Soft crossed modules

In this master thesis, the concepts of crossed module, soft group and soft crossed module were examined by giving definitions and solved examples related to "soft set theory". This thesis consists of seven chapters. In the first part, a literature review was conducted on the development process of the concepts that form the basis of the thesis. In the second part, the basic concepts and the concept of action are presented in order to ensure the continuity and integrity of the thesis. In the third part, the action of a group on a set is defined and some important characterizations are studied by exemplifying. In the fourth chapter, soft set theory, which is put forward as a strong mathematical approach to uncertainty, is presented, examples and basic definitions related to soft set theory are given. In the fifth chapter, the action of one group on another group are examined by examining soft groups, definitions are given, examples are analyzed and some important features are given. In the sixth chapter, the concept of soft crossed module is presented and this thesis study is completed by giving examples, and in the last chapter, the result is given.