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Introduction to Fuzzy Control Lecture 10.1 Appendix E

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Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

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Fuzzy Logic

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Normal “Crisp” logic where everything must be either True or False leads to PARADOXES

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The sentence on the other side of the line is false The sentence on the other side of the line is false

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A barber has a sign that reads: “I shave everyone who does not shave himself” Who shaves the barber?

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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)

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Membership Functions Young Age Not Young

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Membership Functions Old Age Not Old

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Membership Functions Age Not Old Not Young Middle Age = Not Old AND Not Young

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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.

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Probability: There is a 50% chance of an apple being in the refrigerator. Fuzzy: There is a half an apple in the refrigerator.

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Fuzzy logic acknowledges and exploits the tolerance for uncertainty and imprecision.

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Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

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Fuzzy Membership Functions

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Fuzzy Control Map to Fuzzy Sets Fuzzy Rules IF A AND B THEN L * * Defuzzification Inputs Output get_inputs(); fire_rules(); find_output();

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Algorithm for a fuzzy controller do_forever { get_inputs(); fire_rules(); find_output(); }

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Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

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Fuzzification of inputs

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get_inputs(); Given inputs x1 and x2, find the weight values associated with each input membership function. ZNMNSPSPM X1 0.2 0.7 W = [0, 0, 0.2, 0.7, 0]

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Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

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Fuzzy Inference

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Comparing the MAX rule and the SUM rule

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Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

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Fuzzy Systems and Applications

Fuzzy Systems and Applications

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