Uncertainty management in expert systems using fuzzy Petri nets

The paper aims at developing new techniques for uncertainty management in expert systems for two generic class of problems using fuzzy Petri net that represents logical connectivity among a set of imprecise propositions. One class of problems addressed in the paper deals with the computation of fuzzy belief of any proposition from the fuzzy beliefs of a set of independent initiating propositions in a given network. The other class of problems is concerned with the computation of steady-state fuzzy beliefs of the propositions embedded in the network, from their initial fuzzy beliefs through a process called belief-revision. During belief-revision, a fuzzy Petri net with cycles may exhibit 'limitcycle behavior' of fuzzy beliefs for some propositions in the network. No decisions can be arrived at from a fuzzy Petri net with such behavior. To circumvent this problem, techniques have been developed for the detection and elimination of limitcycles. Further, an algorithm for selecting one evidence from each set of mutually inconsistent evidences, referred to as nonmonotonic reasoning, has also been presented in connection with the problems of belief-revision. Finally, the concepts proposed for solving the problems of belief-revision have been applied successfully for tackling imprecision, uncertainty, and nonmonotonicity of evidences in an illustrative expert system for criminal investigation. Index Terms - Belief propagation, belief revision, expert systems, fuzzy belief, fuzzy Petri nets, limitcycles, nonmonotonic reasoning, reachability, stability, uncertainty management.