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Mathematics 2019, 7(3), 233; https://doi.org/10.3390/math7030233

Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

1
Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
2
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
*
Author to whom correspondence should be addressed.
Received: 25 December 2018 / Revised: 23 February 2019 / Accepted: 26 February 2019 / Published: 4 March 2019
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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. View Full-Text
Keywords: ordered ternary semigroup; bipolar fuzzy ideal; bipolar fuzzy generalized bi-ideal; (α,β)-bipolar fuzzy generalized bi-ideal ordered ternary semigroup; bipolar fuzzy ideal; bipolar fuzzy generalized bi-ideal; (α,β)-bipolar fuzzy generalized bi-ideal
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bashir, S.; Fatima, M.; Shabir, M. Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals. Mathematics 2019, 7, 233.

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