Affiliation:
1. Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, Thailand
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 = ( μ A P , μ A N ) 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 = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . 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.
Subject
Artificial Intelligence,General Engineering,Statistics and Probability
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