Rough Sets

Abstract

Rough set theory, proposed by Professor Zdzisław Pawlak in 1982 [163, 165, 166, 169], can be seen as a new mathematical approach to dealing with imperfect knowledge, in particular with vague concepts. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information (data, knowledge). For example, if objects are patients suffering from a certain disease, symptoms of the disease form information about patients. Objects characterized by the same information are indiscernible (similar) in view of the available information about them. The indiscernibility relation generated in this way is the mathematical basis of rough set theory. This understanding of indiscernibility is related to the idea of Gottfried Wilhelm Leibniz that objects are indiscernible if and only if all available functionals take on identical values (Leibniz's Law of Indiscernibility: The Identity of Indiscernibles) [4, 97]. However, in the rough set approach, indiscernibility is defined relative to a given set of functionals (attributes). © Springer-Verlag Berlin Heidelberg 2013.