The notion of consensus through repeated averaging was first introduced by DeGroot in the context of synchronous environments. Since then, consensus has been extensively studied in a diverse range of fields, including biology, physics, and control engineering. The Krause mean process is a generalized model of opinion dynamics among many agents that represents opinions as vectors. In this paper, we investigate an opinion sharing dynamics in the multi-agent system by means of Krause mean processes which are generated by doubly stochastic hyper-matrices. This is arguably a feasible generalization of the classical models such as DeGroot’s model as well as Chatterjee-Seneta’s model from square stochastic matrices to higher-order stochastic hyper-matrices. We then demonstrate how consensus can be achieved in the multi-agent system when doubly stochastic hyper-matrices have positive influences. This is a novel generalization of the Perron-Frobenius theorem from doubly stochastic square matrices to doubly stochastic hyper-matrices with positive influences.