The most important consideration in designing protocols for wireless sensor networks is the energy constraint of nodes because in most cases battery recharging is inconvenient or impossible. Therefore, many research have been done to overcome this demerit. Clustering is one of the main approaches in designing scalable and energy-efficient protocols for wireless sensor networks. The cluster heads take the task of data aggregation and data routing to decrease the amount of communication and this prolongs the network lifetime. To the best of our knowledge, in spite of the importance of clustering in extending network lifetime, no metrics have been proposed for evaluating the quality of generated clusters. In this paper, we define some metrics to compare different protocols in terms of clustering qualification. Then we combine these metrics using fuzzy logic to better conclude about the superiority of different clustering schemes. The correction and feasibility is validated in simulations of three different protocols (LEACH, HEED, and HEED-NPF) in Matlab software.

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