III' FUZZY LOGIC Lecture 3

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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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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
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A. Introduction (figure from Earl Cox)
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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

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Input vocabulary, fuzzification (creating a
fuzzy set) by using our previous methods of
frequency, combination, experts/surveys (figure
from Earl Cox)
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Input (figure from KlirYuan)
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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.

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Fuzzy Proposition type 1 and 2 (from Earl Cox)
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Fuzzy Propositions type 1 and 2 (from Earl Cox)
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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.

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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

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Fuzzy Hedges (from Earl Cox)
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Fuzzy Hedges (from Earl Cox)
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Illustrations of Fuzzy Propositions
Composition/Evaluation (from KlirYuan)
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Illustrations of Fuzzy Propositions
Composition/Evaluation (Earl Cox)
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Illustrations of Fuzzy Propositions
Composition/Evaluation (from Earl Cox)
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Illustrations of Fuzzy Propositions Decomposition
Defuzzification/Action (from Earl Cox)
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Defuzzification (from Earl Cox)
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Defuzzification (from Earl Cox)