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Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups

Author(s)
Aziz-Ul-Hakim Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan.
Hidayatullah Khan Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan.
Imtiaz Ahmad Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan.
Asghar Khan Department of Mathematics, Abdul Wali Khan University Mardan, KPK, Pakistan
Abstract
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 ¸A over S is a fuzzy bipolar soft semiprime quasi-ideal.
Publication Details
Page(s) 375-409
DOI 10.52280/pujm.2022.540603
Published Journal: Punjab University Journal of Mathematics, Volume: 54, Issue: 6, Year: 2022

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Keywords
FBS right ideal, FBS left ideal., FBS quasi-ideal, FBS ideal, FBS ordered semigroup, Ordered semigroup, FBS set
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