Fuzzy Critical Path Method Based on Signed-Distance Ranking and Statistical Confidence-Interval Estimates

Activity networks have proved very useful for certain types of project performance evaluations. The purpose of the critical path method (CPM) is to identify the critical activities in the critical path of an activity network. However, the unknowns or vagueness about the time duration for activities in network planning, has led to the development of fuzzy CPM. In this paper, we propose an approach that combines fuzzy mathematics with statistics to solve practical problems in unknown or vague situations. We introduce a fuzzy CPM based on statistical confidence-interval estimates and a signed-distance ranking for (1−α) fuzzy number levels. We not only derive the level (1−α) of fuzzy numbers from (1−α)×100% statistical data confidence-interval estimates, but also use the signed-distance ranking method to define the ordering. The primary result obtained from this study, is a theorem through which the critical path in the fuzzy sense is obtained based on statistical confidence-interval estimates.