Mathematics and Statistics Vol. 11(5), pp. 820 - 826
DOI: 10.13189/ms.2023.110508
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Aspects of Algebraic Structure of Rough Sets

S. Sangeetha , Shakeela Sathish ^*
Department of Mathematics, SRM Institute of Science and Technology, Ramapuram Campus, India

ABSTRACT

Rough sets are extensions of classical sets characterized by vagueness and imprecision. The main idea of rough set theory is to use incomplete information to approximate the concept of imprecision or uncertainty, or to treat ambiguous phenomena and problems based on observation and measurement. In Pawlak rough set model, equivalence relations are a key concept, and equivalence classes are the foundations for lower and upper approximations. Developing an algebraic structure for rough sets will allow us to study set theoretic properties in detail. Several researchers studied rough sets from an algebraic perspective and a number of structures have been developed in recent years, including rough semigroups, rough groups, rough rings, rough modules, and rough vector spaces. The purpose of this study is to demonstrate the usefulness of rough set theory in group theory. There have been several papers investigating the roughness in algebraic structures by substituting an algebraic structure for the universe set. In this paper, rough groups are defined using upper and lower approximations of rough sets from a finite universe instead of considering the whole universe. Here we have considered a finite universe along with a relation which classifies the universe into equivalence classes. We have identified all rough sets with respect to this relation. The upper and lower approximated sets have been taken separately and these form a rough group equivalence relation () and it partitions the group () into equivalence classes. In this paper, the rough group approximation space () has been defined along with upper and lower approximations and properties of subsets of with respect to rough group equivalence relations have been illustrated.

KEYWORDS
Rough Group, Rough Group Approximation Space, Rough Group Equivalence Relation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] S. Sangeetha , Shakeela Sathish , "Aspects of Algebraic Structure of Rough Sets," Mathematics and Statistics, Vol. 11, No. 5, pp. 820 - 826, 2023. DOI: 10.13189/ms.2023.110508.

(b). APA Format:
S. Sangeetha , Shakeela Sathish (2023). Aspects of Algebraic Structure of Rough Sets. Mathematics and Statistics, 11(5), 820 - 826. DOI: 10.13189/ms.2023.110508.