New fuzzy generalized bi Γ-ideals of the type (∈,∈∨qk) in ordered Γ-semigroups


  • Ibrahim Gambo Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Universiti Teknologi Malaysia
  • Hidayat Ullah Khan University of Malakand
  • Faiz Muhammad Khan University of Swat



Generalized bi Γ-ideal, ordered Γ-semigroup, fuzzy point, (∈, ∈∨qk) fuzzy generalized bi Γ-Ideal.


A fuzzy subset A defined on a set X is represented as A = {(x, A (x), where x ∈ X}. It is not always possible for membership functions of type λA : X → [0,1] to associate with each point x in a set X a real number in the closed unit interval [0,1] without the loss of some useful information. The importance of the ideas of “belongs to” (∈) and “quasi coincident with” (q) relations between a fuzzy point and fuzzy set is evident from the research conducted during the past two decades. Ordered Γ-semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups. In this paper, we provide an extension of fuzzy generalized bi Γ-ideals and introduce (∈,∈∨qk)-fuzzy generalized bi Γ-ideals of ordered Γ-semigroup. The purpose of this paper is to link this new concept with ordinary generalized bi Γ-ideals by using level subset and characteristic function.


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