Representing fuzzy, uncertain evidences having variable weights: Confidence propagation for rule-based systems

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Abstract

Representing knowledge uncertainty, aggregating evidence confidences, and propagating uncertainties are three key elements that affect the ability of a rule-based expert system to represent domains with uncertainty. Fuzzy set theory provides a good mathematical tool for representing the vagueness associated with a variable when, as the condition of a rule, it only partially corresponds to the input data. However, the aggregation of anded and ored confidences is not as simple as the intersection and union operators defined for fuzzy set memberships. There is, in fact, a certain degree of compensation that occurs when an expert aggregates confidences associated with compound evidence. Further, experts often consider individual evidences to be of varying importance, or weight, in their support for a conclusion. This paper presents a flexible approach for evaluating evidence and conclusion confidences. Evidences may be represented as fuzzy or nonfuzzy variables with an associated degree of certainty. Different weights can also be assigned to the individual conditions in determining the confidence of compound evidence. Conclusion confidence is calculated using a modified approach combining the evidence confidence and a rule strength. The techniques developed offer a flexible framework for representing knowledge and propagating uncertainties. This framework has the potential to reflect human aggregation of uncertain information more accurately than simple minimum and maximum operators do.

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