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Addressing this issue requires the development of energy-efficient Objective Functions (OFs) within the RPL (Routing Protocol for Low-Power and Lossy Networks) routing protocol. Traditional OFs primarily used routing layer metrics for parent selection. Therefore, our analysis demonstrates that transmission dynamics at the MAC layer significantly impact overall energy consumption. To tackle this, we introduce a cross-layer energy-efficient objective function (CL-RPL-OF) that incorporates a novel metric, energy per packet (EPP), which quantifies the energy consumed during the transmission and reception of a single data packet. This metric integrates strobe per packet rate (SPPR) and strobe packet success rate, both of which are influenced by radio duty cycling (RDC) mechanisms at the media access control (MAC) layer. The proposed CL-RPL-OF considers node-to-node communication variations arising from relative phase shifts by combining EEP with expected transmission count (ETX) and SPPR using fuzzy logic to select the best path to optimize energy consumption across both routing and MAC layers. Simulation using Cooja and real-world experimentation using the FIT IoT-LAB testbed demonstrate that CL-RPL-OF significantly improves energy efficiency, increases packet delivery ratio, and reduces strobe overhead compared to existing objective functions.<\/jats:p>","DOI":"10.1007\/s44196-025-00916-2","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T08:20:21Z","timestamp":1752654021000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Fuzzy-Based Novel Cross-Layer RPL Objective Function for Energy-Aware Routing in IoT"],"prefix":"10.1007","volume":"18","author":[{"given":"M. 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