DMCA
Characterizations of ordered semigroups in terms of ...-fuzzy Interior Ideals (2012)
BibTeX
@MISC{Khan12characterizationsof,
author = {Asghar Khan and Young Bae Jun and Muhammad Zaheer Abbas},
title = { Characterizations of ordered semigroups in terms of ...-fuzzy Interior Ideals},
year = {2012}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
In this paper, we give characterizations of ordered semigroups in terms of ([, [ _q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of ([, [ _q)-fuzzy interior ideals (resp. ([, [ _q)fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of ([, [ _q)-fuzzy ideals and ([, [ _q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is ([, [ _q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of ([, [ _q)-fuzzy ideals (resp. ([, [ _q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.
