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Introduction to Fuzzy Control. Lecture 10.1 Appendix E. Fuzzy Control. Fuzzy Sets Design of a Fuzzy Controller Fuzzification of inputs: get_inputs() Fuzzy Inference Centroid Defuzzification. Fuzzy Logic. Normal “Crisp” logic where everything must be either True or False leads to
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Introduction to Fuzzy Control Lecture 10.1 Appendix E
Fuzzy Control • Fuzzy Sets • Design of a Fuzzy Controller • Fuzzification of inputs: get_inputs() • Fuzzy Inference • Centroid Defuzzification
Normal “Crisp” logicwhere everything must be eitherTrue or False leads to PARADOXES
The sentence on the other side of the line is false The sentence on the other side of the line is false
A barber has a sign that reads: “I shave everyone who does not shave himself” Who shaves the barber?
Fuzzy Logic • Lotfi Zadeh - Fuzzy Sets - 1965 • Membership functions • Degree of membership between 0 and 1 • Fuzzy logic operations on fuzzy sets A and B • NOT A => 1 - A • A AND B => MIN(A,B) • A OR B => MAX (A,B)
Membership Functions Young Not Young Age
Membership Functions Not Old Old Age
Membership Functions Not Old Not Young Middle Age = Not Old AND Not Young Age
Probabiltiy vs. Fuzziness Probability describes the uncertainty of an event occurrence. Fuzziness describes event ambiguity. Whether an event occurs is RANDOM. To what degree it occurs is FUZZY.
Probability: There is a 50% chance of an apple being in the refrigerator. Fuzzy:There is a half an apple in therefrigerator.
Fuzzy logic acknowledges and exploits the tolerance for uncertainty and imprecision.
Fuzzy Control • Fuzzy Sets • Design of a Fuzzy Controller • Fuzzification of inputs: get_inputs() • Fuzzy Inference • Centroid Defuzzification
Fuzzy Control Inputs Map to Fuzzy Sets get_inputs(); Fuzzy RulesIF A AND B THEN L** fire_rules(); Defuzzification find_output(); Output
Algorithm for a fuzzy controller do_forever { get_inputs(); fire_rules(); find_output(); }
Fuzzy Control • Fuzzy Sets • Design of a Fuzzy Controller • Fuzzification of inputs: get_inputs() • Fuzzy Inference • Centroid Defuzzification
get_inputs(); Given inputs x1 and x2, find the weightvalues associated with each input membership function. NM NS Z PS PM 0.7 0.2 X1 W = [0, 0, 0.2, 0.7, 0]
Fuzzy Control • Fuzzy Sets • Design of a Fuzzy Controller • Fuzzification of inputs: get_inputs() • Fuzzy Inference • Centroid Defuzzification
Fuzzy Control • Fuzzy Sets • Design of a Fuzzy Controller • Fuzzification of inputs: get_inputs() • Fuzzy Inference • Centroid Defuzzification