Krause mean processes generated by off-diagonally positive doubly stochastic hyper-matrices

Abstract

Back in 1974, DeGroot first introduced the concept of achieving consensus through iterative averaging processes using square stochastic matrices. A pivotal question arises regarding the feasibility of extending the classical DeGroot model from square stochastic matrices to higher-order stochastic hyper-matrices. In the paper, we introduce a novel mathematical model for opinion-sharing dynamics employing the Krause mean process that is generated by off-diagonally positive doubly stochastic hyper-matrices. The principal objective is to achieve consensus within the multi-agent system.