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http://dx.doi.org/10.5831/HMJ.2014.36.3.569

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

Khan, Hidayat Ullah (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia)
Sarmin, Nor Haniza (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia)
Khan, Asghar (Department of Mathematics, Abdul Wali Khan University Mardan)
Publication Information
Honam Mathematical Journal / v.36, no.3, 2014 , pp. 569-596 More about this Journal
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 (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${\in},{\in}{\vee}\bar{q}_k$)-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 (${\in},{\in}{\vee}\bar{q}_k$)-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; ($\bar{\in},\bar{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals; ($\bar{\in},\bar{\in}{\vee}\bar{q}_k$)-fuzzy left (right) ideals; (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy bi-ideals;
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