Fuzzy critical path method

There have been several attempts in the literature to apply fuzzy numbers to the critical path method. The result delivers the earliest expected time for each event of the project. This paper shows that further extension can be made by considering the interactive fuzzy subtraction and by observing that only the nonnegative part of the fuzzy numbers can have physical interpretation. Based on these two observations, the formulas for the latest allowable time and slack for each event are presented. The availability of fuzzy slacks provides enough information, at least for certain α-level of the slack, to identify the critical path in the network model of the project. Thus, practically we can generalize the critical path method by accepting imprecise, fuzzy data for the duration of the activities