Near sets and applications

This study, which is prepared as a master thesis, consists of four sections. In the first section, the concept of fuzzy sets, rough sets, soft sets and near sets concept fundamental approximation spaces and nearness approximation spaces concept are discussed for better understanding of other sections. At the end of the first chapter definition based set operations are also included. In the second section; the relationship between the concepts of classical set, near sets, soft sets and fuzzy sets are investigated. With the relations between classic Cantor set theory and the new approaches, the transitions between these set theories and the basic definitions and theorems related to these set approaches are specified. In the third section, applications on new set approaches are discussed. Information about these set approaches were examined in terms of giving detailed information and the same examples were discussed in each set type. It has been made applications on the science of graphology which makes character analysis with handwriting and forensic document analysis that is used quite a lot.The relationship between the personal characters of mass groups was investigated by associating new set approaches with the science of graphology. The third section generates the original part of this thesis. In the fourth chapter, the superiority and the shortcomings between the new cluster approaches and the results obtained from the concept of subset in classical cluster theory were examined.