1,2) = 1 )<br />PROD – AND ( ex – PROD (1,2) = 1)<br />
  15. 15. 4.Information flow in Fuzzy System<br />
  16. 16. Example<br />INPUT<br />Fuzzification<br />Rule Association<br />Defuzzification<br />Temp = 10 C<br />Temp = Low<br />Temp = High<br />Temp = 25<br />
  17. 17. Fuzzy Sets<br />Sets with fuzzy boundaries<br />A = Set of tall people<br />X<br />X<br />Fuzzy set A<br />Crisp set A<br />Membership<br />function<br />1.0<br />1.0<br />0.9<br />0.5<br />Y<br />Y<br />5.10<br />5.10<br />Height<br />Height<br />6.2<br />
  19. 19. FUZZY LOGIC IN OTHER FIELDS<br /><ul><li> Business
  20. 20. Hybrid Modelling
  21. 21. Expert Systems</li></li></ul><li>How is Fuzzy Logic Used?<br />Fuzzy Mathematics<br /><ul><li>Fuzzy Numbers – almost 5, or more than 50
  22. 22. Fuzzy Geometry – Almost Straight Lines
  23. 23. Fuzzy Algebra – Not quite a parabola
  24. 24. Fuzzy Calculus
  25. 25. Fuzzy Graphs – based on fuzzy points</li></li></ul><li>GeneralFuzzified Applications<br />Quality Assurance<br />Error Diagnostics<br />Control Theory<br />Pattern Recognition<br />
  26. 26. Specific Fuzzified Applications<br />Otis Elevators<br />Vacuum Cleaners<br />Hair Dryers<br />Air Control in Soft Drink Production<br />Noise Detection on Compact Disks<br />Cranes<br />Electric Razors<br />Camcorders<br />Television Sets<br />Showers<br />
  27. 27. Expert Fuzzified Systems<br />Medical Diagnosis <br />Legal <br />Stock Market Analysis<br />Mineral Prospecting<br />Weather Forecasting<br />Economics<br />Politics<br />
  28. 28. Common Objections to Fuzzy Logic<br />Much of the opposition to fuzzy logic is based on the misconception <br />Fuzzy logic invites the belief that the modeling process generates imprecise answers<br />
  29. 29. Conclusion<br />The exact directions and extent of future developments will be dictated by advancing technology and market forces<br />Fuzzy logic is a tool and can only useful and powerful when combined with Analytical Methodologies and Machine Reasoning Techniques<br />
  30. 30. <ul><li> Fuzzy logic provides an alternative way to represent linguistic and subjective attributes of the real world in computing.
  31. 31. It is able to be applied to control systems and other applications in order to improve the efficiency and simplicity of the design process.</li></li></ul><li>References<br /> Fuzzy Logic. Fuzzy Logic - a powerful new technology.<br /><br />FuzzyNet On-line. Automatic Transmission<br /> Garner, Martin. Weird Water and Fuzzy Logic: More notes of a Fringe Watcher. <br /> Generation 5. An Introduction to Fuzzy Logic.<br /> Sowell, Thomas . FUZzy Logic For “Just Plain Folks” .<br />