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Mathematics 2017, 5(4), 71; https://doi.org/10.3390/math5040071

Some Types of Subsemigroups Characterized in Terms of Inequalities of Generalized Bipolar Fuzzy Subsemigroups

1
Departament of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2
Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
*
Author to whom correspondence should be addressed.
Received: 14 November 2017 / Revised: 21 November 2017 / Accepted: 23 November 2017 / Published: 27 November 2017
(This article belongs to the Special Issue Fuzzy Mathematics)
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Abstract

In this paper, we introduce a generalization of a bipolar fuzzy (BF) subsemigroup, namely, a ( α 1 , α 2 ; β 1 , β 2 ) -BF subsemigroup. The notions of ( α 1 , α 2 ; β 1 , β 2 ) -BF quasi(generalized bi-, bi-) ideals are discussed. Some inequalities of ( α 1 , α 2 ; β 1 , β 2 ) -BF quasi(generalized bi-, bi-) ideals are obtained. Furthermore, any regular semigroup is characterized in terms of generalized BF semigroups. View Full-Text
Keywords: generalized bipolar fuzzy (BF) semigroup; (α1, α2; β1, β2)-bipolar fuzzy subsemigroup; fuzzy quasi(generalized bi-, bi-) ideal; regular semigroup generalized bipolar fuzzy (BF) semigroup; (α1, α2; β1, β2)-bipolar fuzzy subsemigroup; fuzzy quasi(generalized bi-, bi-) ideal; regular semigroup
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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Khamrot, P.; Siripitukdet, M. Some Types of Subsemigroups Characterized in Terms of Inequalities of Generalized Bipolar Fuzzy Subsemigroups. Mathematics 2017, 5, 71.

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