Title: Fuzzy Hyperideals of Left Almost Semihypergroups
Author(s): Asghar Khan, Muhammad Farooq, Muhammad Izhar, Bijaz Davvaz
Pages: 155-171
Cite as:
Asghar Khan, Muhammad Farooq, Muhammad Izhar, Bijaz Davvaz, Fuzzy Hyperideals of Left Almost Semihypergroups, Int. J. Anal. Appl., 15 (2) (2017), 155-171.


This paper explores the foundations of fuzzy left (resp. right) hyperideals of left almost semihypergroups (briefly, LA-semihypergroups). We investigate the properties of fuzzy left hyperideals and fuzzy right hyperideals in regular and intra-regular LA-semihypergroups. We also characterize regular and intra-regular LA-semihypergroups in terms of fuzzy hyperideals.

Full Text: PDF



  1. M. A. Kazim and M. Naseeruddin, On almost semigroups, The Aligarh Bulletin of Mathematics 2 (1972), 1-7.

  2. J. R. Cho, Pusan, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Mathematical Journal, 49 (124) (1996), 277-290.

  3. P. Holgate, Groupoids satisfying a simple invertive law, Mathematics Students, 61 (1992), 101-106.

  4. P. V. Protic and N. Stevanovic, On Abel-Grassmann’s groupoids (review), Proceeding of Mathematics Conference in Pristina, (1999), 31-38.

  5. M. Naseeruddin, Some studies on almost semigroups and flocks, Ph.D. Thesis, The Aligarh Muslim University India, 1970.

  6. Q. Mushtaq and S. M. Yusuf, On AG-groupoids, The Aligarh Bulletin of Mathematics, 8 (1978), 65-70.

  7. M. Khan, T. Asif, Characterizations of Intra-Regular Left Almost Semigroups by Their Fuzzy Ideals, J. Math. Research 2 (3) (2010), 87-96.

  8. F. Yousafzai, A. Khan, V. Amjad, A. Zeb, On fuzzy fully regular AG-groupoids, J. Intell. & Fuzzy Syst. 26 (2014), 2973-2982.

  9. L. A. Zadeh, Fuzzy sets, Inform Control 8 (1965), 338–353.

  10. M. Khan, Faisal and A. Manan, Intra-regular AG-groupoids characterized by their intuitionistic fuzzy ideals, J. Adv. Res. Dyn. Control Syst. 3(2) (2011), 17–33.

  11. J. N. Mordeson, D.S. Malik and N. Kuroki Fuzzy semigroups, Springer-Verlag, Berlin, 2003.

  12. K. Hila, J. Dine, On hyperideals in left almost semihypergroups. ISRN Algebra (2011), Article ID953124.

  13. N. Yaqoob, P. Corsini, F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math. doi:10.1155/2013/510790.

  14. F. Yousafzai, P. Corsini, Some characterization problems in LA-semihypergroups, J. Algebra Number Theory Adv. Appl. 10 (2013), 41–55.

  15. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517.

  16. N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5 (1981), 203-215.

  17. P. Corsini and V. Leoreanu-Fotea, Applications of hyperstructure theory, Advanced in Mathematics, Kluwer Aca- demic Publisher, (2003).

  18. B. Davvaz, Intuitionistic Hyperideals of Semihypergroups, Bull. Malays. Math. Sci. Soc. 29(1) (2006), 203–207

  19. B. Pibaljommee, K. Wannatong and B. Davvaz, An investigation on fuzzy hyperideals of ordered semihypergroups, Quasigroups and related systems 23 (2015), 297-308.

  20. F .Marty, Sur Une generalization de la notion de group,” 8 iem congress, Math Scandinaves Stockholm (1934), 45-49.

  21. M. Farooq, A. Khan and B. Davvaz, Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals, Soft Comput DOI 10.1007/s00500-017-2550-6.

  22. A. Khan, M. Farooq and B. Davvaz, Int-soft interior-hyperideals of ordered semihypergroups. Intl. J. Anal. Appl. 14(2) (2017), 193-202.