Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Near Sets. Special Theory about Nearness of Objects
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Nearness of Objects: Extension of Approximation Space Model
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Nature-inspired framework for measuring visual image resemblance: A near rough set approach
Theoretical Computer Science
Parallel computation in finding near neighbourhoods
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Nearness approximation space based on axiomatic fuzzy sets
International Journal of Approximate Reasoning
Perceptual indiscernibility, rough sets, descriptively near sets, and image analysis
Transactions on Rough Sets XV
Maximal clique enumeration in finding near neighbourhoods
Transactions on Rough Sets XVI
Soft Nearness Approximation Spaces
Fundamenta Informaticae - Cognitive Informatics and Computational Intelligence: Theory and Applications
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The paper aims to establish topological links between perception of objects (as it is defined in the framework of near sets) and classification of these objects (as it is defined in the framework of rough sets). In the near set approach, the discovery of near sets (i.e. sets containing objects with similar descriptions) starts with the selection of probe functions which provide a basis for describing and discerning objects. On the other hand, in the rough set approach, the classification of objects is based on object attributes which are collected into information systems (or data tables). As is well-known, an information system can be represented as a topological space (U, τ E). If we pass froman approximation space (U,E) to the quotient space U/E, where points represent indiscernible objects of U, then U/E will be endowed with the discrete topology induced (via the canonical projection) by τ E. The main objective of this paper is to show how probe functions can provide new topologies on the quotient set U/E and, in consequence, new (perceptual) topologies on U.