In sensor networks, a compromised node can generate fabricated reports, which cause severe damage such as false alarms and energy drain. An interleaved hop-by-hop authentication (IHA) scheme addresses the attack by detecting and filtering false reports in a deterministic and hop-by-hop fashion. Unfortunately, in IHA, all en-route nodes must join to verify reports while only a few are actually necessary to the authentication procedure. In this paper, we propose an energy-aware fuzzy-based interleaved multi-hop authentication scheme enhanced from IHA. Our fuzzy logic system only selects some nodes for verification based on the network characteristics. Through performance evaluation, the proposed scheme is found to outperform IHA in saving energy while maintaining a sufficiently high filtering power.