In Cognitive Radio Sensor Network (CRSN), a cognitive radio sensor node operated on a dynamic spectrum allocation with limited computational and energy resource. A cognitive radio sensor node must vacate an occupied channel degrading its performance due to reclustering as the common channel no longer available. Furthermore, energy is mostly consumed during data transmission mechanism. Clustering is the best architecture model to minimize energy consumption among the nodes. With the objective of a robust cluster while maximizing network lifetime, a fuzzy logic technique is proposed. A metric named relative common channel is also proposed. The fuzzy logic combines two input parameters, the relative common channel and residual energy to elect the best suitable cluster head to minimize reclustering and maximize the network lifetime. The performance of the proposed algorithm is compared with LEACH, SAFCA and CogLEACH. The results show that the CRSN has more extended network lifetime and more balanced energy consumption attributed to the robust cluster formation.