Search

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.

As two mathematical tools for dealing with uncertainty, the covering rough set theory and the evidence theory have close relationships with each other. Different covering rough set models are characterized by evidence theory. The purpose of this paper is to interpret belief functions with two pairs of covering approximation operators. The two pairs of covering approximation operators are equivalent to a pair of relation approximation operators. Then, based on a necessary and sufficient condition for a belief structure to be the belief structure induced by the pair of relation approximation operators, necessary and sufficient conditions for a belief structure to be the belief structure induced by the covering approximation operators are presented. Moreover, two kinds of covering reductions in covering information systems defined from the two pairs of covering approximation operators are characterized by the belief and plausibility functions. [ABSTRACT FROM AUTHOR]

The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented. [ABSTRACT FROM AUTHOR]

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]

A method for ranking of alternatives or objects and its extensions by incomplete pairwise comparisons using random set theory are proposed in the paper. The main feature of the method is that it allows us to deal with comparisons of arbitrary groups of alternatives. The method is extended on the case of independent groups of experts. The imprecise Dirichlet model is also used to make cautious decisions in several cases. Various numerical examples illustrate the proposed method and its extensions. [ABSTRACT FROM AUTHOR]

Abstract: Methods for ranking of alternatives or objects by pairwise comparisons using random set theory are proposed in the paper. Efficient algorithms weekly depending on the number of independent sources of data are considered. Methods using the imprecise Dirichlet model are used for obtaining cautious comparison measures when the number of expert judgments is rather small and standard methods of random set theory may give risky results. The methods allow us to overcome some difficulties concerning the conflicting or contradictory sources of data. Various numerical examples illustrate the proposed algorithms and methods. [Copyright &y& Elsevier]