M.Sc. Tezi Görüntüleme

Student:	Canan EKİZ
Supervisor:	Asst.Prof.Dr. Sultan YAMAK
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	(I,T)-L- Fuzzy Rough Sets in Semigroups
Level:	M.Sc.
Acceptance Date:	10/7/2009
Number of Pages:	59
Registration Number:	i2049

Summary:

(I,T)-L-Fuzzy Rough Sets in Semigroups

In this thesis, some new properties of generalized rough sets and generalized (I,T)-L-Fuzzy Rough Sets are investigated. Taking their general cases into consideration, generalized rough sets and generalized (I,T)-L-fuzzy rough sets are adapted to the semigroups and some new theorems are obtained.

In the first part, the notions of lattice, t-norm, t-conorm, implication, semigroup, L-fuzzy subset, L-fuzzy relation, TL-fuzzy subsemigroup (ideal, bi-ideal, prime ideal) are dealt with and some definitions, theorems and examples necessary for this study are given.

In the second part; first of all, for generalized approximation space, general properties of lower and upper approximations of a crisp set or for generalized L-fuzzy approximation space, I-lower and T-upper approximations of a L-fuzzy subset are investigated. Afterwards when two semigroups are chosen as universal sets, some theorems are proved.

Key Words: L-Fuzzy Subset, Semigroup, Generalized (L-Fuzzy) Approximation Space, Rough Set, (I,T)-L-Fuzzy Rough Set