Delay-tolerant networks allow communication using store-carry-forward technique between source and destination nodes where no end-to-end connectivity exists. In case of network disconnection, messages get stored in a node and wait till the connection is restored, which could be forwarded to another node. To explore the possibility of improvement, many researchers have applied protocol based on fuzzy in DTN, but none of them proposed any solution for the situation where the node density is very low. This situation may result in low buffer availability. Hence, the nodes become unavailable for forwarding messages due to low buffer availability. In general, the remote area does not have a dense network thus, required buffer size might not be available at all the nodes for enabling communication. In this paper, we proposed a solution for the scenario where nodes cannot accept any message due to the unavailability of storage. To make communication possible, we formulated a methodology to search for the best node available in the communication range for relaying the message. The selected node is tested for buffer availability. As per negative result, it is subjected to buffer cleaning and then used for sending a message to that node. If the result is positive, the message will be sent directly to the relay node. A Fuzzy logic system is used for relay node selection and buffer cleaning process. ONE simulator has been adopted for simulating the environment and the simulation results indicate that the proposed technique enhanced the network's performance.