TL-vague module

The purpose of this thesis is to study basic properties of vague notions such as TL-vague group, TL-vague ring and TL-vague module which are vague versions of the structure of group, ring and module.This thesis consists of two chapters. Chapter one deals with the basic concepts of lattice, group, ring, module, L-fuzzy subset theories, L-fuzzy relations and TL-fuzzy functions which will be needed. Also basic material concerning TL-vague groups and TL-vague rings which make up the basis of the thesis are established.Second chapter, which is the original part of this study, consists of three sections. In the first and second parts, some new properties of TL-vague group and TL-vague ring are investigated and give some examples. In the last chapter, the notions of TL-vague module and TL-vague submodule are transmitted in TL-vague module of the basic theorems of module is given.Key Words: TL-vague group, TL-vague ring, TL-vague module.