# 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 (&alpha;,&szlig;)-bipolar fuzzy ideals and (&alpha;,&szlig;)-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 (&isin;,&isin; &or; 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 (&isin;,&isin; &or; q)-bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the (&isin;,&isin; &or; q)-bipolar fuzzy generalized bi-ideals.