Affiliations: Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. [email protected]; [email protected] | Department of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland, [email protected]
Note: [] Address for correspondence: Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097 Warszawa, Poland This work was supported by grants N N516 368334 and N N516 077837 from the Ministry of Science and Higher Education of the Republic of Poland and by the National Centre for Research and Development (NCBiR) under Grant No. SP/I/1/77065/10 in frame of the strategic scientific research and experimental development program: “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.
Abstract: We discuss the problem of measuring the quality of decision support (classification) system that involves granularity based on rough set concepts. We put forward the proposal for such quality measure in the case when the underlying granular system is based on rough sets and makes use of approximation spaces. We introduce the notion of approximation, loss function, and quality measures that are inspired by empirical risk assessment for classifiers in the field of statistical learning. We further discuss the possibilities of improving the quality measure by extrapolating the loss function using function approximation methods originating in extensions of the concept of approximation space.
