Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

Shahida Bashir, Medhit Fatima and Muhammad Shabir
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Shahida Bashir: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Medhit Fatima: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Muhammad Shabir: Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan

Mathematics, 2019, vol. 7, issue 3, 1-16

Abstract: Our main objective is to introduce the innovative concept of ( α , β ) -bipolar fuzzy ideals and ( α , β ) -bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = ( S ; h n , h p ) in an ordered ternary semigroup S is the ( ∈ , ∈ ∨ q ) -bipolar fuzzy generalized bi-ideal of S , it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the ( ∈ , ∈ ∨ q ) -bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the ( ∈ , ∈ ∨ q ) -bipolar fuzzy generalized bi-ideals.

Keywords: ordered ternary semigroup; bipolar fuzzy ideal; bipolar fuzzy generalized bi-ideal; ( ? , ? )-bipolar fuzzy generalized bi-ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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