Abstract:
In this study, we investigate the problem of how to define Gamma-nearness semiring in the sense of Nobusawa theory which extends the notion of a nearness rings, nearness semirings and Gamma-rings [N. Nobusawa, On a generalization of the ring theory, Osaka Journal of Mathematics 1 (1964) 81-89; M. A. Ozturk, Semirings on weak nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics 15(3) (2018) 227 241; M. A. Ozturk and E. Inan, Nearness rings, Annals of Fuzzy Mathematics and Informatics 17(2) (2019) 115-132]. Also, we introduce some properties of approximations and their algebraic structures.
