Defining rough sets using tolerances compatible with an equivalence
We consider tolerances T compatible with an equivalence E on U, meaning that the relational product E ∘ T is included in T. We present the essential properties of E-compatible tolerances and study rough approximations defined by such E and T. We consider rough set pairs (XE, XT), where the lower approximation XE is defined as is customary in rough set theory, but XT allows more elements to be possibly in X than XE. Motivating examples of E-compatible tolerances are given, and the essential lattice-theoretical properties of the ordered set of rough sets {(XE, XT)∣X ⊆ U} are established.
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Hivatkozás
MLA: Järvinen, Jouni, László Kovács, and Sándor Radeleczki. "Defining rough sets using tolerances compatible with an equivalence." Information Sciences 496 (2019): 264-283.
APA: Järvinen, J., Kovács, L., & Radeleczki, S. (2019). Defining rough sets using tolerances compatible with an equivalence. Information Sciences, 496, 264-283.
ISO690: JÄRVINEN, Jouni; KOVÁCS, László; RADELECZKI, Sándor. Defining rough sets using tolerances compatible with an equivalence. Information Sciences, 2019, 496: 264-283.
BibTeX:
@article{jarvinen2019defining,
title={Defining rough sets using tolerances compatible with an equivalence},
author={J{"a}rvinen, Jouni and Kov{'a}cs, L{'a}szl{'o} and Radeleczki, S{'a}ndor},
journal={Information Sciences},
volume={496},
pages={264--283},
year={2019},
publisher={Elsevier}
}