Szczuka, Marcin; Skowron, Andrzej; Stepaniuk, Jarosław Function approximation and quality measures in rough-granular systems. (English) Zbl 1246.68235 Fundam. Inform. 109, No. 3, 339-354 (2011). The paper provides a rough-set perspective on the approximation of loss functions and on the estimation of empirical risk in statistical learning theory [V. N. Vapnik, Statistical learning theory. Chichester: Wiley (1998; Zbl 0935.62007)]. The treatment is limited to some definitions and useful illustrative examples. Applications to decision support are indicated in examples, but there are no results about the properties of the definitions. The paper includes a new definition of the lower approximation of a function with respect to a generalized notion of approximation space. This differs from the usual definition [Z. Pawlak and A. Skowron, Inf. Sci. 177, No. 1, 3–27 (2007; Zbl 1142.68549)] of the lower approximation of a relation and should be more appropriate in some cases as the result is less frequently empty. Reviewer: John G. Stell (Leeds) Cited in 2 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence 68T30 Knowledge representation Keywords:rough sets; granularity; classification; loss function; empirical risk Citations:Zbl 0935.62007; Zbl 1142.68549 PDFBibTeX XMLCite \textit{M. Szczuka} et al., Fundam. Inform. 109, No. 3, 339--354 (2011; Zbl 1246.68235) Full Text: DOI