Rough Set Topology

Any human being, having rational behavior, must have the ability to classify real or abstract objects. In order to classify, one has to ignore some differences among objects. One may claim that in the same class, the objects are not different. These (indiscernible) classes are used to build up knowledge about reality. For example, if the objects are classified according to colour, then the class of objects is classified as red from the concept of redness. In this approach the knowledge can be understood as an ability to classify. A concept, which is expressed in terms of the assumed classification patterns, is crisp or precise. Otherwise, the concept is imprecise. However the imprecise concepts can be defined approximately in the available knowledge by employing two precise concepts called their lower and upper approximations. Using the pair of these approximations, Prof. Z. Pawlak of Poland introduced the concept of Rough Sets in 1981. Since then it became an important mathematical tool to deal with vagueness.