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Knowledge reduction of information systems is one of the most important parts of rough set theory in real-world applications. Based on the connections between the rough set theory and the theory of topology, a kind of topological reduction of incomplete information systems is discussed. In this study, the topological reduction of incomplete information systems is characterized by belief and plausibility functions from evidence theory. First, we present that a topological space induced by a pair of approximation operators in an incomplete information system is pseudo-discrete, which deduces a partition. Then, the topological reduction is characterized by the belief and plausibility function values of the sets in the partition. A topological reduction algorithm for computing the topological reducts in incomplete information systems is also proposed based on evidence theory, and its efficiency is examined by an example. Moreover, relationships among the concepts of topological reduct, classical reduct, belief reduct, and plausibility reduct of an incomplete information system are presented.

The analyses carried out within the Seismic Probabilistic Risk Assessments (SPRAs) of Nuclear Power Plants (NPPs) are affected by significant aleatory and epistemic uncertainties. These uncertainties have to be represented and quantified coherently with the data, information and knowledge available, to provide reasonable assurance that related decisions can be taken robustly and with confidence. The amount of data, information and knowledge available for seismic risk assessment is typically limited, so that the analysis must strongly rely on expert judgments. In this paper, a Dempster-Shafer Theory (DST) framework for handling uncertainties in NPP SPRAs is proposed and applied to an example case study. The main contributions of this paper are two: (i) applying the complete DST framework to SPRA models, showing how to build the Dempster-Shafer structures of the uncertainty parameters based on industry generic data, and (ii) embedding Bayesian updating based on plant specific data into the framework. The results of the application to a case study show that the approach is feasible and effective in (i) describing and jointly propagating aleatory and epistemic uncertainties in SPRA models and (ii) providing ‘conservative’ bounds on the safety quantities of interest (i.e. Core Damage Frequency, CDF) that reflect the (limited) state of knowledge of the experts about the system of interest.

Our basic understanding of evidential reasoning, in its vast and intricate complexity, has been guided by different methods including probabilistic and possibilistic models. However, restrictions surrounding evidence must be fully precisiated/validated before discussing their probability or possibility which is rarely achieved, especially in uncertain or imprecise environments. In this paper, a new generalization of the Dempster-Shafer Theory (DST) is presented that accounts for this issue. In the proposed generalization, we include information about the validity of a fuzzy body of evidence to represent its bearing on unprecisiated information, and then we distribute this knowledge over the belief structure. We provide an epistemic framework of evidence and study its behavior and its constraints in terms of validity, probability, and possibility to establish a foundation for evidential reasoning and unprecisiated uncertainty that exists in evidence. The suggested belief structure is crafted by min-max optimization method. Then, the proposed structure is used to estimate the probability density function (pdf) and is explored by the application diagnosis of aphasia, in which unprecisiated uncertainty is involved due to the subjectivity of the test items, inconsistency in the interpretation of aphasic syndromes, and the changeable precision of medical tests. Even in requiring more parameters, an accuracy improvement in the results is noticeably observed, especially when compared with the results of alternative approaches applied in the same database. [ABSTRACT FROM AUTHOR]