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A NEW FORM OF FUZZY GENERALIZED BI-IDEALS IN ORDERED SEMIGROUPS
Khan, Hidayat Ullah,Sarmin, Nor Haniza,Khan, Asghar The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.3
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.
A New Form of Fuzzy Generalized Bi-Ideals in Ordered Semigroups
( Hidayat Ullah Khan ),( Nor Haniza Sarmin ),( Asghar Khan ) 호남수학회 2014 호남수학학술지 Vol.36 No.3
In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzified algebraic structures especially ordered semigroups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (-e,-ev-qk,)-fuzzy subsystems of ordered semigroups namely (-e,-ev-qk,)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (-e,-ev-qk,)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semigroups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (-e,-ev-qk,)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.