Perception and Classification. A Note on Near Sets and Rough Sets

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.