2. Inexact Reasoning 1 Session 9
Course : T0273 – EXPERT SYSTEMS
Year : 2014
Inexact Reasoning 1 Session 9

3. Learning Outcomes LO 3 : Solve problems by using Expert Systems
After taking this course, students should be expected to understand and explain about inexact reasoning.
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4. Lecture Outline Introduction Uncertainty and Rules Certainty Factors
Dempster-Shafer Theory
Summary
Exercise
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5. Introduction
Probability theory has been called by mathematicians a theory of reproducible uncertainty.
The term reproducible means in a statistical sense when there is a large population and the results are averaged over many trials.
Inexact reasoning is when the antecedent, the conclusion, and even the meaning of the rule itself are uncertain to some extent.
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6. Antecedent and consequent
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7. Uncertainty and Rules
High level view of uncertainty may come from the individual rules, conflict resolution, and incompatibilities among the consequents of rules.
Minimizing the uncertainties of individual rules is part of the verification of the rule.
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8. Uncertainty and Rules
The figure below is the top-level view of uncertainties in individual rules
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9. Uncertainty and Rules
Conflict resolution is part of a major source of uncertainty caused by the interactions between rules.
The interaction of rules depends on conflict resolution, and the compatibility of rules.
The compatibility of rules has uncertainty from five major causes as illustrated in the following figure:
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10. Uncertainty and Rules
There is uncertainty in conflict resolution regarding priority for firing. This uncertainty depends on a number of factors as illustrated in the following figure:
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11. Certainty Factor
In MYCIN, the degree of confirmation was originally defined as the certainty factor, which is the difference between belief and disbelief:
CF (H, E) = MB (H, E) – MD (H, E)
CF is the certainty factor in the hypothesis H due to evidence E
MB is the measure of increased belief in H due to E
MD is the measure of increased disbelief in H due to E
The certainty factor is a way of combining belief and disbelief into a single number.
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12. Certainty Factor
The measures of belief and disbelief were defined in terms of probabilities by:
The original definition of CF is:
CF = MB – MD
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13. Dempster-Shafer Theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories.
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14. Dempster-Shafer Theory
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15. Dempster-Shafer Theory
Difficulty with the Dempster-Shafer theory:
occurs with normalization and may lead to results that are contrary to our expectations. The problem with normalization is that it ignores the belief that the object being considered does not exist.
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16. Summary
Inexact reasoning is when the antecedent, the conclusion, and even the meaning of the rule itself are uncertain to some extent.
High level view of uncertainty may come from the individual rules, conflict resolution, and incompatibilities among the consequents of rules.
The certainty factor is a way of combining belief and disbelief into a single number.
The Dempster-Shafer theory assumes that there is a fixed set of mutually exclusive and exhaustive elements called the environment.
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17. Diskusi Create an Expert System Program using CF
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18. References
Joseph Giarratano, Gary Riley Expert Systems: Principles and Programming Chapter 5. Thomson Course Technology. Australia. ISBN:
Peter Jackson Introduction to Expert Systems. Addison-Wesley. Harlow, England. ISBN:
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