In: International Journal of Intelligent Systems, Vol. 14, No. 8, pages 841-858. 1999.
Abstract: The first goal of this paper is to extend a model of timed safe Petri nets to allow the treatment of preference between transitions. In the proposed timed safe Petri net, a duration is attached to each transition, which can be precise, imprecise, or fuzzy, accounting for the maximal amount of time in which that transition can be completed once fired, and there is also a possibility degree attached between a place and a transition to account for the preference of this transition on relation to the other transition going out of that place. The second goal of this work is to address the problem of the management in incomplete information in the proposed model, what makes it possible to order the most plausible marking at a given moment of time. In particular, a new way to represent and deal with uncertain markings is investigated. All possible precise markings compatible with the uncertain marking are determined and a weight is attached to each one accounting for the possibility of it being the real marking. Then the Petri net is dealt with as with precise marking, but with special operations performed on the weights.
Keywords: fuzzy durations, imprecise durations, precise durations, timed safe Petri nets.