Student:	Rabia İşçi
Supervisor:	Dr. Öğr. Üyesi Şerife Yılmaz
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	CONSTRUCTION OF T-NORMS ON ALGEBRAIC LATTICES AND ELEMENTS DEPENDING ON A T-NORM IN LATTICES
Level:	M.Sc.
Acceptance Date:	15/1/2020
Number of Pages:	39
Registration Number:	i3721

Summary:

The aim of this study is to provide a construction method for obtaining a t-norm on an

algebraic lattice 𝐿 by using the t-norms given on the set of generating elements of the lattice 𝐿 and

also to investigate some algebraic properties of the sets of the irreducible and prime elements

depending on a t-norm given on complete lattices.

This study consists of two parts. In the first chapter, some basic definitions and theorems are

given. In the second chapter, firstly, a construction method is given for obtaining a t-norm and a tconorm

on an algebraic lattice 𝐿. Then, the relationship between the set of T-prime elements and

the set of coatoms is discussed under some conditions in a complete lattice 𝐿. Finally, some

characterizations are given for the set of T-irreducible elements and the set of T-prime elements in

the direct product of complete lattices.

Key Words: Algebraic lattice, Triangular norm, Irreducible element.