Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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)
  • Received : 2014.06.16
  • Accepted : 2014.08.26
  • Published : 2014.09.25
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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.

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References

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