AI TECHNIQUES

1
AI TECHNIQUES

• Fuzzy Logic
• (Fuzzy System)

2
Fuzzy Logic An Idea
3
Fuzzy Logic Background
The concept of a set and set theory are powerful
concepts in mathematics. However, the principal
notion underlying set theory, that an element can
(exclusively) either belong to set or not belong
to a set, makes it well high impossible to
represent much of human discourse. How is one to
represent notions like  large profit high
pressure tall man wealthy woman moderate
temperature
4
Background Definitions
Many decision-making and problem-solving tasks
are too complex to be understood quantitatively,
however, people succeed by using knowledge that
is imprecise rather than precise. Fuzzy set
theory, originally introduced by Lotfi Zadeh in
the 1960's, resembles human reasoning in its use
of approximate information and uncertainty to
generate decisions. It was specifically designed
to mathematically represent uncertainty and
vagueness and provide formalized tools for
dealing with the imprecision intrinsic to many
problems. By contrast, traditional computing
demands precision down to each bit.
5
Fuzzy Sets Fuzzy Logic
A fuzzy set is a collection of objects that might
belong to the set to a degree, varying from 1 for
full belongingness to 0 for full
non-belongingness, through all intermediate
values. "Fuzzy logic is a generalization of
standard logic, in which a concept can possess a
degree of truth anywhere between 0.0 and 1.0.
Standard logic applies only to concepts that are
completely true (having degree of truth 1.0) or
completely false (having degree of truth 0.0).
Fuzzy logic is supposed to be used for reasoning
about inherently vague concepts, such as
'tallness.' For example, we might say that
Michael Jordan is tall,' with degree of truth of
0.9
6
Fuzzy Logic ExampleWhat is Tall?

• In-Class Exercise
• Proportion
• Height Voted for
• 510 0.05
• 511 0.10
• 6 0.60
• 61 0.15
• 62 0.10
• Jack is 6 feet tall
• Probability theory - cumulative probability
• There is a 75 percent chance that Jack is tall

7
Membership Functions in Fuzzy Sets
8

• Fuzzy logic - Jack's degree of membership within
  the set of tall people is 0.75
• We are not completely sure whether he is tall or
  not.
• Fuzzy logic - We agree that Jack is more or less
  tall.
• Membership Function lt Jack, 0.75 ? Tall gt
• Knowledge-based system approach Jack is tall
  (CF .75)
• Can use fuzzy logic in rule-based systems (belief
  functions)

9
Fuzzy Logic Fuzzy Systems

• The term fuzzy logic is used in two senses
• Narrow sense Fuzzy logic is a branch of fuzzy
  set theory, which deals (as logical systems do)
  with the representation and inference from
  knowledge. Fuzzy logic, unlike other logical
  systems, deals with imprecise or uncertain
  knowledge. In this narrow, and perhaps correct
  sense, fuzzy logic is just one of the branches of
  fuzzy set theory.
• Broad Sense Fuzzy logic synonymously with fuzzy
  set theory.

10
Fuzzy systems

• A fuzzy system consists of
• Fuzzy (linguistic) variables
• Fuzzy rules
• Fuzzy inference

11
Example Fuzzy variables
Linguistic variables/
12
Example Fuzzy rules

• A fuzzy rule is a linguistic expression of causal
  dependencies between linguistic variables in form
  of if-then statements.
• General form IF ltantecedentgt then ltconsequencegt
• Example
• If temperature is cold and oil price is cheap
• Then heating is high

Linguistic variables
Linguistic values
13
Example Fuzzy inference

• Inputs to a fuzzy system can be
• fuzzy, e.g. (Score Moderate), defined by
  membership functions
• exact, e.g. (Score 190) defined by crisp
  values
• Outputs from a fuzzy system can be
• fuzzy, i.e. a whole membership function.
• exact, i.e. a single value is produced .

14
Fuzzy system applications

• Pattern recognition and classification
• Fuzzy clustering
• Image and speech processing
• Fuzzy systems for prediction
• Fuzzy control
• Monitoring
• Diagnosis

15
Speech processing
16
Monitoring
17
Fuzzy systems
The MathWorks
http//www.mathworks.com/access/helpdesk/help/tool
box/fuzzy/index.html
http//www.austinlinkscom/Fuzzy
http//www.industry.siemens.de/water/en/solutions/
sector_fuzzy-logic.htm
18
Fuzzy Logic Advantages

• Provides flexibility
• Allows for observation
• Shortens system development time
• Increases the system's maintainability
• Handles control or decision-making problems not
  easily defined by mathematical models

19
Intelligence Density Dimension

• Accuracy
• Response speed
• Flexibility
• Tolerance for complexity