Characterizations of Abel Grassmann's Groupoids by the Properties of Their Double-Framed Soft Ideals

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Asghar Khan, Muhammad Izhar, Aslihan Sezign, Characterizations of Abel Grassmann's Groupoids by the Properties of Their Double-Framed Soft Ideals, Int. J. Anal. Appl., 15 (1) (2017), 62-74.

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Asghar Khan, Muhammad Izhar, Aslihan Sezign

Abstract

In this paper, we introduce the concept of double-framed soft ideals and investigate properties of these ideals in regular, intra-regular, right regular and left regular AG-groupoids. We also characterize intra-regular AG-groupoids in terms of the double-framed soft ideals.

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References

  1. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl., 37 (1999) 19-31.
  2. P. K. Maji, R. Biswas and A. R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002) 1077-1083.
  3. P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003) 555-562.
  4. Y. B. Jun, K. J. Lee and A. Khan, Soft ordered semigroups, Math. Logic Q., 56, (2010) 42-50.
  5. U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, (2010) 3458-3463.
  6. A. O. Atagun and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, (2011) 592-601.
  7. N. Cagman and S. Enginoglu, FP-soft set theory and its applications, Ann. Fuzzy Math. Inform., 2, (2011) 219-226.
  8. F. Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform., 2, (2011) 69-80.
  9. F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56, (2008) 2621-2628.
  10. Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56, (2008) 1408-1413.
  11. Y. B. Jun, K. J. Lee and C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl., 57, (2009) 367-378.
  12. Y. B. Jun, K. J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl., 58, (2009) 2060-2068.
  13. Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci., 178, (2008) 2466-2475.
  14. Y. B. Jun, G. Muhiuddin, A. M. Al-roqi, Ideal theory of BCK/BCI-algebras based on Double-framed Soft Set, Appl. Math. Inf. Sci., 7 (5) (2013) 1879-1887.
  15. M. A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972) 1-7.
  16. J. R. Cho, Pusan, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49 (124) (1996) 277-290.
  17. P. Holgate, Groupoids satisfying a simple invertive law, Math. Stud., 61, (1992) 101-106.
  18. P. V. Protic and N. Stevanovic, On Abel-Grassmann's groupoids (review), Proc. Math. Conf. Pristina, (1999) 31-38.
  19. M. Naseeruddin, Some studies on almost semigroups and flocks, Ph.D. Thesis, The Aligarh Muslim University India, 1970.
  20. Q. Mushtaq and S. M. Yusuf, On AG-groupoids, Aligarh Bull. Math., 8 (1978), 65-70.
  21. Y. B. Jun and S. S. Ahn, Double-framed soft sets with applications in BCK/BCI-algebras, J. Appl. Math., 2012 (2012), Article ID 178159.
  22. A. S. Sezer, A new approach to LA-semigroup theory via the soft sets, J. Intell. Fuzzy Syst. 26 (2014), 2483-2495.
  23. A. Khan, T. Asif and Y. B. Jun, Double-framed soft ordered semigroups, to appear.
  24. A. Khan, M. Izhar, Double framed soft LA-semigroups, to appear.
  25. M. Khan, T. Asif, Characterizations of Intra-Regular Left Almost Semigroups by Their Fuzzy Ideals, J. Math. Research 2 (3) (2010), 87-96.
  26. F. Yousafzai, A. Khan, V. Amjad, A. Zeb, On fuzzy fully regular AG-groupoids, J. Intell. Fuzzy Syst. 26 (2014), 2973-2982.