Solving Fuzzy PERT Using Gradual Real Numbers

From a set of a partially ordered tasks, one goal of the project scheduling problem is to compute earliest starting dates, latest starting dates and floats of the different tasks, and to identify critical tasks. When durations of tasks are not precisely known, the problem is much trickier. Recently we provided polynomial algorithms to compute upper bound of activity floats in the interval-valued model. The aim of this paper is to extend those new algorithms to the fuzzy-valued problem. To this end, we use the new notion of gradual numbers [7], that represents soft boundaries of a fuzzy interval. We show that algorithms in the interval–valued case can be adapted to fuzzy intervals considering them as crisp intervals of gradual numbers.