Complex fuzzy soft groups

The aim of this thesis is to give complex fuzzy subgroup and complex fuzzy soft subgroup structures, to investigate their basic properties and to evaluate the results obtained. This study consists of five main sections. In the first chapter, an introduction section containing the literature review regarding the thesis topic was included. In the second chapter, some definitions and theorems that are fundamental to our study are stated. In the third chapter, some concepts such as complex fuzzy subet, complex fuzzy subgroup, normal complex fuzzy subgroup, π-fuzzy subset and π-fuzzy subgroup are introduced. Some basic properties of complex fuzzy subgroups are investigated and theorems regarding the image and inverse image of complex fuzzy subgroup under a group homomorphism are given. The fourth chapter consist of two parts. In the firs part, the complex fuzzy soft set structure is introduced and some binary operations on this structure are given and examples of these are presented. In the second part, the complex fuzzy soft group structure was introduced, its basic properties were investigated and the results were presented. In addition, theorems regarding the image and inverse image of complex fuzzy soft groups under complex fuzzy soft homomorphism are given and their basic properties are examined. In the first chapter the results obtained from the thesis study are expressed and suggestions are given.