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 University of Sistan and Baluchestan, Department of Mathematics, 98167-45845, Daneshjoo Boulevard Zahedan, Iran Author https://orcid.org/0000-0001-5693-402X
Rajab Ali Borzooei Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics, 1983969411, Daneshjoo Boulevard Tehran, Iran Author https://orcid.org/0000-0001-7538-7885
Mona Aaly Kologani Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics, 1983969411, Daneshjoo Boulevard Tehran, Iran Author https://orcid.org/0000-0002-5234-2876
Young Bae Jun Gyeongsang National University, Department of Mathematics Education, Jinju 52828, Korea Author https://orcid.org/0000-0002-0181-8969

DOI:

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

Keywords:

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

Abstract

Rough set theory 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 define 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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