Rough semigroups on approximation spaces

Abstract

In this paper, we introduced the notion of rough semigroups, rough subsemigroups, rough ideals, rough bi-ideals and homomorphisms of rough semigroups in approximation spaces. Then we give some properties of these rough structures.

Near Approximations in Vector Spaces

“…Feng and li [1] have obtained the rough soft set by associating the concepts of rough set and soft set, and similarly, Tasbozan [25] has obtained the near soft set builts up a connection between soft set and near set. The algebraic side of the rough set has been studied by many scientists [7,6,26,27,10,11,13,12,8,9] . Biswas and Nanda made the definition of subgroup with the approximation and Kuroki [12] made the definition of sub-ring with the approximation.…”

Direct Products of Rough Subgroups

“…After this, Miao et al [16] developed these concepts and proved their some new features. In addition, Bağırmaz and Özcan [17] gave new definition of rough semigroups groups on rough approximation spaces.…”

“…Proposition17 Let N₁ and N₂ be normal subgroups of groups ₁ and ₂, respectively. Let A₁ and A₂ be normal subgroups of ₁ and ₂, respectively.…”

Near Ideals in Near Semigroups

“…Xiao and Zhang [30], studied the notions of rough prime ideals and rough fuzzy prime ideals in a semigroup. Bagırmaz andÖzcan [1], studied the notion of rough semigroup on approximation space. Moreover, Bagırmaz [2], investigated rough prime ideals on approximation spaces.…”

“…We introduced the notion of near ideal that our notion depends on the upper approximation and does not depend on the lower approximation. So, our definition of near ideal is similar to the definition of rough ideal [1].…”