Approximation of soft ideals by soft relations in semigroups

Article type: Research Article

Authors: Kanwal, Rani Sumaira^{; *} | Shabir, Muhammad

Affiliations: Department of Mathematics, Quaid-i-azam University, Islamabad Pakistan

Correspondence: [*] Corresponding author. Rani Sumaira Kanwal, Department of Mathematics, Quaid-i-azam university, Islamabad Pakistan. E-mails: [email protected], [email protected].

Abstract: A soft set handles indeterminate data. By using an equivalence relation, Pawlak introduced the rough set concept for dealing uncertainty to approximate a set. Many authors generalized the concept and used binary relations to approximate a set. A soft set is approximated in this paper by soft binary relations in the context of the aftersets and foresets. Along these lines, we get two sets of soft sets, called the lower approximation and upper approximation with respect to the aftersets and foresets. We applied these concepts on semigroups and approximations of soft subsemigroups, soft left (right) ideals, soft interior ideals and soft bi-ideals of semigroups are studied. Moreover, for the illustration of the concept, some examples are considered.

Keywords: Soft relations, Soft set approximation, Soft substructures

DOI: 10.3233/JIFS-190328

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 7977-7989, 2019