August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 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

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall OUTLINE III. 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

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall A. Introduction (figure from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 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

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Input – vocabulary, fuzzification (creating a fuzzy set) by using our previous methods of frequency, combination, experts/surveys (figure from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Input (figure from Klir&Yuan)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 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.

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Fuzzy Proposition – type 1 and 2 (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Fuzzy Propositions – type 1 and 2 (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 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.

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 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

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Fuzzy Hedges (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Fuzzy Hedges (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Illustrations of Fuzzy Propositions – Composition/Evaluation (from Klir&Yuan)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Illustrations of Fuzzy Propositions – Composition/Evaluation (Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Illustrations of Fuzzy Propositions – Composition/Evaluation (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Illustrations of Fuzzy Propositions Decomposition – Defuzzification/Action (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Defuzzification (from Earl Cox)

August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall Defuzzification (from Earl Cox)