Calculus of fuzzy hierarchical censored production rules (FHCPRs)

Abstract

The article addresses the problem of reasoning under time constraints with incomplete, vague, and uncertain information. It is based on the idea of Variable Precision Logic (VPL), introduced by Michalski and Winston, which deals with both the problem of reasoning with incomplete information subject to time constraints and the problem of reasoning efficiently with exceptions. It offers mechanisms for handling trade-offs between the precision of inferences and the computational efficiency of deriving them. As an extension of Censored Production Rules (CPRs) that exhibit variable precision in which certainty varies while specificity stays constant, a Hierarchical Censored Production Rules (HCPRs) system of Knowledge Representation proposed by Bharadwaj and Jain exhibits both variable certainty as well as variable specificity. Fuzzy Censored Production Rules (FCPRs) are obtained by augmenting ordinary fuzzy conditional statement: “if X is A then Y is B” (or A(x) ⇒ B(y) for short) with an exception condition and are written in the form: “if X is A then Y is B unless Z is C” (or A(x) ⇒ B(y) ∥ C(z)). Such rules are employed in situations in which the fuzzy conditional statement “if X is A then Y is B” holds frequently and the exception condition “Z is C” holds rarely. Thus, using a rule of this type we are free to ignore the exception condition, when the resources needed to establish its presence are tight or there simply is no information available as to whether it holds or does not hold. Thus if … then part of the FCPR expresses important information while the unless part acts only as a switch that changes the polarity of “Y is B” to “Y is not B” when the assertion “Z is C” holds. Our aim is to show how an ordinary fuzzy production rule on suitable modifications and augmentation with relevant information becomes a Fuzzy Hierarchical Censored Production Rules (FHCPRs), which in turn enables to resolve many of the problems associated with usual fuzzy production rules system. Examples are given to demonstrate the behavior of the proposed schemes. © 1996 John Wiley & Sons, Inc.