Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals
Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
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
Our main objective is to introduce the innovative concept of
-bipolar fuzzy ideals and
-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
in an ordered ternary semigroup
-bipolar fuzzy generalized bi-ideal of
, it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the
-bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the
-bipolar fuzzy generalized bi-ideals.
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Bashir, S.; Fatima, M.; Shabir, M. Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals. Mathematics 2019, 7, 233.
Bashir S, Fatima M, Shabir M. Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals. Mathematics. 2019; 7(3):233.
Bashir, Shahida; Fatima, Medhit; Shabir, Muhammad. 2019. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals." Mathematics 7, no. 3: 233.
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