AI Workshop Texas A&M University-Corpus Christi 12-13 January 2007 Taxonomy of Fuzzy Logic Artificial Intelligence “Soft”computing Expert Systems Machine Learning Fuzzy Logic AI Workshop Texas A&M University-Corpus Christi 12-13 January 2007 Fuzzy Logic Philosophy, Theory and Applications John K. Williams NCAR Research Applications Laboratory jkwillia@ucar.edu Artificial Intelligence Workshop, Texas A&M University at CorpusChristi, 12-13 January 2007 Photo: Paul Bowen …

Why Use Fuzzy Logic? (1) “The guiding principle of soft computing is: Exploit the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, and low solution cost…. What makes [fuzzy logic] so powerful is the fact that most of human reasoning and concept formation is linked to the use of fuzzy rules. By providing a systematic framework for computing with fuzzy rules, [fuzzy logic] greatly amplifies the power of human reasoning.” -Lotfi Zadeh Why Use Fuzzy Logic? (2) “So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality.” – Albert Einstein “As complexity rises, precise statements lose meaning and meaningful statements lose precision.”-Lotfi Zadeh….. A Brief History of Fuzzy Logic (2) •1987 -Subway system using predictive fuzzy controllers enters service in Sendai, Japan •Explosion of applications: medical expert systems, consumer electronics and appliances, financial analysis, industrial process control, …. •1993 -MIT Lincoln Laboratories develops Machine Intelligent Gust Front Algorithm (MIGFA) •1994 -NCAR/RAP develops Doppler radar Microburst Automatic Detection (MAD) algorithm •1998 -NCAR/RAP develops NCAR Improved Moments Algorithm (NIMA) for wind profilers… AI Workshop Texas A&M University-Corpus Christi 12-13 January 2007 Fuzzy Sets (2) Set A A Complement (Not A) Ac Intersection (AND): A ?B A B Union (OR): A ?B Fuzzy Sets (3) The membership functionof a fuzzy set A comprises a value for each element representing its degree of membership in set A: m A (x) ?[0, 1] for all x 1 0.5 0 m A (x) x Degree of membership in A…. Computing with Fuzzy Numbers •The extension principleturns ordinary functions to maps between fuzzy sets: if f: X ?Y, and A is a fuzzy set in X, then •One application is the propagation of measurement uncertainty through a calculation.

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