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Due to limited radio transmission range, sporadic node densities and power limitations, mobile ad hoc networks (MANETs) may become intermittently connected thereby disrupting the data routing process. Existing routing schemes for MANETs are not equipped to address this routing problem. In an attempt to resolve this, various "store-carry-forward" routing mechanisms have been proposed in literature. Although they exploit the mobility of the nodes for message delivery, most of them only focus on one particular routing factor such as delivery probabilities in particular cases, and cannot work well under various mobility scenarios. Furthermore, application-specific and user-centric service requirements are also not considered in any of these routing approaches. As such, in this paper we present a novel routing framework, AHP-GRA based routing framework (AGRF), that utilizes two mathematical models namely analytic hierarchy process (AHP) and grey relational analysis (GRA) to offer routing capability in intermittently connected MANETs (ICMANs). In the proposed mechanism, when any two nodes meet each other in the network, each node selects the messages it prefers to store, carry and forward in the future by ranking all possible messages according to various preferred factors. Simulation results demonstrate the enhanced performance measure offered by the proposed framework over existing schemes.