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Decision-theoretic rough set model interprets the parameters of existing probabilistic rough sets by introducing Bayesian theory to minimize the risks of classification. It is a representative probabilistic rough set model. As an important extension of decision-theoretic rough set model, fuzzy decision-theoretic rough set model can deal with numerical data directly. To investigate the attribute reduction...
It has been known that neighborhood system is the first granular computing model. From the view point of knowledge engineering, each neighborhood is considered as a unit of basic knowledge. In this paper, we mainly focus on knowledge operations in neighborhood system. The knowledge operations are defined on the neighborhood system of the object and the universe respectively. By using the proposed...
Rough set models based on the tolerance and similarity relations, are constructed to deal with incomplete information systems. Unfortunately, tolerance and similarity relations have their own limitations because the former is too loose while the latter is too strict in classification analysis. To make a reasonable and flexible classification in incomplete information system, a new binary relation...
Neighborhood System(NS) is revisited from the view of Formal GrC Model. NS formalize the ancient intuition, infinitesimals, which led to the invention of calculus, topology and non-standard analysis. In this paper, we show that Ziarko's variable precision model can be expressed by NS. Together with previously known results (NS includes topology, binary relation(binary neighborhood system) and covering...
In this paper, the dominance-based variable precision rough fuzzy set is proposed in the fuzzy information system. It is proved that the proposed rough fuzzy approach is a generalization of the dominance-based rough fuzzy approach. Important properties of the dominance-based variable precision rough fuzzy set are investigated. Further on the problem of inducing "at least" and "at most"...
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