Roughness of filters in equality algebras

Gholam Reza Rezaei; Rajab Ali Borzooei; Mona Aaly Kologani; Young Bae Jun

doi:10.18778/0138-0680.2023.01

Authors

Gholam Reza Rezaei Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Rajab Ali Borzooei Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Mona Aaly Kologani Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

DOI:

https://doi.org/10.18778/0138-0680.2023.01

Keywords:

equality algebra, approximation space, (lower) upper approximation, filter, (D-lower) D-upper filter

Abstract

Rough is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and the upper approximations are introduced and some properties of them are given. Moreover, it is proved that the lower and the upper approximations are an interior operator and a closure operator, respectively. Also, using D-lower and D-upper approximation, conditions for a nonempty subset to be definable are provided and investigated that under which condition D-lower and D-upper approximation can be filter.

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