Analysis of different fuzzy CPM network planning procedures

With great progress in fuzzy set theory there have been also several efforts in using this theory in network planning methods such as PERT and CPM to make more realistic usage of them and better dealing with uncertainties that is intrinsic in estimating duration of activities. In this paper, using noninteractive fuzzy subtraction, we have proposed an algorithm that reads fuzzy numbers as activity durations along with their initial and final node numbers; constructs network and computes earliest expected time, latest allowable time, and slack time for each node. At the end, critical path, or paths for different a-cuts are calculated. Instead of classical descriptive methods, we have used numeric methods and whenever the shape of the fuzzy number differs from initial shape (e.g. triangular), using defuzzification with center of gravity and refuzzification; we convert the number to its initial shape.