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Fuzzy Logic and Fuzzy Expert Systems

Fuzzy Logic and Fuzzy Expert Systems. Steve O’Hara UTSA CS 7123. Preview.

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Fuzzy Logic and Fuzzy Expert Systems

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  1. Steve O’Hara, Fuzzy Systems, 10/29/07

  2. Fuzzy LogicandFuzzy Expert Systems Steve O’Hara UTSA CS 7123 Steve O’Hara, Fuzzy Systems, 10/29/07

  3. Preview • Fuzzy sets and logic must be viewed as a formal mathematical theory for the representation of uncertainty. Uncertainty is crucial for the manage-ment of real systems: if you had to park your car PRECISELY in one place, it would not be possible. • Fuzzy logic is a mathematical formalism, and a membership function is a precise number. What's crucial to realize is that fuzzy logic is a logic OF fuzziness, not a logic which is ITSELF fuzzy. But that's OK: just as the laws of probability are not random, so the laws of fuzziness are not vague. • Source: http://www.cs.cmu.edu/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-8.html Steve O’Hara, Fuzzy Systems, 10/29/07

  4. Sources • Compendium of many sources: • http://www.austinlinks.com/Fuzzy/index.html • Main source for today: • http://www.esru.strath.ac.uk/Reference/concepts/fuzzy/fuzzy.htm • “The” seminal paper: • Zadeh, L.A., "Fuzzy Sets," Information and Control, Vol. 8, pp. 338-353, 1965. Steve O’Hara, Fuzzy Systems, 10/29/07

  5. What is Fuzzy Logic? • Fuzzy Logic. Logic that allows values other than “true” and “false”. Every statement has a numerical range from 0.0 (false) to 1.0 (true). • Fuzzy Set Membership. A given element can be member of a set with a numerical range of 0.0 (not at all a member) to 1.0 (completely a member) Steve O’Hara, Fuzzy Systems, 10/29/07

  6. Example • What is a “big” house? • “small” might be under 1800 sf • “medium” might be 1500 to 2200 sf • “large” might be 2000 to 3000 sf • “huge” might be over 2800 sf • What is an “expensive” house? • What is an “old” house? • What do you call a 2100 sf house? • “Medium-large-ish”? • partially “medium” AND partially “large” Steve O’Hara, Fuzzy Systems, 10/29/07

  7. Is it Just Probability? • If a house is partially “medium” and partially “large”, can it be quantified? • Can it be 60% of a member in the “medium” category, and 30% a member in the “large” category at the same time? • Does this mean there is a 60% chance it is medium and a 30% chance is large? Steve O’Hara, Fuzzy Systems, 10/29/07

  8. Membership Functions #1 • House Sizes • “piece-wise linear” • extends easily to 2d (planes) and larger dimensions 100% small medium large huge 0% 1500 sf 2100 sf 2700 sf 3300 sf Steve O’Hara, Fuzzy Systems, 10/29/07

  9. Membership Functions #2 Sigmoid (Logistic) Radial Basis (Gaussian) Steve O’Hara, Fuzzy Systems, 10/29/07

  10. Fuzzy “Logic” • For the fuzzy variables A and B: not A = 1 - A A B A and B = min (A, B) A or B = max (A, B) Steve O’Hara, Fuzzy Systems, 10/29/07

  11. Fuzzy Qualifiers • Hedges for extreme values • VERY <x> = more extreme • SOMEWHAT <x> = less extreme Powering Shifting Steve O’Hara, Fuzzy Systems, 10/29/07

  12. Fuzzy Expert Systems • Fuzzy Logic and Expert Systems • Rule-based System • Requires Domain Expertise • Tuning is Difficult • Low-dimensional Problems • Many Rules fire at the same time Steve O’Hara, Fuzzy Systems, 10/29/07

  13. Inverted Pendulum http://cnx.org/content/m12977/latest/ Steve O’Hara, Fuzzy Systems, 10/29/07

  14. Inverted Pendulum Control • Two Inputs: • One Output: Steve O’Hara, Fuzzy Systems, 10/29/07

  15. Inverted Pendulum Rules SPEED = fn (ANGLE, ANGULAR VELOCITY) ANGLE ANGULARVELOCITY Steve O’Hara, Fuzzy Systems, 10/29/07

  16. Sample Inputs for Inv. Pend. Steve O’Hara, Fuzzy Systems, 10/29/07

  17. Sample Rule “Firing” Steve O’Hara, Fuzzy Systems, 10/29/07

  18. Four Rules “Fire” } if angle is zero and angular velocity is zero then speed is zero if angle is positive low and angular velocity is zero then speed is PL if angle is zero and angular velocity is NL then speed is NL if angle is positive low and angular velocity is NL then speed is zero Steve O’Hara, Fuzzy Systems, 10/29/07

  19. A Few Fuzzy Applications • Automatic control of dam gates for hydroelectric-powerplants (Tokyo Electric Power) • Simplified control of robots (Hirota, Fuji Electric, Toshiba, Omron) • Camera aiming for the telecast of sporting events (Omron) • Substitution of an expert for the assessment of stock exchange activities(Yamaichi, Hitachi) • Preventing unwanted temperature fluctuations in air-conditioning systems(Mitsubishi, Sharp) • Efficient and stable control of car-engines (Nissan) • Cruise-control for automobiles(Nissan, Subaru) • Improved efficiency and optimized function of industrial control applications(Aptronix, Omron, Meiden, Sha, Micom, Mitsubishi, Nisshin-Denki, Oku-Electronics) • Positioning of wafer-steppers in the production of semiconductors(Canon) • Optimized planning of bus time-tables(Toshiba, Nippon-System, Keihan-Express) • Archiving system for documents(Mitsubishi Elec.) • Prediction system for early recognition of earthquakes (Inst. of Seismology Bureau of Metrology, Japan) • Medicine technology: cancer diagnosis (Kawasaki Medical School) • Combination of Fuzzy Logic and Neural Nets(Matsushita) • Recognition of handwritten symbols with pocket computers(Sony) • Recognition of motives in pictures with video cameras (Canon, Minolta) • Automatic motor-control for vacuum cleaners with recognition of surface and degree of soiling (Matsushita) • Back light control for camcorders(Sanyo) • Compensation against vibrations in camcorders(Matsushita) • Single button control for washing-machines(Matsushita, Hitatchi) • Recognition of handwriting, objects, voice (CSK, Hitachi, Hosai Univ., Ricoh) • Flight aid for helicopters (Sugeno) • Simulation for legal proceedings(Meihi Gakuin Univ, Nagoy Univ.) • Software-design for industrial processes (Aptronix, Harima, Ishikawajima-OC Engeneering) • Controlling of machinery speed and temperature for steel-works(Kawasaki Steel, New-Nippon Steel, NKK) • Controlling of subway systems to improve driving comfort, precision of halting and economy (Hitachi) • Improved fuel-consumption for automobiles(NOK, Nippon Denki Tools) • Improved sensitiveness and efficiency for elevator control(Fujitec, Hitachi, Toshiba) • Improved safety for nuclear reactors (Hitachi, Bernard, Nuclear Fuel div.) Steve O’Hara, Fuzzy Systems, 10/29/07

  20. Summary • Fuzzy Logic is an extension of Classical Logic. • Fuzzy Expert Systems have many commercial applications. • Worth understanding and having available in your toolbox. Steve O’Hara, Fuzzy Systems, 10/29/07

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