A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 3,  2014, pp.569-596
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.3.569
Title & Authors
A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS
Khan, Hidayat Ullah; Sarmin, Nor Haniza; Khan, Asghar;

Abstract
In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of ($\small{{\in},{\in}{\vee}\bar{q}_k}$)-fuzzy subsystems of ordered semigroups namely ($\small{{\in},{\in}{\vee}\bar{q}_k}$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and ($\small{{\in},{\in}{\vee}\bar{q}_k}$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a ($\small{{\in},{\in}{\vee}\bar{q}_k}$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.
Keywords
Ordered semigroups;regular;left (right) regular;completely regular and weakly regular ordered semigroups;generalized bi-ideals;fuzzy left (right) ideals;fuzzy generalized bi-ideals;($\small{\bar{\in},\bar{\in}{\vee}\bar{q}_k}$)-fuzzy generalized bi-ideals;($\small{\bar{\in},\bar{\in}{\vee}\bar{q}_k}$)-fuzzy left (right) ideals;($\small{{\in},{\in}{\vee}\bar{q}_k}$)-fuzzy bi-ideals;
Language
English
Cited by
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