Bi ideals are the generalisation of quasi ideals. In this article, it is defined that the notion of bi-ideals in semirings on weak nearness approximation spaces. Afterwards, it is explained that some of the concepts and definitions related to the subject. Also, it is given that the definition of nearness −bi ideals and nearness ( , ) −quasi ideals. Thus, we examine the relationship between nearness m-bi ideals and nearness (m,n)-quasi ideals .

This article introduces quasi-ideals in semirings on weak nearness approximation spaces. Concepts and definitions are given to clarify the subject of quasi ideals in semirings on weak nearness approximation spaces. Some basic properties of quasi ideals are also given. Furthermore, it is given that the definition of upper-near quasi ideals. And, it is examined that the relationship between quasi ideals and upper near quasi ideals. Therefore, the features described in this study will contribute greatly to the theoretical development of the nearness semirings theory.

The aim of this paper is to introduce Nobusawa [Formula: see text]-nearness hemiring theory and also to study some properties of ideals and prime (semiprime) ideals for Nobusawa [Formula: see text]-nearness hemirings.

In this paper, we study some concepts of subgroups on weak nearness approximation spaces. We show some properties that are satisfied by usual subgroups are not satisfied in nearness subgroups. In addition to this, it is defined that nearness subgroup generated by a subset on weak nearness approximation spaces.

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