Fuzzy Bipolar Soft Quasi-ideals in Ordered Semigroups

Author:

Ul-Hakim Aziz-1,Khan Hidayatullah1,Ahmad Imtiaz1,Khan Asghar2

Affiliation:

1. Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan.

2. 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 λA over S is a fuzzy bipolar soft semiprime quasi-ideal.

Publisher

Department of Mathematics, University of the Punjab

Subject

Pharmacology (medical)

Reference35 articles.

1. J. Ahsan, R. M. Latif and M. Shabir, Fuzzy quasi-ideals in semigroups, J. Fuzzy Math.9, No. 2 (2001) 259-270.

2. M. Akram, N. O. Alsherei, K.P. Shum and A. Farooq, Application of bipolar fuzzy soft sets in K-algebras, Ital. J. Pure Appl. Math. 32 (2014) 533-546.

3. Aziz Ul Hakim, H. Khan, I. Ahmad and A. Khan, On fuzzy bipolar soft ordered semigroups, Punjab Univ. j. math. 53, No.4 (2021) 261-293.

4. Aziz Ul Hakim, H. Khan, I. Ahmad and A. Khan, Fuzzy bipolar soft semiprime ideals in ordered semigroups, Heliyon, 7 (2021) 1-12.

5. Aziz Ul Hakim, H. Khan, I. Ahmad, A. Khan, A note on fuzzy bipolar soft bi-ideals in ordered semigroups, Punjab Univ. j. math (to appear).

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