On 2-absorbing bipolar fuzzy ideals over LA-semigroups

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 = (mu P-A, mu(N)(A)) over an LA -semigroup S is weakly 2-absorbing if and only if [B circle dot C] circle dot D <= A implies B circle dot C <= A or C circle dot D <= A or B circle dot D <= A for any bipolar fuzzy sets B = (mu(P)(B), mu(N)(B)), C = (mu(P)(C), mu(N)(C)) and D = (mu(P)(D), mu(N)(D)). 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.