## 2 Related Works  
To better understand the related works and research motivation of the proposed scheme, first we must define the guaranteed networks lifetime. In this paper, we use the term guaranteed lifetime to describe the time in which a wireless sensor network must perform given operations before it is expired. As for network lifetime, much of the research literature has studied this in the last few decades. In this section, we briefly describe the related research works for energy consumption and network lifetime. Several techniques have been suggested to reduce the energy consumption of sensors and to prolong network lifetime. As a centralized approach for scheduling and prolonging a WSN lifetime, the concept of utilizing artificial intelligence (AI) or computational intelligence (CI) techniques to support the decision-making process is widely used in the recent literature to obtain more efficient WSN algorithms. Several protocols applied AI or CI techniques to design energy-efficient WSNs and routing algorithms [8]. Such techniques emphasized the efficiency and performance of WSN routing protocols by merging sensed data obtained from nodes and their communication in order to improve network performance. Furthermore, these approaches require a large number of messages to be exchanged to improve the global network performance. Other AI- and CI-based protocols require high computational capabilities and a complete knowledge of the WSN prior to deploying the sensor nodes. On the other hand, fuzzy logic-based approaches performed very well in energy efficient routing and clustering heuristics in WSNs. In [9], a fuzzy logic approach is used to select a cluster head by considering energy and distance to efficiently route data in WSNs. Another fuzzy logic-based energy-efficient algorithm, (Cluster Head Election mechanism using Fuzzy logic (CHEF) [10], selected cluster heads in a distributed way over energy and distance as input descriptors. Among other researchers, the energy-aware distributed dynamic clustering protocol [11] is proposed through fuzzy logic to consider the cost and distance of a node in the selection of a cluster head. Fuzzy routing algorithms (FML) were proposed in [12] to maximize lifetime routing problem in WSNs. FML results showed that the use of fuzzy functions and operators provides a promising direction for devising efficient solutions to numerous related energy-aware routing problems in WSNs. Although all of these schemes showed better performance than other mathematical models, they were limited only to energy-efficient routing in WSNs. In WSNs, the approaches based on fuzzy logic can be easily found for efficient energy utilization and routing [7; 8; 9; 10; 11; 12; 13]. However, due to the unbalanced remaining energy schemes among nodes, the existing techniques of maximizing WSN lifetime cannot be directly applied to a guaranteed lifetime. In addition to minimizing the energy usage to extend the WSN lifetime, few research works have been proposed guaranteeing a pre-configured WSN lifetime. An integer linear programming (ILP)-based model is proposed in [14] to design a sensor network with guaranteed lifetime by periodically determining the minimum number of relay nodes as cluster heads. In [15], the pre-configured network lifetime is guaranteed by the duty cycle of each node. However, this algorithm relied on traffic load to reduce end-to-end latency and did not monitor the energies among nodes to provide provable guarantees on the network lifetime. Differently from the two above-mentioned approaches, adjustable battery packs were used in [16] to precisely determine the energy budget at deployment to guarantee the WSN lifetime. However, an extra introduced lifetime variable created a large amount of communication overhead. Similarly, a new cost function is introduced to balance the load over each link and to reduce the queuing delay to guarantee network lifetime [17].