Nearness gamma semi-rings

This study, which is prepared as a MSc thesis, consists of five chapters. The first chapter consists of an introduction. In the second chapter, the references used and benefited in the thesis are summarized under the title of previous studies. The third part consists of three parts; rough sets, near sets and basic approximation spaces, weak nearness approximation spaces and their properties to better understand the rest of the thesis. The fourth section consists of two parts. In the first part of this chapter, gamma semi-rings on the weak close approximation space are defined, and the concept of complete indiscernibility relation and some features of the upper and lower approaches on weak approximation spaces are given. In addition, gamma nearness sub semi ring and its ideal was introduced, and the theorems were obtained considering gamma nearness semi ring. In the second part of this chapter, the prime (semi-prime) ideals of the gamma nearness semi ring were introduced and the theorems were obtained by taking into consideration the gamma nearness semi ring. The results of the last section, which is the result of the study done in comparison with previous studies. In the final section, the results of the study were compared with the previous studies.