Student:	Dilek BAYRAK
Supervisor:	Doç.Dr. Sultan YAMAK
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Summary:

(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 are investigated and

give some examples. In the last chapter, the notions of TL -vague module and TL -vague sub

module 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