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An in-depth understanding of uncertainty is the first step to makingeffective decisions under uncertainty. Deep/machine learning (ML/DL) has beenhugely leveraged to solve complex problems involved with processinghigh-dimensional data. However, reasoning and quantifying different types ofuncertainties to achieve effective decision-making have been much less exploredin ML/DL than in other Artificial Intelligence (AI) domains. In particular,belief/evidence theories have been studied in KRR since the 1960s to reason andmeasure uncertainties to enhance decision-making effectiveness. We found thatonly a few studies have leveraged the mature uncertainty research inbelief/evidence theories in ML/DL to tackle complex problems under differenttypes of uncertainty. In this survey paper, we discuss several popular belieftheories and their core ideas dealing with uncertainty causes and types andquantifying them, along with the discussions of their applicability in ML/DL.In addition, we discuss three main approaches that leverage belief theories inDeep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and RoughDNNs, in terms of their uncertainty causes, types, and quantification methodsalong with their applicability in diverse problem domains. Based on ourin-depth survey, we discuss insights, lessons learned, limitations of thecurrent state-of-the-art bridging belief theories and ML/DL, and finally,future research directions.

A Survey on Uncertainty Reasoning and Quantification for Decision Making: Belief Theory Meets Deep Learning