Local rough sets and rough subgroupoids

The first chapter of this thesis, which is consisting of five chapters, has been arranged as an introduction chapter and the literature survey has also been given in this chapter. In the second chapter, basic concepts to be used in the upcoming chapters are introduced. In this chapter, the basic topological concepts; category theory and sheaf theory are presented with relevant definitions and theorems. In sheaf theory, the concept of local equivalence relation,which is the global section of sheaf, are given. In the third chapter, some definitions and basic features of rough sets are given. In addition, the concept of rough group, which is a rough algebraic structures, is presented with the help of the lower and the upper approximations of a subset of a group. Fourth and fifth chapters constitute the original parts of this thesis. In the fourth chapter, the concept of rough subgroupoid, which is a new definition, is introduced by using the concepts of groupoid and rough theory and relevant theorems are given. In the final chapter, local rough set that is a new rough set is presented with the help of the concept of local equivalence relation. In addition, the lower and the upper approximations of local rough sets are presented and some of their features have been given.