A path enumeration approach for the analysis of critical activities in fuzzy networks

This paper addresses the problem of determining the degree of possible and necessary criticality of activities as well as determining paths in networks that have fuzzy activity durations. In such networks, activities and paths are reported in a fuzzy representation as being critical, with certain degrees of possibility and necessity, instead of being declared critical or not in a binary way. Although the problem of computing the possibility and necessity degrees of criticality for paths have been investigated in the literature, those problems for activities have not yet been addressed. Herein, an efficient algorithm that relies on a path enumeration technique is proposed to compute the possibility degrees of criticality of activities. Additionally, the proposed algorithm computes paths with maximum and minimum degrees for the necessity of criticality, which correspond to activities. Real-world project networks were used to evaluate the performance of the algorithm.