×

Function approximation and quality measures in rough-granular systems. (English) Zbl 1246.68235

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.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation
PDFBibTeX XMLCite
Full Text: DOI