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.

A global satisfaction degree method for fuzzy capacitated vehicle routing problems.

There are several uncertain capacitated vehicle routing problems whose delivery costs and demands cannot be estimated using deterministic/statistical methods due to a lack of available and/or reliable data. To overcome this lack of data, third-party information coming from experts can be used to represent those uncertain costs/demands as fuzzy numbers which combined to an iterative-integer programming method and a global satisfaction degree is able to find a global optimal solution. The proposed method uses two auxiliary variables and the cumulative membership function of a fuzzy set to obtain real-valued costs and demands prior to find a deterministic solution and then iteratively find an equilibrium between fuzzy costs/demands via and .