The previous application of fuzzy members to the critical path method, as is known from literature, provides only the earliest expected time for each event of the project. The author shows that a further extension can be made by considering interactive fuzzy subtraction and by observing that only the positive part of the fuzzy numbers can have a physical interpretation. Based on these two observations, the formulas for latest allowable time and slack for each event are given. The possible critical paths in the network model of the project can then be identified. An indicator of degree of involvement of an event in the critical path is introduced, followed by an example. >