ICT619 Intelligent Systems

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• ICT619 Administrative Notices
• Note No class Thursday 20th Sept.
• If you haven't already, please submit your 1
  page project proposal as soon as possible

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ICT619 Intelligent SystemsTopic 3 Fuzzy Systems
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Fuzzy Systems

• PART A
• Introduction
• Applications
• Fuzzy sets and fuzzy logic
• Probability and fuzzy logic
• Fuzzy reasoning
• Design of a fuzzy controller
• PART B
• Building fuzzy systems
• Advantages and limitations of fuzzy systems
• Case Studies

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Building fuzzy systemsPrincipal issues

• Validation of proposed application
• Fuzzy set and data representation
• Fuzzy set hedges
• Dealing with Boolean variables
• Uncertain and noisy data
• Fuzzy system design methodology

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Validation of proposed application

• Involves comparing the problem attributes with
  those of a typical fuzzy model
• Characteristics of a fuzzy model
• Intrinsically imprecise parameters (control
  variables)
• The domain expert expresses heuristics using
  vague linguistic expressions for example,
  relatively high profit margin, small-to-medium
  sized companies.
• Draws on knowledge from multiple experts

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Validation of proposed application (contd)

• Characteristics of a fuzzy model (contd)
• Experts express apparently conflicting opinions.
  For example,
• Our price must be high Company financial
  expert
• Our price must be low Company marketing and
  sales expert.
• Complex, poorly understood, nonlinear problems
• No mathematical model exists to represent it.
• Too difficult for traditional expert systems,
  mathematical and statistical approaches.

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Fuzzy set and data representation

• Problem variables define data used and produced
  by the system
• Variables decomposed into one or more fuzzy sets,
  with each set describing some range of the
  variables values
• Each domain value (for example, profit figures in
  dollars) must belong to at least one fuzzy set

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Fuzzy set and data representation(contd)
There should be between 25 and 50 overlaps
between adjacent fuzzy sets.
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Designing and eliciting fuzzy sets

• Knowledge acquisition
• Sources include domain experts, articles,
  procedure manuals, or other documents
• All relevant objects (variables) and their
  properties (fuzzy sets) are extracted
• Derivation of fuzzy sets
• Voting by multiple experts
• Statistical analysis of domain data
• Data mining techniques

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Derivation of fuzzy sets

• Voting by multiple experts
• A fuzzy sets membership function can be based on
  cumulative frequency of votes by experts
• Eg, Membership value of 170 cm in tall determined
  by how many regard 170 cm as tall
• Experts must agree on the underlying domain
  tall for a man? tall for a basket ball player?

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Derivation of fuzzy sets (contd)

• Statistical analysis of domain data
• For example, data are normally distributed, mean
  and standard deviation are known
• But data in financial analysis, marketing, risk
  assessment, project management and so on are
  seldom normally distributed and can be subject to
  sudden changes
• Data mining techniques
• Used to decompose underlying variables into
  arbitrary collections of fuzzy sets

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Fuzzy set hedges

• Hedges are modifiers of fuzzy set membership
  functions.
• Act like adjectives and adverbs in English, such
  as "very" or "often"
• Allow a closer and more intuitive modelling of
  the underlying knowledge as expressed in language
• Defining hedges can be a subjective process and
  may vary from one problem domain to another

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Fuzzy set hedges (contd)

• Some examples
• Very, almost, about, roughly, quite, more or
  less, somewhat, rather
• Membership very of variable x (membership of
  variable x)2
• If income is low to a degree of 0.8, then income
  will be very low to a degree of (0.8)2 0.64.
• Membership more or less of variable x
  ?(membership of variable x)
• Hedges reduce the number of fuzzy sets that need
  to be created
• Hedges also increase the readability of rules and
  consequently ease maintenance.

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Dealing with Boolean variables

• Problem with Boolean expressions
• Boolean variables in the antecedents of rules may
  saturate consequent fuzzy space, and pre-empt all
  the other rules
• Example
• Rules from a vehicle underwriting risk
  assessment model
• IF age is young THEN risk is increased
• IF distance_to_work is far THEN risk is slightly
  increased
• IF accidents_in_last2years is excessive THEN risk
  is very increased
• IF drink_driving_convictions is significant THEN
  risk is totally increased
• Now consider the addition of the following rule
• IF sexmale THEN risk is increased
• may cause the consequent truth value to evaluate
  to 1.0 if sex happens to be male

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Dealing with Boolean variables(contd)

• Boolean filters
• A Boolean filter can be added to the antecedent
  of a rule as a qualifying proposition to avoid
  saturation
• IF sexmale AND age is young THEN risk is
  highly increased
• If the expression sexmale is true (value
  1), and the truth of age is young is say 0.38,
  the consequent will be assigned the truth value
  minimum(1.0, 0.38) or 0.38 (using the min-max
  rule).
• When the expression sexmale is false (value
  0),
• the minimum is zero and the rule is not executed
  (which is the original intent).
• Explicit truth values for Boolean propositions
• For example the rule
• IF sexmale.60 THEN risk is increased
• agrees with the intuition overall risk is
  increased independent of any other factors if the
  driver is male

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Uncertain and noisy data

• Data may be noisy or uncertain due to
• imprecise measurement processes or
• lack of confidence in the data source
• May be handled by associating a fuzzy set with
  the data also
• As an example, one of the input variables in the
  rule
• IF income is moderately_high THEN credit_risk
  is medium
• is the income stated by the candidate

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Uncertain and noisy data (contd)

• The assessor may associate a degree of
  confidence, say 0.8, with the income
• the lower the confidence value, the broader
  the fuzzy numbers bell curve
• The truth value of the antecedent is found by
  finding the point of maximum correlation between
  the antecedent fuzzy set moderately_high and the
  fuzzy set associated with the stated income
  (135,000 in this example)

Confidence set
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Uncertain and noisy data (contd)

• Application of the rule
• IF income is moderately_high THEN credit_risk
  is medium
• with cf0.8 for variable income will thus
  truncate the fuzzy space for medium credit risk
  to the level 0.7.

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Fuzzy system design methodology

• The basic steps
• Validate application
• Define functional and operational characteristics
• Decompose variables into fuzzy sets
• Write rules to describe behaviour
• Define defuzzification methods
• Define performance metrics
• Test system
• Evaluate and tune system

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Definition of fuzzy sets

• No formal procedure for designing these
  functions
• Practical experience and intuition used
• Experimental evidence indicates a high tolerance
  to fuzzy shapes
• In control applications, the fuzzy sets are
  usually trapezoidal or triangular
• Bell-shaped fuzzy sets may also be used instead
  of triangles
• Sigmoids (S-curves) and linear surfaces are also
  used in information systems and applications in
  social sciences.

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Writing rules

• Rules are usually written in the form
• IF x is S THEN y is T
• where x and y are linguistic variables and S and
  T are fuzzy sets
• In this rule, x is a control (input) variable and
  y is the solution (output) variable
• Any unconditional rules of the form
• x is S
• is also entered.
• Such rules act to constrain the shape of the
  solution fuzzy set.

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Review of rules and addition of any hedges

• If the fuzzy system supports hedges, the rule set
  should be examined to write any hedged rules
• These rules generally capture extreme behaviour
  patterns, eg,
• IF x is very S THEN y is very T
• Addition of any alpha cuts to individual rules
• An alpha cut establishes the minimum truth
  threshold for a rule
• For example, given the rule
• (Alpha0.2) IF age is young THEN risk is high
• if the truth of the proposition age is young
  falls below 0.2, this rule will not fire
• Prevents production of residual fuzzy spaces
  with very small but finite truth values

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Entering rule execution weights

• Importance of rules can be indicated by giving a
  weight multiplier. For example,
• (Weight0.8) IF age is young THEN risk is high
• Definition of defuzzification method
• Defuzzification selects the expected value of a
  solution variable from the aggregated fuzzy
  region.
• The most popular method is the centre of gravity
  or centroid as it gives a smoother transition
  from one observation to the next.

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Advantages of fuzzy systems

• Important attributes used by organisations in
  evaluating systems
• Mean-time-between-failure (MTBF)
• Mean-time-to-repair (MTTR)
• Extensibility of existing systems
• Agreement with real-world processes
• Understandability
• Business intelligent systems based on fuzzy logic
  show advantages in all these aspects

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Advantages of fuzzy systems (contd)

• Some benefits of fuzzy systems are
• Ability to model highly complex business problems
• Conventional expert systems failed to grow in
  business applications mainly due to the complex
  nature of many business problems
• Fuzzy systems are highly suited for modelling
  computationally complex non-linear problems which
  are poorly understood
• Efficient knowledge base
• Fuzzy rule based systems require fewer rules and
  execute faster than conventional rule based
  systems.
• A single rule applies by different degrees to a
  variety of situations.

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Advantages of fuzzy systems (contd)

• Improved cognitive modelling of expert systems
• Specialized knowledge is often best expressed
  using imprecise terms. Conventional expert
  systems force experts to express rules using
  crisp boundaries
• This contributes to poor performance in many
  systems.
• Ability to model systems involving multiple
  experts
• Since rules are applied in parallel rather than
  in sequence,
• two rules reflecting two different opinions can
  both contribute to the final outcome.

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Advantages of fuzzy systems (contd)

• Reduced model complexity
• Fuzzy systems use fewer and the rules are closer
  to the way knowledge is expressed in natural
  language. These factors greatly improve overall
  MTTR.
• The understandability and ease of maintenance
  also leads to improved MTBF.
• Improved handling of uncertainty
• Fuzzy systems provide a better, more consistent
  and mathematically sound method of handling
  uncertainties
• Example
• IF height is tall THEN weight is heavy
• A given height will produce an estimated weight
  with its degree of membership in the fuzzy set
  heavy.
• An expert system would contain many rules, like
• IF height is gt 135 and height is lt 165 THEN
  weight is 75, CF0.8

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Limitations of fuzzy intelligent systems

• Lack of learning capability
• Hybrid, particularly neurofuzzy systems, attempt
  to remedy this
• Determining and tuning membership functions
• Is not an easy task
• Difficult to say how many are really required
• Requires extensive testing and fine tuning
• Though easier to design and prototype than
  conventional systems, fuzzy systems require more
  fine tuning before they are operational.
• Bias among traditionalists, especially in Western
  countries, for crisp logic based systems
• Mistrust of fuzzy logic

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Case Studies

• Case 1 Quality control and monitoring (Dhar
  Stein 1997 p.203-210)
• German superstore chain Kaufhof
• Manufacturers supply directly to 16 warehouses.
• Problem
• 112,000 deliveries from manufacturers each day
• About 1 have a problem (quality, type, number,
  breakages, etc.)
• Checking all items individually is very labour
  intensive

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Case Study 1 (contd)

• Solution goal
• A continual monitoring system for identifying
  shipments with high risk
• Constraints
• Should concentrate on riskier shipments
• Be flexible enough to deal with new products,
  suppliers and quality control policies
• Be fast enough not to disrupt the workflow at the
  warehouse

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Case Study 1 (contd)

• Relevant issues
• Factors affecting shipments
• The nature of items being delivered
• Past performance of the supplier
• Recent performance trends of the supplier
• The size of the order
• Factors interact in complex ways
• Evaluation
• Error rate of the brute-force system to be used
  as a benchmark for evaluating new system.

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Case Study 1 (contd)

• Possible solutions
• ANN and statistical analysis solutions ruled out
  Reason No data available relating input
  (shipment attributes) to output (shipment errors)
• Expert systems considered Reason Experts able
  to articulate criteria for wanting to inspect
  shipments

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Case Study 1 (contd)

• The fuzzy system solution - Invent/W
• Fuzzy system solution chosen due to ability to
• model processes with varying degrees of truth and
  
• deal with the interaction of continuously varying
  variables
• Information in shipment barcode (eg, product,
  supplier) used by Invent/W to gather input
  variables based on
• historical data
• trend data
• product type data etc

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Case Study 1 (contd)

• Invent/W uses
• Inputs from Kaufhof stores in the inventory
  system
• ancillary databases
• special tables used for building risk profiles
• Analyses these data and produces the solution
  variable - a score between 0 and 100
• The lower the number, the more the shipment
  should be inspected

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Case Study 1 (contd)

• The Invent/W rule base
• 164 rules in the system
• Rules consider suppliers' recent performance
• A typical rule
• IF recent_shipment_problem is high AND
  item_shipment_risk is high THEN risk is high
• System integrated into a COBOL-based inventory
  management system, which runs on Kaufhofs
  mainframe computer
• A Windows based graphical environment enable
  users to easily define rules and the shapes of
  fuzzy sets

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Case Study 1 (contd)

• Invent/W performance test
• All shipments inspected regardless of score
  output by Invent/W
• In first four months of testing, 98.5 of all
  erroneous shipments identified correctly
• Currently performing at about 99.5 accuracy
• Shipment inspection capacity required reduced by
  more than 50.

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Case Study 2 Bond rating (McNeill Thro 1994)

• A neuro-fuzzy system for rating the investment
  safety of bonds
• Developed by Fujitsu in Japan
• The system uses 10 fuzzy rules
• Fuzzy membership functions and the rule weights
  adjusted using a neural network.
• Rules cover the inputs and the financial
  condition of the company issuing the bonds

See http//www.fuzzysys.com/books/FLLib/FUZZYPDF
/FUZZYLOG.PDF
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Case Study 2 (contd)

• Financial condition of company issuing bonds
  determined by
• Ordinary profit (with membership functions for
  fuzzy sets large, medium, small)
• Owned capital (large, small)
• Interest coverage ratio (high, low)
• Long-term loan ratio (low, high)
• Owned capital ratio (low)
• Outputs (bond ratings) are high, medium, and low

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Case Study 2 (contd)

• The system uses two classes of rules
• Basic rules
• receive an initial weighting of 1, are related to
  ordinary profits
• IF ordinary profit is large THEN rating is high
• IF ordinary profit is medium, THEN rating is
  medium
• IF ordinary profit is small, THEN rating is low
• Auxiliary rules

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Case Study 2 (contd)

• Auxiliary rules
• Cover the other inputs and receive an initial
  weighting of 0.2
• IF owned capital is large, THEN rating is high
• IF owned capital is small, THEN rating is small
• IF interest coverage ratio is high, THEN rating
  is high
• IF interest coverage ratio is low, THEN rating is
  low
• IF long-term loan ratio is high, THEN rating is
  high
• IF long-term loan ratio is low, THEN rating is
  low
• IF owned capital ratio is low, THEN rating is
  low
• Initial weight values associated with rules
  either increased or decreased after learning by
  the ANN.

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REFERENCES

• Cox, E., The Fuzzy Systems Handbook, AP
  Professional, San Diego 1999.
• Dhar, V., Stein, R., Seven Methods for
  Transforming Corporate Data into Business
  Intelligence., Prentice Hall 1997, pp. 126-148,
  203-210.
• Mcneill, F., Thro, E., Fuzzy Logic a Practical
  Approach, AP Professional, Boston 1994.
• Munakata, T., Jani, Y., Fuzzy Systems an
  Overview, Communications of the ACM, Vol.37,
  No.3, 1994, pp.69-76.
• Medsker,L., Hybrid Intelligent Systems, Kluwer
  Academic Press, Boston 1995.
• Negnevitsky, M. Artificial Intelligence A Guide
  to Intelligent Systems, Addison-Wesley 2005.
  Sangalli, A., The Importance of being Fuzzy,
  Princeton University Press, 1998.
• Zahedi, F., Intelligent Systems for Business,
  Wadsworth Publishing, Belmont, California, 1993.

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ICT619 Student Projects from 2004
Iris dataset - ANN (MATLAB)
SW project cost estimation - ANN
Social skills assessment for kids - ES (EXpert2go)
HDD problem diagnosis - ES
PC troubleshooting - ES
Display troubleshooting - ES (CLIPS)
NW troubleshooting - ES (Exper2go)
Char recognition - ANN (JOONE)
Wine recommender - ES(Exp2Go)