Title: Characterizations of Abel Grassmann’s Groupoids by the Properties of Their Double-Framed Soft Ideals
Author(s): Asghar Khan, Muhammad Izhar, Aslihan Sezign
Pages: 62-74
Cite as:
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.

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.

Full Text: PDF

 

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.