Network virtualization in wireless sensor networks (WSNs) enables the utilization of shared sensing capabilities in many industrial internet of things (IIoT) applications. Efficient assignment of WSN resources can be achieved through virtual network embedding (VNE) while considering the Quality of Information (QoI) (as the accuracy of sensing), the Quality of Service (QoS) (as the reliability), and wireless interference handling constraints. The shared and complex nature of VNE exposes WSNs to security risks. In this paper, we develop a novel offline distributed trust-aware virtual wireless sensor networks (DTA-VWSN) algorithm that considers the QoI, QoS, and security, by adding required trust level constraints to virtual nodes and links and trust level constraints to the substrate counterparts. Since centralized algorithms suffer from scalability issues, this paper presents our new approach to the virtual network embedding problem in a distributed manner. We use the techniques of multi-agent systems as a well-known approach for distributed systems to scale these algorithms to network size. Our simulation results show that DTA-VWSN improves the execution time of embedding algorithms, acceptance ratio, and cost in substrate networks.