Every large project consists of many activities and for a given activity digraph, we would like to determine the minimum amount of time needed to complete all activities. The longest path in an activity digraph is called critical path. The length of the critical path in an activity digraph is equal to the minimum time required to complete the whole project. Thus, the task of finding the longest path in weighted digraphs (network) is one of the most studied optimization problems on a non-fuzzy network over the past five decades. When the values associated with the arc lengths in the network are fuzzy numbers, then we have a fuzzy longest path problem. In this paper, it has been proposed to state a theorem for the fuzzy longest path problem for project scheduling, assuming that the duration of activities as trapezoidal fuzzy numbers and an algorithm is also proposed for searching the longest path in a network, where the arc lengths are taken as triangular fuzzy numbers.

acyclic network, longest path problem (LPP), crisp numbers, level l‑trapezoidal fuzzy numbers, level (l, r) interval valued trapezoidal fuzzy numbers, signed distance, triangular fuzzy numbers, triangular density function, similarity measure (SM), euclidean distance (ED), centroid measure (CM), project scheduling.