Abstract
Rough Set Theory may be considered as a formal interpretation of observation of phenomena. On one side we have objects and on the other side we have properties. This is what we call a Property System. Observing is then the act of perceiving and then interpreting the binary relation (of satisfaction) between the two sides. Of course, the set of properties can be given a particular structure. However, from a pure ”phenomenological” point of view, a structure is given by the satisfaction relation we observe. So it is a result and not a precondition. Phenomena, in general, do not give rise to topological systems but to pre-topological systems. In particular, ”interior” and ”closure” operators are not continuous with respect to joins, so that they can ”miss” information. To obtain continuous operators we have to lift the abstraction level of Property Systems by synthesizing relations between objects and properties into systems of relations between objects and objects. Such relations are based on the notion of a minimal amount of information that is carried by an item. This way we can also account for Attribute Systems, that is, systems in which we have attributes instead of properties and items are evaluated by means of attribute values. But in order to apply our mathematical machinery to Attribute Systems we have to transform them into Property Systems in an appropriate manner.
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Pagliani, P., Chakraborty, M.K. (2007). Formal Topology and Information Systems. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_15
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