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III. FUZZY LOGIC – Lecture 3. OBJECTIVES 1. To define the basic notions of fuzzy logic 2. To introduce the logical operations and relations on fuzzy sets 3. To learn how to obtain results of fuzzy logical operations 4. To apply what we learn to GIS.
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III. FUZZY LOGIC – Lecture 3 OBJECTIVES 1. To define the basic notions of fuzzy logic 2. To introduce the logical operations and relations on fuzzy sets 3. To learn how to obtain results of fuzzy logical operations 4. To apply what we learn to GIS III. FUZZY LOGIC: Math Clinic Fall 2003
OUTLINEIII. FUZZY LOGIC A. Introduction B. Inputs to fuzzy logic systems - fuzzification C. Fuzzy propositions D. Fuzzy hedges E. Computing the results of a fuzzy proposition given an input F. The resulting action III. FUZZY LOGIC: Math Clinic Fall 2003
A. Introduction (figure from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Introduction Steps (Earl Cox based on previous slide): 1. Input – vocabulary, fuzzification (creating fuzzy sets) 2. Fuzzy propositions – IF X is Y THEN Z (or Z is A) … there are four types of propositions 3. Hedges – very, extremely, somewhat, more, less 4. Combination and evaluation – computation of the results given the inputs 5. Action - defuzzification III. FUZZY LOGIC: Math Clinic Fall 2003
Input – vocabulary, fuzzification (creating a fuzzy set) by using our previous methods of frequency, combination, experts/surveys (figure from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Input (figure from Klir&Yuan) III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Propositions – types 1 and 2 GENERAL FORMS 1. Unconditional and unqualified proposition: Q is P Example: Temperature(Q) is high(P) 2. Unconditional and qualified proposition: proposition(Q is P) is R Example: That Coimbra and Catania are beautiful is very true. III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Proposition – type 1 and 2 (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Propositions – type 1 and 2 (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Propositions – type 3 3. Conditional and unqualified proposition: IF Q is P THEN R is S Example: If Robert is tall, then clothes are large. If car is slow, then gear is low. III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Propositions – type 4 4. Conditional and qualified proposition: IF Q is P THEN R is S is T {proposition(IF Q is P THEN R is S )} is T III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Hedges (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Fuzzy Hedges (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Illustrations of Fuzzy Propositions – Composition/Evaluation (from Klir&Yuan) III. FUZZY LOGIC: Math Clinic Fall 2003
Illustrations of Fuzzy Propositions – Composition/Evaluation (Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Illustrations of Fuzzy Propositions – Composition/Evaluation (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Illustrations of Fuzzy Propositions Decomposition – Defuzzification/Action (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Defuzzification (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003
Defuzzification (from Earl Cox) III. FUZZY LOGIC: Math Clinic Fall 2003