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

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. T0273 - Expert Systems

Lecture Outline Introduction Uncertainty and Rules Certainty Factors Dempster-Shafer Theory Summary Exercise T0273 - Expert Systems

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. T0273 - Expert Systems

Antecedent and consequent T0273 - Expert Systems

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. T0273 - Expert Systems

Uncertainty and Rules The figure below is the top-level view of uncertainties in individual rules T0273 - Expert Systems

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: T0273 - Expert Systems

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: T0273 - Expert Systems

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. T0273 - Expert Systems

Certainty Factor The measures of belief and disbelief were defined in terms of probabilities by: The original definition of CF is: CF = MB – MD T0273 - Expert Systems

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. T0273 - Expert Systems

Dempster-Shafer Theory T0273 - Expert Systems

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. T0273 - Expert Systems

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. T0273 - Expert Systems

Diskusi Create an Expert System Program using CF http://www.jogjalab.com/program/sistem_pakar_certainty_factor T0273 - Expert Systems

References Joseph Giarratano, Gary Riley. 2005. Expert Systems: Principles and Programming Chapter 5. Thomson Course Technology. Australia. ISBN:0-534-38447-1. Peter Jackson. 1998. Introduction to Expert Systems. Addison-Wesley. Harlow, England. ISBN:0201876868 T0273 - Expert Systems