Cost-allocation problems for fuzzy agents in a fixed-tree network

Cost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule.