Lexicographic maximum dynamic evacuation modeling with partial lane reversal based on hesitant fuzzy TOPSIS

Abstract

Decision-making under evacuation environment is extremely complex due to the variety of aspects to be considered as well as the necessity of high-speed reaction. Therefore, the elaboration of the evacuation pattern, particularly, finding the priority order of shelters for evacuation, requires multiple experts to be involved in the decision-making process. Moreover, decision-makers cannot provide precise assessments of alternatives due to the uncertainty inherent in the network parameters, dynamic nature of transportation, complexity of the task. In this regard, the method of finding the priority order of terminals for the evacuation based on the fuzzy hesitant TOPSIS method is proposed. The method handles a modified ranking index to find the priority order based on assigned weights of separations. In this method, experts’ assessments are presented as linguistic terms, which are further converted to fuzzy triangular numbers. This leads to the hesitant fuzzy TOPSIS decision-making with completely unknown attribute weights.The existing state of the art of evacuation modeling lacks fuzzy statements of evacuation flow problems. Our work aims to contribute to the design of the algorithm for the lexicographic maximum flow finding in the evacuation dynamic network with fuzzy transit arc capacities and transit traversal time parameters with partial contraflow. The approach reverses only necessary arcs by reversing the traffic in vacant segments, which allows using these segments for movement towards the safe areas as well. In addition, the method based on linear combinations of spreads is proposed to handle fuzzy values, which does not lead to the blurring of a fuzzy number. A case study to find the priority order of four destinations d1,d2,d3,d4 along with the maximum dynamic flow determining is provided to illustrate the proposed method. The hesitant fuzzy TOPSIS evaluated the priority order of destinations for evacuation the maximum number of aggrieved as {d4,d3,d1,d2} along with maximum lexicographic flow with partial lane reversal 62˜ flow units. The method for finding the spreads without blurring a fuzzy number was used to determine the final triangular number (50, 62, 75) units.The sensitivity analysis shows that in all ten cases, the alternatives have unique rank: A4 is the best, A2 is the worst. In the pessimistic case, DMs prefers the alternative that is furthest to FNIS. In the optimistic case, DMs prefer the alternative that is closest to FPIS. We proved that the proposed algorithm is reliable because despite the changes in parameters ω, the same priority order of alternatives is chosen. The obtained results are confirmed by efficiency frontier and coincide with the results of original TOPSIS, Doukas et al.’s, method, Kuo’s method, Yoon and Kim’s behavioral TOPSIS.