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This paper considers the selection of the cluster head based on Fuzzy input variables. Cluster head is the main entity, and all the responsibility for the data communication relies on this single entity. As it is learnt that cluster head is the backbone of the entire cluster and is considered as the single point of failure for the entire cluster formation. If the cluster head fails to accomplish his function, all the members of the concerned cluster have to communicate directly with the base station. This causes the increase of power consumption which directly affects the total life of the network. This paper not only considers the selection criterion of cluster head but also presents the cluster back up approach, so that in case of cluster failure, the system still works in an efficient way. Simulation results show that, our proposed method Fuzzy Clustering Algorithm with backup support (FCA-BS) uses 17~20% less messages traffic for the same number of nodes as compared to LEACH and V-LEACH protocols which decreases the power consumption in the nodes and enhance the life of the entire network.