Nobusawa Gamma Nearness Semirings.

In this study, we investigate the problem of how to define Γ -nearness semiring in the sense of Nobusawa theory which extends the notion of a nearness rings, nearness semirings and Γ -rings [N. Nobusawa, On a generalization of the ring theory, Osaka Journal of Mathematics1 (1964) 81–89; M. A. Öztürk, Semirings on weak nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics15(3) (2018) 227–241; M. A. Öztürk and E. İnan, Nearness rings, Annals of Fuzzy Mathematics and Informatics17(2) (2019) 115–132]. Also, we introduce some properties of approximations and their algebraic structures. [ABSTRACT FROM AUTHOR]