A novel approach towards fuzzy Γ-ideals in ordered Γ-semigroups

Faiz Muhammad Khan (), Nor Haniza Sarmin () and Asghar Khan ()
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Faiz Muhammad Khan: University of Swat
Nor Haniza Sarmin: Universiti Teknologi Malaysia, UTM
Asghar Khan: Abdul Wali Khan University

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 3, 343-362

Abstract: Abstract In many applied disciplines like computer science, coding theory and formal languages, the use of fuzzified algebraic structures especially ordered semigroups play a remarkable role. In this paper, we introduce a new concept of fuzzy Γ-ideal of an ordered Γ-semigroup G called an (∈, ∈ ∀q k )-fuzzy Γ-ideal of G. Fuzzy Γ-ideal of type (∈, ∈ ∨q k ) are the generalization of ordinary fuzzy Γ-ideals of an ordered Γ-semigroup G. A new characterization of ordered Γ-semigroups in terms of an (∈, ∈ ∨q k )-fuzzy Γ-ideal is given. We show that a fuzzy subset λ of an ordered Γ-semigroup G is an (∈, ∈ ∨q k )-fuzzy Γ-ideal of G if and only if U (λ; t) is a Γ-ideal of G for all $$t \in \left( {0,\frac{{1 - k}} {2}} \right]$$ . We also investigate some important characterization theorems in terms of this notion. Finally, regular ordered Γ-semigroups are characterized by the properties of their (∈, ∈ ∨q k )-fuzzy Γ-ideals.

Keywords: Ordered Γ-semigroups; regular ordered Γ-semigroups; fuzzy sets; fuzzy Γ-ideals; (∈; ∈ ∨q k )-fuzzy Γ-ideals (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0067-6

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