Properties of Lower and Upper Approximation Operators under Various Kinds of Relations

DOI

10.2991/icmce-14.2014.81How to use a DOI?

Keywords

Rough Sets, Lower and Upper Approximation Operators, Binary Relation, Equivalence Relation.

Abstract

One of the direction of rough sets theory is to extend the equivalence relation, using more general binary relation such as the partial order relation, tolerance relation or similarity relations instead of the strict equivalence relation. So the scope of application of rough sets theory could be extended. But in the use of these more general relation instead of equivalence relation, some good properties of the original Pawlak approximation space (U,R) may no longer be satisfied. In this paper, various properties of two pairs of lower and upper approximation operators and the relationship between them are acquired through analysis and proof. The two pairs of lower and upper approximation operator will have good properties when the binary relation R only satisfies reflexivity, and the two pairs of approximation operators are the same under the equivalence relation. Theoretical analysis shows that, in the process of extending classical rough set theory to generalized rough set theory, reflexivity is a minimum conditions to be satisfied, under this condition, the lower and upper approximation operators meeting the corresponding properties can be chosen to adapt to the requirement of practical application.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Wei-Feng DU
AU  - Teng ZI
PY  - 2014/12
DA  - 2014/12
TI  - Properties of Lower and Upper Approximation Operators under Various Kinds of Relations
BT  - Proceedings of the 2014 International Conference on Mechanics and Civil Engineering
PB  - Atlantis Press
SP  - 472
EP  - 477
SN  - 2352-5401
UR  - https://doi.org/10.2991/icmce-14.2014.81
DO  - 10.2991/icmce-14.2014.81
ID  - DU2014/12
ER  -