The reducibility of matrix sweeping operations: A computational issue in linear belief functions

Matrix sweeping operations are the basis for the knowledge representation and combination of linear belief functions. Yet, their basic properties are not well studied and often misunderstood. This paper attempts to fill the void and corrects a long lasting mistake in the literature on whether a block-level sweeping from a nonsingular submatrix can be reduced into sequential element-level sweepings from individual leading diagonal elements of the submatrix. It proposes a new alternative to workaround the failure of reducibility and introduces a prototype system, dubbed LMOS, in support of irreducible sweeping operations. © 2019 Elsevier Inc.