A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.
@article{bwmeta1.element.bwnjournal-article-bcpv28z1p135bwm,
author = {Pawlak, Z. and Skowron, A.},
title = {Rough membership functions: a tool for reasoning with uncertainty},
journal = {Banach Center Publications},
volume = {28},
year = {1993},
pages = {135-150},
zbl = {0794.03045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv28z1p135bwm}
}
Pawlak, Z.; Skowron, A. Rough membership functions: a tool for reasoning with uncertainty. Banach Center Publications, Tome 28 (1993) pp. 135-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv28z1p135bwm/
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