Rough Sets for Knowledge Representation in Artificial Intelligence Systems: A Critical Review

Rough sets, rough set-theoretic definitions and axiomatic frameworks have been, for some time now, a mainstream mathematical approach from fuzzy mathematics to model and encode (un)certainty in traditional information systems across different domains. With the pervasive rise and shift from traditional information systems to Artificial Intelligence (AI)-based intelligent information systems, however, the issue of representing and encoding (un)certain knowledge of different domains and at different levels of abstraction within such systems has emerged as an unsolved pivotal research problem in AI. The paper is interdisciplinary in nature, being positioned at the intersection of mathematics and AI research, and, to that end, will have two objectives. First, it will focus on critically reviewing key state-of-the-art interdisciplinary research literature on how rough sets and rough set-theoretic frameworks are being employed for (un)certain knowledge representation, e.g., via ontologies and Knowledge Graphs, in AI-based information systems across different domains. Second, based on the aforementioned critical review, it will elucidate research implications and potential research strategies which will inform future research towards developing an integrated mathematical philosophy and mathematico-logical formalism for (un)certain knowledge representation in AI systems.