© 2016, Springer Science+Business Media New York. Even though some velocity based routing protocols for (m,k)-firm stream have been recently proposed in multimedia wireless sensor networks, there are still many perspective parameters to be considered for forwarding procedure. Moreover, since they are not correlated with each other, multi-criteria system for forwarding is desirable to select next hop. However, current existing protocols apply these parameters sequentially without any prioritization. To address this issue, in this paper, we propose two (m,k)-firm specific routing protocols based on fuzzy interference system and analytical hierarchical process in conjunction with the gray relational analysis. In each protocol, delivery ratio, energy, speed, (m,k)-firm stream requirement as well as current stream status are used to select the best appropriate next hop while considering given node’s constraints. Through the simulation results, we demonstrate that the proposed scheme gracefully maintains (m,k)-firm requirement while extending the network lifetime. Finally, superiority of the proposed approach to existing velocity based routing protocols is also proven through diverse simulation scenarios.