Extension of Petri Nets for Representing and Reasoning with Tasks with Imprecise Durations

This paper presents an extension of Petri net framework with imprecise temporal properties. We use possibility theory to represent imprecise time by time-stamping tokens and assigning durations to firing of the transitions. A method for approximation of an arbitrary temporal distribution with a set of possibilistic intervals is used to introduce the composition operation for two possibilistic temporal distributions. We developed a method to determining an effective enabling time of a transition with incoming tokens with possibilistic distributions. The utility of the proposed theory is illustrated using an example of an automated manufacturing system. The proposed approach is novel and has a broad utility beyond a timed Petri network and its applications.