Mobile ad hoc networks (MANETs) are originally designed for a cooperative environment, which are vulnerable to a wide variety of attacks due to their intrinsic characteristics. Trust can be introduced to address this security issue at some level. In this paper, we focus on the concept of trust and abstract a decentralized trust inference model, where the trust an entity has for a neighbor forms the basic building block of this model. Basing on the interest entity's historical behaviors, multi-dimensional trust attributes are incorporated to reflect trust relationship's complexity in various angles. The weight vector of attributes is calculated by fuzzy AHP scheme based on entropy weight measure. The trust inference framework provides the considerable security with an additional small overhead, which can be incorporated into any routing protocol. In this paper, the standard Ad hoc On-demand Multi-path Distance Vector protocol (AOMDV) is extended as the base routing protocol to evaluate this model. The proposed lightweight trust-enhanced routing protocol (TeAOMDV) can provide a feasible approach to choose an optimal two-way trusted route without containing the untrustworthy entities instead of the shortest route, thus mitigate the impairment effects from such entities. It is lightweight in the sense that the trust framework uses only passive and local monitoring information to evaluate the behaviors of an interest entity which is translated to an estimate of the trust, consumes limited computational resource. Moreover, the new proposed data-driven route maintenance mechanism reduces routing overhead and route discovery frequency. The simulations show that the proposed routing scheme behaves better in attack resistance (i.e., grey-hole attack and black-hole attack), and makes an improvement on the packets delivery ratio, routing packets overhead, route discovery frequency and malicious node detection. Finally, as an extension of the trust model, by utilizing the trust assessment data sequence, we propose an improved SCGM(1,1)-Markov chain prediction method based on the system cloud grey model and Markov stochastic chain theory to forecast entity's trust level for future decision making.