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Fuzzy Logic

Fuzzy Logic. By Mitch Pence Boise State University. Overview. Fuzzy Logic – A Definition A Little History How is Fuzzy Logic used? General Fuzzified Applications Specific Fuzzified Applications Expert Fuzzified Systems An Example Summary Bibliography. Fuzzy Logic – A Definition.

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Fuzzy Logic

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  1. Fuzzy Logic By Mitch Pence Boise State University

  2. Overview • Fuzzy Logic – A Definition • A Little History • How is Fuzzy Logic used? • General Fuzzified Applications • Specific Fuzzified Applications • Expert Fuzzified Systems • An Example • Summary • Bibliography

  3. 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.

  4. A little History • The idea behind fuzzy logic dates back to Plato, who recognized not only the logic system of true and false, but also an undetermined area – the uncertain. • In the 1960’s Lotfi A. Zadeh Ph.D,. University of California, Berkeley, published an obscure paper on fuzzy sets . His unconventional theory allowed for approximate information and uncertainty when generating complex solutions; a process that previously did not exist. • Fuzzy Logic has been around since the mid 60’s but was not readily excepted until the 80’s and 90’s. Although now prevalent throughout much of the world, China, Japan and Korea were the early adopters

  5. 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

  6. GeneralFuzzified Applications • Quality Assurance • Error Diagnostics • Control Theory • Pattern Recognition

  7. Otis Elevators Vacuum Cleaners Hair Dryers Air Control in Soft Drink Production Noise Detection on Compact Disks Cranes Electric Razors Camcorders Television Sets Showers Specific Fuzzified Applications

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

  9. The following, illustrates a basic “fuzzy” automatic transmission system. The transmission uses four fuzzy sensor inference inputs to control the best gear selection for the given conditions. The inputs are throttle, vehicle speed, engine speed and engine load. An Example

  10. An Example (cont.) Labels and Membership Functions of Throttle.

  11. An Example (cont.) Labels and Membership Functions of vehicle speed.

  12. An Example (cont.) Labels and Membership Functions of engine speed.

  13. An Example (cont.) Labels and Membership Functions of engine load.

  14. An Example (cont.) Labels and Membership Functions of shift.

  15. An Example (cont.) Using the labels as defined in the previous slides, rules can be written for the fuzzy interface unit shown in slide 9. The rules provide a tangible knowledge base required for the decision process and are represented as English like if-then statements.

  16. An Example (cont.) To create the fuzzy interface unit, rules such as the following would be developed to facilitate the automatic shifting of the vehicle. If vehicle speed is low, variation of vehicle speed is small, slope resistance is positive large and accelerator is medium then mode is steep uphill mode. If vehicle speed is medium, variation of vehicle speed is small, slope resistance is negative large and accelerator is small then mode is gentle downhill mode.

  17. An Example (cont.) If Mode is Steep uphill mode, the Shift is No. 2 If Mode is Gentle downhill mode, then Shift is No. 3 The previous slides illustrate how fuzzy logic can provide a powerful tool when addressing complex situations that are not feasible using conventional approaches. By employing fuzzy logic, we have the ability to include additional variables and rules to take into account factors that might improve the behavior of the control system. * See notes

  18. Summary Advances in technology today are occurring at an amazing rate. The speed and complexity of application production would not be possible without systems like fuzzy logic. Lotfi A. Zadeh’s introduction of fuzzy logic generated the ability for companies, who choose to employ it, a competitive edge. They now have the ability to significantly reduce engineering development time in addition to producing extremely complex systems that would not be possible by employing previous methods.

  19. Bibliography Fuzzy Logic. Fuzzy Logic - a powerful new technology. http://www.austinlinks.com/Fuzzy/ FuzzyNet On-line. Automatic Transmissionhttp://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” .

  20. Bibliography (cont.) You Fuzzin’ with me? http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol1/sbaa/article1.html Zadeh, Lotfi A. Professional affiliation and title http://http.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html

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