Punjab University Journal of Mathematics, Vol 54, No 6 (2022)

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Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups

Aziz- Ul- Hakim, Hidayatullah Khan, Imtiaz Ahmad, Asghar Khan


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 fuzzybipolar soft semiprime quasi-ideals and characterize completely regularordered semigroups by their fuzzy bipolar soft (semiprime) quasi-ideals.It is proved that an ordered semigroup S is completely regular if and onlyif every fuzzy bipolar soft quasi-ideal ¸A over S is a fuzzy bipolar softsemiprime quasi-ideal.

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