august 12, 2003 iii. fuzzy logic: math clinic fall 20031 iii. fuzzy logic – lecture 3 objectives...
Post on 24-Jan-2016
214 views
TRANSCRIPT
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
1
III. FUZZY LOGIC – Lecture 3
OBJECTIVES1. To define the basic notions of fuzzy logic2. To introduce the logical operations and relations
on fuzzy sets3. To learn how to obtain results of fuzzy logical
operations4. To apply what we learn to GIS
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
2
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
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
3
A. Introduction (figure from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
4
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 propositions3. Hedges – very, extremely, somewhat, more, less4. Combination and evaluation – computation of the
results given the inputs5. Action - defuzzification
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
5
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 2003
6
Input (figure from Klir&Yuan)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
7
Fuzzy Propositions – types 1 and 2
GENERAL FORMS1. Unconditional and unqualified proposition: Q is PExample: Temperature(Q) is high(P) 2. Unconditional and qualified proposition: proposition(Q is P) is RExample: That Coimbra and Catania are beautiful is
very true.
).( then )( 1 PQresultxx
)( then ,)}(),(min{ 1 vtruecaco resultxxx
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
8
Fuzzy Proposition – type 1 and 2 (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
9
Fuzzy Propositions – type 1 and 2 (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
10
Fuzzy Propositions – type 3
3. Conditional and unqualifiedproposition: IF Q is P THEN R is SExample: If Robert is tall, then clothes are large. If car is slow, then gear is low.
)( then ,)(
)( then ,)(1
1
SR
PQ
lresultfinaresultx
resultxx
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
11
Fuzzy Propositions – type 4
4. Conditional and qualifiedproposition: IF Q is P THEN R is S is T {proposition(IF Q is P THEN R is S )} is T
)()( then ,)(
)( then ,)(
1
1
1
T
SR
PQ
lresultfinaositionresultpropresultx
resultxx
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
12
Fuzzy Hedges (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
13
Fuzzy Hedges (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
14
Illustrations of Fuzzy Propositions – Composition/Evaluation (from Klir&Yuan)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
15
Illustrations of Fuzzy Propositions – Composition/Evaluation (Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
16
Illustrations of Fuzzy Propositions – Composition/Evaluation (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
17
Illustrations of Fuzzy Propositions Decomposition – Defuzzification/Action (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
18
Defuzzification (from Earl Cox)
August 12, 2003 III. FUZZY LOGIC: Math Clinic Fall 2003
19
Defuzzification (from Earl Cox)