Affiliations: Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, Thailand
Correspondence:
[*]
Corresponding author. Pairote Yiarayong, Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. E-mail: E-mail: pairote0027@hotmail.com..
Abstract: The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in
LA
-semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in
LA
-semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set
A=(μAP,μAN)
over an
LA
-semigroup S is weakly 2-absorbing if and only if
[B⊙C]⊙D⪯A
implies
B⊙C⪯A
or
C⊙D⪯A
or
B⊙D⪯A
for any bipolar fuzzy sets
B=(μBP,μBN),C=(μCP,μCN)
and
D=(μDP,μDN)
. Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an
LA
-semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an
LA
-semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.
