Rulebase Expert System and Uncertainty by qfc10548

VIEWS: 10 PAGES: 33

									Rulebase Expert System and Uncertainty
            Rule-based ES
• Rules as a knowledge representation
  technique
• Type of rules :- relation, recommendation,
  directive, strategy and heuristic
            ES development tean

                 Project manager


Domain expert   Knowledge engineer   Programmer




                    End-user
 Structure of a rule-based ES
                  External
                  database          External program



Knowledge base                            Database

Rule: IF-THEN                                Fact


                     Inference engine

                 Explanation facilities


User interface                       Developer interface


    User                                  Knowledge engineer
                                                               Expert
   Structure of a rule-based ES
• Fundamental characteristic of an ES
  – High quality performance
     • Gives correct results
     • Speed of reaching a solution
     • How to apply heuristic
  – Explanation capability
     • Although certain rules cannot be used to justify a
       conclusion/decision, explanation facility can be used
       to expressed appropriate fundamental principle.
  – Symbolic reasoning
    Structure of a rule-based ES
• Forward and backward chaining inference
                          Database
        Fact: A is x
                                        Fact: B is y



Match                                                  Fire

                       Knowledge base


                   Rule: IF A is x THEN is y
          Conflict Resolution
• Example
  – Rule 1:
              IF   the ‘traffic light’ is green
              THEN the action is go
  – Rule 2:
              IF   the ‘traffic light’ is red
              THEN the action is stop
  – Rule 3:
              IF   the ‘traffic light’ is red
              THEN the action is go
   Conflict Resolution Methods
• Fire the rule with the highest priority
  – example
• Fire the most specific rules
  – example
• Fire the rule that uses the data most recently
  entered in the database - time tags attached
  to the rules
  – example
           Uncertainty Problem
• Sources of uncertainty in ES
  –   Weak implication
  –   Imprecise language
  –   Unknown data
  –   Difficulty in combining the views of different
      experts
        Uncertainty Problem
• Uncertainty in AI
  – Information is partial
  – Information is not fully reliable
  – Representation language is inherently imprecise
  – Information comes from multiple sources and it
    is conflicting
  – Information is approximate
  – Non-absolute cause-effect relationship exist
          Uncertainty Problem
• Representing uncertain information in ES
  –   Probabilistic
  –   Certainty factors
  –   Theory of evidence
  –   Fuzzy logic
  –   Neural Network
  –   GA
  –   Rough set
          Uncertainty Problem
• Representing uncertain information in ES
  –   Probabilistic
  –   Certainty factors
  –   Theory of evidence
  –   Fuzzy logic
  –   Neural Network
  –   GA
  –   Rough set
         Uncertainty Problem
• Representing uncertain information in ES
  – Probabilistic
     • The degree of confidence in a premise or a
       conclusion can be expressed as a probability
     • The chance that a particular event will occur


                  Number of outcomes favoring the occurence of
       P( X ) 
                            Total number of events
         Uncertainty Problem
• Representing uncertain information in ES
  – Bayes Theorem
     • Mechanism for combining new and existent
       evidence usually given as subjective probabilities
     • Revise existing prior probabilities based on new
       information
     • The results are called posterior probabilities
              Number of outcomes favoring the occurence of
     P( X ) 
                        Total number of events
           Uncertainty Problem
• Bayes theorem
                                P( B / A * P( A))
    P( A / B) 
                  p( B / A) P( A)  P( B / not A) * P(not A)

  – P(A/B) = probability of event A occuring, given that B
    has already occurred (posterior probability)
  – P(A) = probability of event A occuring (prior
    probability)
  – P(B/A) = additional evidence of B occuring, given A;
  – P(not A) = A is not going to occur, but another event is
    P(A) + P(not A) = 1
           Uncertainty Problem
• Representing uncertain information in ES
  –   Probabilistic
  –   Certainty factors
  –   Theory of evidence
  –   Fuzzy logic
  –   Neural Network
  –   GA
  –   Rough set
         Uncertainty Problem
• Representing uncertain information in ES
  – Certainty factors
     • Uncertainty is represented as a degree of belief
     • 2 steps
        – Express the degree of belief
        – Manipulate the degrees of belief during the use of
          knowledge based systems
     • Based on evidence (or the expert’s assessment)
     • Refer pg 74
             Certainty Factors
• Form of certainty factors in ES
     IF <evidence>
     THEN <hypothesis> {cf }

     • cf represents belief in hypothesis H given that
       evidence E has occurred
     • Based on 2 functions
        – Measure of belief MB(H, E)
        – Measure of disbelief MD(H, E)
     • Indicate the degree to which belief/disbelief of
       hypothesis H is increased if evidence E were
       observed
              Certainty Factors
• Uncertain term and their intepretation
   Term                     Certainty Factor
   Definitely not           -1.0
   Almost certainly not     -0.8
   Probably not             -0.6
   Maybe not                -0.4
   Unknown                  -0.2 to +0.2
   Maybe                    +0.4
   Probably                 +0.6
   Almost certainly         +0.8
   Definitely               +1.0
            Certainty Factors
• Total strength of belief and disbelief in a
  hypothesis (pg 75)
              MB ( H , E )  MD ( H , E )
     cf 
          1  min[ MB ( H , E ), MD ( H , E )]
            Certainty Factors
• Example : consider a simple rule
     IF A is X
     THEN B is Y
  – In usual cases experts are not absolute certain
    that a rule holds
     IF A is X
     THEN B is Y {cf 0.7};
             B is Z {cf 0.2}
     • Interpretation; how about another 10%
     • See example pg 76
                Certainty Factors
• Certainty factors for rules with multiple
  antecedents
  – Conjunctive rules
     • IF <E1> AND <E2> …AND <En> THEN <H> {cf}
     • Certainty for H is

     cf(H, E1 E2  … En)= min[cf(E1), cf(E2),…, cf(En)] x cf

     See example pg 77
               Certainty Factors
• Certainty factors for rules with multiple
  antecedents
  – Disjunctive rules rules
     • IF <E1> OR <E2> …OR <En> OR <H> {cf}
     • Certainty for H is

     cf(H, E1 E2  … En)= max[cf(E1), cf(E2),…, cf(En)] x cf

     See example pg 78
               Certainty Factors
• Two or more rules effect the same hypothesis
  – E.g
  – Rule 1 :      IF     A is X THEN C is Z {cf 0.8}
                  IF     B is Y THEN C is Z {cf 0.6}
  Refer eq.3.35 pg 78 : combined certainty factor
        Uncertainty Problem
• Representing uncertain information in ES
  –   Probabilistic
  –   Certainty factors
  –   Theory of evidence
  –   Fuzzy logic
  –   Neural Network
  –   GA
  –   Rough set
       Theory of evidence
• Representing uncertain information in ES
     • A well known procedure for reasoning with
       uncertainty in AI
     • Extension of bayesian approach
     • Indicates the expert belief in a hypothesis given a
       piece of evidence
     • Appropriate for combining expert opinions
     • Can handle situation that lack of information
       Rough set approach
• Rules are generated from dataset
  – Discover structural relationships within
    imprecise or noisy data
  – Can also be used for feature reduction
     • Where attributes that do not contributes towards the
       classification of the given training data can be
       identified or removed
Rough set approach:Generation of Rules
          [E1, {a, c}],                         Class     a   b   c   dec
          [E2, {a, c},{b,c}],
          [E3, {a}],                            E1       1    2   3   1
          [E4, {a}{b}],                         E2       1    2   1   2
          [E5, {a}{b}]                          E3       2    2   3   2
                                                E4       2    3   3   2
                                                E5,1     3    5   1   3
                                                E5,2     3    5   1   4
              Reducts
                                                       Equivalence Classes



                          a1c3  d1
                          a1c1  d2,b2c1  d2
                          a2  d2
                          b3  d2
                          a3  d3,a3  d4
                          b5  d3,b5  d4



                                      Rules
Rough set approach:Generation of Rules
Class    Rules        Membership
                      Degree
E1       a1c3  d1    50/50 = 1
E2       a1c1  d2    5/5 = 1
E2       b2c1  d2    5/5 = 1
E3, E4   a2  d2      40/40 = 1
E4       b3  d2      10/10 = 1
E5       a3  d3      4/5 = 0.8
E5       a3  d4      1/5 = 0.2
E5       b5  d3      4/5 = 0.8
E5       b5  d4      1/5 = 0.2
     Rules Measurements : Support

Given a description contains a conditional part  and the
   decision part , denoting a decision rule   . The support
   of the pattern  is a number of objects in the information
   system A has the property described by .
                       sup port( )  

The support of  is the number of object in the IS A that have
  the decision described by .
                       sup port(  )  

The support for the decision rule    is the probability of
  that an object covered by the description is belongs to the
  class.
               sup port(   )  sup port(   )
              Rules Measurement : Accuracy

The quantity accuracy (  ) gives a measure of how
  trustworthy the rule is in the condition . It is the probability
  that an arbitrary object covered by the description belongs to the
  class. It is identical to the value of rough membership function
  applied to an object x that match . Thus accuracy measures the
  degree of membership of x in X using attribute B.

                                  sup port(   )
             Accuracy(   ) 
                                   sup port( )
             Rules Measurement : Coverage

Coverage gives measure of how well the pattern 
  describes the decision class defined through . It is a
  probability that an arbitrary object, belonging to the class
  C is covered by the description D.

                                     sup port(   )
                Coverage(   ) 
                                      sup port(  )
   Complete, Deterministic and Correct Rules


The rules are said to be complete if any object
  belonging to the class is covered by the description
  coverage is 1 while deterministic rules are rules with
  the accuracy is 1. The correct rules are rules with
  both coverage and accuracy is 1.

								
To top