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.

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References


  1. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl., 37 (1999) 19-31. Google Scholar

  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. Google Scholar

  3. P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003) 555-562. Google Scholar

  4. Y. B. Jun, K. J. Lee and A. Khan, Soft ordered semigroups, Math. Logic Q., 56, (2010) 42–50. Google Scholar

  5. U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, (2010) 3458–3463. Google Scholar

  6. A. O. Atagun and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, (2011) 592–601. Google Scholar

  7. N. Cagman and S. Enginoglu, FP-soft set theory and its applications, Ann. Fuzzy Math. Inform., 2, (2011) 219–226. Google Scholar

  8. F. Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform., 2, (2011) 69–80. Google Scholar

  9. F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56, (2008) 2621–2628. Google Scholar

  10. Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56, (2008) 1408–1413. Google Scholar

  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. Google Scholar

  12. Y. B. Jun, K. J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl., 58, (2009) 2060–2068. Google Scholar

  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. Google Scholar

  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. Google Scholar

  15. M. A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972) 1-7. Google Scholar

  16. J. R. Cho, Pusan, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49 (124) (1996) 277-290. Google Scholar

  17. P. Holgate, Groupoids satisfying a simple invertive law, Math. Stud., 61, (1992) 101-106. Google Scholar

  18. P. V. Protic and N. Stevanovic, On Abel-Grassmann’s groupoids (review), Proc. Math. Conf. Pristina, (1999) 31-38. Google Scholar

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

  20. Q. Mushtaq and S. M. Yusuf, On AG-groupoids, Aligarh Bull. Math., 8 (1978), 65-70. Google Scholar

  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. Google Scholar

  22. A. S. Sezer, A new approach to LA-semigroup theory via the soft sets, J. Intell. Fuzzy Syst. 26 (2014), 2483-2495. Google Scholar

  23. A. Khan, T. Asif and Y. B. Jun, Double-framed soft ordered semigroups, to appear. Google Scholar

  24. A. Khan, M. Izhar, Double framed soft LA-semigroups, to appear. Google Scholar

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

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