LAUSR

The paper deals with the combination of multiple criteria decision making, fuzzy modelling, and robust optimization for shortest path planning (graph theory) in emergency management. Many factors can be included in the evaluation of uncertainty in emergency situations. Graph theory is used for representation of affected area, fuzzy modelling approach and fuzzy linguistic scales are used for the assessment of these factors and the resulting uncertainty. Based on the aggregation of the multiple criteria evaluation, the edges of the graph are divided into subsets according to their levels of uncertainty. Finally, we introduce a robust approach that reflects these different subsets and allows us to plan paths under uncertainty in travel times on edges. Different relevant scenarios are calculated and compared with each other. The results show that setting different uncertainty levels has a significant impact on the solution. The suggested approach using vague terms is shown as a possible tool for setting up the uncertainty set for the robust optimization approach in shortest path planning. This approach also allows to set and modify properly the solution based on the newly obtained information. The approach suggested for robust and fuzzy models is described in detail and is shown in the example of the area of Oaxaca, Mexico where the earthquake occurred in 2020.