Uncertain project network analysis with fuzzy-PERT and Interval Type-2 fuzzy activity durations

Project network analysis is often subject to different uncertainties that can occur in real world scenarios. These uncertainties are not always measurable which makes its statistical estimation hard, so the use of third party information coming from experts is useful to provide an estimation of activity durations of the project. Projects usually have multiple experts who provide different estimates of their perceptions about activity durations which can be represented as Type-2 fuzzy sets in cases where experts do not agree on their estimates. Such disagreement/ambiguitites can be either expressed with Interval Type-2 fuzzy numbers or the proposed fuzzy-PERT set which is an extension of the classical PERT distribution to a fuzzy environment. To do so, a mathematical formulation of the fuzzy problem is presented, two solution methods are described and two illustrative examples are solved.