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Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups
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In this paper, we introduce the concept of fuzzy bipolar soft quasi-ideals in ordered semigroup theory. First some characteristics of the structure are examined and hence a few useful results are established. It is proved, among others, that the concepts of fuzzy bipolar soft bi-ideal and fuzzy bipolar soft quasi-ideal in regular ordered semigroups coincide. In addition, fuzzy bipolar soft quasi-ideals over ordered semigroups are linked with the ordinary quasi-ideals. Thereafter, a few classes of ordered semigroups are characterized in terms of their fuzzy bipolar soft left, fuzzy bipolar soft right and fuzzy bipolar soft quasi-ideals, and thus some important characterization theorems are established. We also define fuzzy bipolar soft semiprime quasi-ideals and characterize completely regular ordered semigroups by their fuzzy bipolar soft (semiprime) quasi-ideals.
It is proved that an ordered semigroup S is completely regular if and only
if every fuzzy bipolar soft quasi-ideal λA over S is a fuzzy bipolar soft
semiprime quasi-ideal.
Department of Mathematics, University of the Punjab
Title: Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups
Description:
In this paper, we introduce the concept of fuzzy bipolar soft quasi-ideals in ordered semigroup theory.
First some characteristics of the structure are examined and hence a few useful results are established.
It is proved, among others, that the concepts of fuzzy bipolar soft bi-ideal and fuzzy bipolar soft quasi-ideal in regular ordered semigroups coincide.
In addition, fuzzy bipolar soft quasi-ideals over ordered semigroups are linked with the ordinary quasi-ideals.
Thereafter, a few classes of ordered semigroups are characterized in terms of their fuzzy bipolar soft left, fuzzy bipolar soft right and fuzzy bipolar soft quasi-ideals, and thus some important characterization theorems are established.
We also define fuzzy bipolar soft semiprime quasi-ideals and characterize completely regular ordered semigroups by their fuzzy bipolar soft (semiprime) quasi-ideals.
It is proved that an ordered semigroup S is completely regular if and only
if every fuzzy bipolar soft quasi-ideal λA over S is a fuzzy bipolar soft
semiprime quasi-ideal.
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