Fuzzy Expert Systems

1
Fuzzy Expert Systems

• CmpE 530
• Presentation
• Emre Yurtsever - 2002701372

2
Outline

• So far as the laws of mathematics refer to
  reality, they are not certain. And so far as they
  are certain, they do not refer to reality." -
  Albert Einstein
• Introduction (Fuzzy Logic)
• Fuzzy Sets Rules
• Fuzzy Expert Systems

3
Introduction - Fuzzy Logic

• Fuzzy logic is a superset of boolean logic
• It was created by Dr. Lotfi Zadeh in 1960s for
  the purpose of modeling the uncertainty inherent
  in natural language
• In fuzzy logic, it is possible to have partial
  truth values

4
Fuzzy Logic

• Unlike two-valued Boolean logic, fuzzy logic is
  multivalued.
• It deals with degrees of membership and degrees
  of truth.

5
Fuzzy Logic contd

• Fuzzy logic is based on the idea that all things
  admit of degrees
• Temperature It is very cold
• Height He is very tall guy
• Speed ...
• Beauty ...

6
Fuzzy Sets Rules

• A fuzzy set is a set with fuzzy boundaries.
• In classical set theory
• fA(x)X ? 0,1, where fA(x)
• In fuzzy sets
• ?A(x)X ? 0,1,
• where ?A(x) 1, if x is totally in A
• ?A(x) 0, if x is not in A
• 0 lt ?A(x) lt 1, if x is partly in A

1, if x?A 0, if x?A
7
Fuzzy Sets Rules contd

• ?A(x) is the membership function.
• Value of this function is between 0 and 1.
• This value represents the degree of membership
  (membership value) of element x in set A.

8
Fuzzy Sets Rules contd

• Classical tall men example.

9
Fuzzy Sets Rules contd

• Crisp and fuzzy sets of tall men

10
Fuzzy Sets Rules contd

• Fuzzy rules.
• A fuzzy rule can be defined as a conditional
  statement as below.
• IF x is A
• THEN y is B

11
Fuzzy Sets Rules contd

• Differences between classical and fuzzy rules.
• IF height is gt 1.80
• THEN select_for_team
• In fuzzy rules
• IF height is tall
• THEN select_for_team

12
Fuzzy Sets Rules contd

• A fuzzy rule can have multiple antecedents.
• IF height is tall
• AND age is small
• THEN select_for_team
• Or, another example
• IF service is excellent
• OR food is delicious
• THEN tip is generous

13
Fuzzy Expert Systems

• A fuzzy expert system is an expert system that
  uses a collection of fuzzy membership functions
  and rules, to reason about data.
• Fuzzy logic is primarily used as the underlying
  logic of Fuzzy Expert systems

14
Fuzzy Expert Systems contd

• Fuzzy logic is used to define rules of inference,
  and membership functions that allow a expert
  system to draw conclusions
• The rules in a fuzzy expert system are usually of
  a form similar to the following
• if x is low and y is high then z medium

15
Fuzzy Expert Systems contd

• How is Fuzzy Logic used?
• Define the control objectives and criteria
• Determine the input and output relationships
• Use the rule-based structure of FL, break the
  control problem down into a series of IF X AND Y
  THEN Z rules

16
Fuzzy Expert Systems contd

• How is Fuzzy Logic used?
• Create FL membership functions that define the
  meaning (values) of Input/Output terms used in
  the rules.
• Create the necessary pre- and post-processing FL
  routines if implementing in S/W, otherwise
  program the rules into the FL H/W engine.
• Test the system, evaluate the results, tune the
  rules and membership functions, and retest until
  satisfactory results are obtained.

17
Fuzzy Expert Systems contd

• Experts rely on common sense when they solve
  problems.
• Fuzzy logic reflects how people think. It
  attempts to model our decision making, and our
  common sense.
• Leads to new, more human, intelligent systems.

18
Fuzzy Expert Systems contd

• Fuzzy rules of inference are used to form what is
  commonly referred to as a knowledge base which
  acts as a repository of information from which an
  expert system can make decisions.

19
Fuzzy Expert Systems contd

• Inference process in fuzzy expert systems has
  four steps.
• FUZZIFICATION
• INFERENCE
• COMPOSITION
• DEFUZZIFICATION

20
Fuzzy Expert Systems contd

• Fuzzification In the fuzzification subprocess,
  the membership functions defined on the input
  variables are applied to their actual values, to
  determine the degree of truth for each rule
  premise. 
• Inference The truth value for the premise of
  each rule is computed, and applied to the
  conclusion part of each rule. This results in one
  fuzzy subset to be assigned to each output
  variable for each rule.

21
Fuzzy Expert Systems contd

• Composition All of the fuzzy subsets assigned
  to each output variable are combined together to
  form a single fuzzy subset for each output
  variable. 
• Defuzzification Sometimes it is useful to just
  examine the fuzzy subsets that are the result of
  the composition process, but more often, this
  fuzzy value needs to be converted to a single
  number - a crisp value. This is what the
  defuzzification subprocess does.

22
Fuzzy Expert Systems contd
23
Fuzzy Expert Systems contd

• Fuzzy expert systems can be used in
• Pattern Recognition
• Financial Systems
• Operation Research
• Data Analysis

24
Questions?
Thank you...