Some characterizations of semigroups in terms of intuitionistic fuzzy interior ideals

Hidayat Ullah Khan
Department of Mathematics, University of Malakand, at Chakdara, District Dir (L), Khyber Pakhtunkhwa, Pakistan.
Nor Haniza Sarmin
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi, Malaysia
81310 UTM, Johor Bahru, Johor, Malaysia.
Asghar Khan
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan.
Faiz Muhammad Khan
Department of Mathematics, University of Swat, Khyber Pakhtunkhwa, Pakistan.

\(^{1}\)Corresponding Author: hidayatullak@yahoo.com

Copyright © 2014 Hidayat Ullah Khan, Nor Haniza Sarmin, Asghar Khan,Faiz Muhammad Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2014.

Abstract

The importance of semigroups and their fuzzy subsystems is evident from their applications and significant role in several applied disciplines like computer sciences, control engineering, error-correcting codes and fuzzy automata theory. In this paper, we give generalizations of intuitionistic fuzzy interior ideals of semigroups and introduced the notions of intuitionistic fuzzy interior ideals of type \((\overline{∈}, \overline{∈} ∨ \overline{q}_{k})\) and \((\overline{∈}, \overline{∈})\) of semigroups. The important mile stone of the present paper is to link ordinary intuitionistic fuzzy interior ideals, \((\overline{∈}, \overline{∈})\)-intuitionistic fuzzy interior ideals and \((\overline{∈}, \overline{∈} ∨ \overline{q}_{k})\)-intuitionistic fuzzy interior ideals. Moreover semigroups are characterized by the properties of these notions.

Keywords:

Interior ideal; Intuitionistic fuzzy interior ideal; Intuitionistic fuzzy interior ideal; \((\overline{∈}, \overline{∈} ∨ \overline{q}_{k})\)-fuzzy interior ideal; ((\overline{∈}, \overline{∈})\)-fuzzy interior ideal.