In sensor networks, a compromised node can either generate fabricated reports with false votes or inject false votes into real reports, which causes severe damage such as false alarms, energy drain and information loss. An interleaved hop-by-hop authentication (IHA) scheme addresses the former 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 necessary to the authentication procedure. In this paper, we propose a fuzzy-based interleaved multi-hop authentication scheme based on IHA. In our scheme, the fuzzy logic system only selects some nodes for verification based on the network characteristics. Moreover, we apply a voting method and a hash-based key assignment mechanism to improve network security. Through performance evaluation, the proposed scheme is found to save up to 13% of the energy consumption and to provide more network protection compared to IHA.