Building Fuzzy Systems

1
Building Fuzzy Systems

• See p. 140-148 Course Readings
• Essentially a five step process
• 1. Specify the problem and define the linguistic
  variables
• 2. Determine the fuzzy sets
• 3. Elicit and construct the fuzzy rules
• 4. Encode the fuzzy sets, fuzzy rules and
  procedures to perform fuzzy inference into the
  fuzzy system
• 5. Evaluate and tune the system

2
Building Fuzzy Systems

• Specify the problem and determine the linguistic
  variables
• Determine system inputs and outputs
• What is the decision (output)? What are key
  values?
• What influences the decision (the inputs)? What
  are the key values
• Express inputs and output(s) in linguistic terms
  with appropriate values
• Possible sources for this knowledge
• human beings (experts or decision makers)
• decision examples

3
Building Fuzzy Systems

• Determine the fuzzy sets
• The course readings (p. 142) suggest that
  trapezoid and triangular sets can adequately
  represent expert knowledge.
• The number of values for each linguistic variable
  determines the number of sets
• It is also desirable that
• The sets are normal
• The total membership of any reference set element
  across all fuzzy sets is one.
• Note that this may lead to the specification of
  an odd number of variable values
• Sometimes referred to as a formal approach

4
Building Fuzzy Systems

• Determine the fuzzy sets
• Some examples

5
Building Fuzzy Systems

• Determine the fuzzy sets
• Some examples

6
Building Fuzzy Systems

• Determine the fuzzy sets
• As an alternative you attempt to measure the sets
• In other words try to find out what people mean
  when they are referring to the concept you are
  trying to represent
• What techniques are available?
• Point estimation
• Interval estimation
• Membership function estimation
• Pair-wise comparison
• The common theme is that you ask people about
  the concept and statistically analyze the results

7
Building Fuzzy Systems

• Determine the fuzzy sets
• Point estimation
• individuals are asked to select a label, from a
  list, that best answers the question
• the label is the linguistic variable value
• For example
• Which best describes a person who is 20 years old
• a. young b. middle-aged c. old
• Proportion of respondents for each label
  indicates the fuzziness of that label
• Comments
• fuzziness (or uncertainty) is not permitted in
  the response
• fuzziness' is equated with the frequency of
  responses i.e. a statistical property

8
Building Fuzzy Systems

• Determine the fuzzy sets
• Interval estimation
• Individuals select a point within an interval
  which best answers the question a lickert model
• The linguistic variable value is related to the
  position of the response
• For example
• Which label (0 to 5 ) best describes a person who
  is 20 years old?
• not young young
• 0 1 2 3 4 5
• Comments
• graphical or numeric response mode is possible
• fuzziness' can be incorporated in the answer
• there should be an odd number of labels

9
Building Fuzzy Systems

• Determine the fuzzy sets
• Membership function estimation
• Individuals indicate a value for the membership
  of an object (reference set value) in a fuzzy set
  (either discretely or continuously)
• For example (discrete example)
• Indicate to which degree from 0 to 100 you
  would expect people of the following ages to be
  considered young
• ltfollowed by a list of agesgt
• person A, aged 19
• person B, aged 46
• ltetcgt
• Comments
• a direct determination of set membership
• requires some understanding of the concept of a
  fuzzy set
• the order of the list may influence the responses

10
Building Fuzzy Systems

• Determine the fuzzy sets
• Pair-wise comparison
• Individuals are asked to indicate which of two
  objects most strongly exhibit a property. They
  are also asked by how much
• This technique is useful for determining
  membership for multi-dimensional fuzzy sets i.e.
  those where membership is not delivered by some
  objective function, but may be due to a
  combination of factors.
• For example
• Who is the most successful football club?
• a. Carlton b. Collingwood
• Indicate, on the following scale, by how much
• 1 2 3 4 5 6 7 8 9

11
Building Fuzzy Systems

• Elicit and construct the fuzzy rules
• The more formal approach is to develop a rule
  matrix sometimes called a fuzzy associative
  memory (FAM) based on the linguistic variable
  values for the inputs
• For a system with two inputs and one output (with
  values high, medium and low)

12
Building Fuzzy Systems

• Elicit and construct the fuzzy rules
• Note that a set of 15 rules could generated
  directly from this table
• A system with three inputs (and one output) could
  be represented as cube
• An alternative is too elicit the rules directly
  from the decision maker
• This may involve the use of linguistic hedges to
  build on the fuzzy sets that form the basis of
  the system
• An interesting design decision that may arise
• Direct elicitation may result in the
  identification of a rule of the type
• IF trading_volume is very small AND price is
  increasing THEN market_order is buy
• You have a choice either treat very small as a
  modified version of small OR as a fuzzy set in
  its own right.

13
Building Fuzzy Systems

• Encode the fuzzy sets, fuzzy rules and
  procedures to perform fuzzy inference into the
  fuzzy system
• basic choice
• use a shell (or fuzzy logic platform) eg MATLAB
• or implement directly yourself from first
  principles
• Evaluate and tune the system
• A review of model performance may result in
  changes to the
• fuzzy set parameters
• fuzzy rule base
• fuzzy reasoning

14
So far

• Knowledge based systems attempt to encode the
  knowledge and reasoning exhibited by people.
• If expertise' is being modeled then we have an
  expert system
• The most common approach used is to build a rule
  based system where there is a clear separation of
  the reasoning from the knowledge base
• The knowledge and the way it is used is acquired
  from the decision maker
• Knowledge based systems can deal with uncertain
  knowledge and uncertain reasoning through
• the use of certainty or confidence factors or
• the use of fuzzy set theory and fuzzy logic (a
  fuzzy system)
• now we will consider automated knowledge
  acquisition in some detail
• another term for this is machine learning'