Relational Formal Characterization of Rough Sets

Adam Grabowski

Formalized Mathematics (2013)

  • Volume: 21, Issue: 1, page 55-64
  • ISSN: 1426-2630

Abstract

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The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough sets [12] trying to formalize some parts of [19] following also [18] in some sense (Propositions 1-8, Corr. 1 and 2; the complete description is available in the Mizar script). Our main problem was that informally, there is a direct correspondence between relations and underlying properties, in our approach however [7], which uses relational structures rather than relations, we had to switch between classical (based on pure set theory) and abstract (using the notion of a structure) parts of the Mizar Mathematical Library. Our next step will be translation of these properties into the pure language of Mizar attributes.

How to cite

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Adam Grabowski. "Relational Formal Characterization of Rough Sets." Formalized Mathematics 21.1 (2013): 55-64. <http://eudml.org/doc/266930>.

@article{AdamGrabowski2013,
abstract = {The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough sets [12] trying to formalize some parts of [19] following also [18] in some sense (Propositions 1-8, Corr. 1 and 2; the complete description is available in the Mizar script). Our main problem was that informally, there is a direct correspondence between relations and underlying properties, in our approach however [7], which uses relational structures rather than relations, we had to switch between classical (based on pure set theory) and abstract (using the notion of a structure) parts of the Mizar Mathematical Library. Our next step will be translation of these properties into the pure language of Mizar attributes.},
author = {Adam Grabowski},
journal = {Formalized Mathematics},
keywords = {rough sets; approximation operators; relational structures; Mizar Mathematical Library},
language = {eng},
number = {1},
pages = {55-64},
title = {Relational Formal Characterization of Rough Sets},
url = {http://eudml.org/doc/266930},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Adam Grabowski
TI - Relational Formal Characterization of Rough Sets
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 1
SP - 55
EP - 64
AB - The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough sets [12] trying to formalize some parts of [19] following also [18] in some sense (Propositions 1-8, Corr. 1 and 2; the complete description is available in the Mizar script). Our main problem was that informally, there is a direct correspondence between relations and underlying properties, in our approach however [7], which uses relational structures rather than relations, we had to switch between classical (based on pure set theory) and abstract (using the notion of a structure) parts of the Mizar Mathematical Library. Our next step will be translation of these properties into the pure language of Mizar attributes.
LA - eng
KW - rough sets; approximation operators; relational structures; Mizar Mathematical Library
UR - http://eudml.org/doc/266930
ER -

References

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