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Mathematics, Vol. 7, Pages 233: Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

Research paper by Bashir, Fatima, Shabir

Indexed on: 09 Mar '19Published on: 04 Mar '19Published in: Mathematics



Abstract

Our main objective is to introduce the innovative concept of (α,ß)-bipolar fuzzy ideals and (α,ß)-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; hn, hp) 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.