SOLUTION OF THE MAXIMUM EVACUATION FLOW PROBLEM DASED ON HESITANT FUZZY AGGREGATIPN OPERATORS

Abstract

Evacuation modeling is an urgent problem that has attracted more and more interest in recent
years. Today, flow theory in macroscopic evacuation allows researchers to find solutions to
optimization problems by treating aggrieved as a homogeneous mass. The main difficulty in constructing
evacuation scenarios is the necessity to take into account the internal uncertainty of the
network. In addition to the inherent ambiguity, the nodes of the network have limited capacities
and can store the flow as well as direct an additional flow to a sink in a given order. Thus, an
expert is a key figure in fuzzy modeling who must evaluate the order of intermediate nodes in order
to obtain the flow. If the decision-maker doubts during the choice of the membership function of an
alternative in relation to an attribute due to possible sub-attributes, he / she can set out all possible
evaluations of the alternative. Therefore, this article discusses the problem of maximum evacuation
with intermediate storage in nodes and compiling a priority of shelters. The hesitant fuzzy
hybrid averaging aggregation operator is used to determine the priority of intermediate nodes.
This evacuation scenario is the safest, since the maximum number of victims can be sent to the
safest shelters, using the capacities of intermediate nodes, so that the amount of incoming flow at
the intermediate node can exceed the outgoing flow. After finding the priority list of vertices, atransport network that is correspond to the residual network is constructed, and the flow is searched for, taking into account the storage of the flow in the shelters. A numerical example is
given to illustrate the proposed algorithm