Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

New types of soft rough sets in groups based on normal soft groups

  • 16 Accesses

Abstract

Hybridization of soft sets and rough sets is an important way to deal with uncertainties. This paper aims to study the concept of roughness in soft sets over groups. In this regard, a pair of two soft sets, viz. soft lower and soft upper approximation spaces, are introduced by applying the normal soft groups corresponding to each parameter. Some important results related to these soft approximation spaces over groups are studied with examples. Furthermore, this paper presents a relationship between the soft approximation spaces based on the soft image and soft pre-image of a normal soft group via group homomorphisms. This work can be applicable in the field of information technology to connect two information systems.

This is a preview of subscription content, log in to check access.

References

  1. Aktaş H, Çağman N (2007) Soft sets and soft groups. Inf Sci 177(13):2726–2735

  2. Ali MI, Feng F, Lin X, Min W, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

  3. Ali MI, Shabir and Samina M (2014) Application of L-fuzzy soft sets to semirings. J Intell Fuzzy Syst 27(4):1731–1742

  4. Ali MI, Shabir M, Tanveer S (2012) Roughness in hemirings. Neural Comput Appl 21(1):171–180

  5. Aslam M, Qurashi SM (2012) Some contributions to soft groups. Ann Fuzzy Math Inf 1(4):177–195

  6. Ayub S, Mahmood W, Nabi FG, Shabir M (2019) Application of roughness in soft-intersection groups. J Comput Appl Math. https://doi.org/10.1007/s40314-019-0978-2

  7. Biswas R, Nanda S (1994) Rough groups and rough subgroups. Bull Polish Acad Sci Math 42(3):251–254

  8. Çağman N, Çitak F, Aktaş H (2012) Soft int-group and its applications to group theory. Neural Comput Appl 21(1):151–158

  9. Chen Z, Ayub S, Mahmood W, Mahmood A, Jung CY (2019) A study of roughness in modules of fractions. IEEE Access 7:93088–93099

  10. Cheng W, Mo Z-W, Wang J (2007) Notes on “the lower and upper approimations in a fuzzy group and rough ideals in semigroups”. Inf Sci 177:5134–5140

  11. Davvaz B, Mahdavipour M (2006) Roughness in modules. Inf Sci 176(24):3658–3674

  12. Dubios D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209

  13. Feng F, Ali MI, Shabir M (2013) Soft relations applied to semigroups. Filomat 27(7):1183–1196

  14. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621–2628

  15. Feng F, Li Y (2013) Soft subsets and soft product operations. Inf Sci 232:44–57

  16. Feng F, Li C, Davvaz B, Ali M (2010) Soft sets combined with fuzzy soft set and rough sets: a tentative approach. Soft Comput 14(9):899–911

  17. Ghosh J, Samanta TK (2013) Rough soft sets and rough soft groups. J Hyperstruct 2(1):18–29

  18. Jiang H, Zhan J, Chen D (2019) Covering based variable precision (I, T)-fuzzy rough sets with applications to multi-attribute decision-making. IEEE Trans Fuzzy Syst 27:1558–1572

  19. Kuroki N, Wang PP (1996) The lower and upper approximations in a fuzzy group. Inf Sci 90(1–4):203–220

  20. Kuroki N (1997) Rough ideals in semigroups. Inf Sci 100(1–4):139–163

  21. Li Z, Zheng D, Hao J (2012) L-fuzzy soft sets based on complete Boolean lattices. Comput Math Appl 64(8):2558–2574

  22. Ma X, Zhan J, Ali MI, Mehmood N (2018) A survey of decision making methods based on two classes of hybrid soft set models. Artif Intell Rev 49(4):511–529

  23. Mahmood W, Nazeer W, Kang SM (2017) The lower and upper approximations and homomorphisms between lower approximations in quotient groups. J Intell Fuzzy Syst 33(4):2585–2594

  24. Mahmood W, Nazeer W, Kang SM (2018) A comparision between lower and upper approximations in groups with respect to group homomorphisms. J Intell Fuzzy Syst 35(1):693–703

  25. Mahmood T, Shabir M, Ayub S, Bashir S (2017) Regular and intra-regular semihypergroups in terms of L-fuzzy soft sets. J Appl Environ Biol Sci 11(7):115–137

  26. Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

  27. Maji P, Biswas R, Roy A (2003) Soft set theory. J Comput Appl Math 45:555–562

  28. Malik DS, Mordeson JN, Sen MK (2007) Introduction to abstract algebra, pp 277

  29. Miao D, Han S, Sun L (2005) Rough group, rough subgroup and their properties. Proceedings of RSFDGrC. (D. \(\grave{S}\)lezak et., cd.) Springer, Berlin, pp 104–113

  30. Moinuddin K (2017) Rough soft sets: a novel approach. Int J Comput Appl Math 12(2):537–543

  31. Molodtsov D (1999) Soft set theory first results. Comput Math Appl 37(4–5):19–31

  32. Pan W, Zhan J (2016) Rough fuzzy groups and rough soft groups. Italy J Pure Appl Math 36:617–628

  33. Pan W, Zhan J (2017) Soft rough groups and corresponding decision making. Italy J Pure Appl Math 38:158–171

  34. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

  35. Sezgin A, Atagun AO (2011) Soft groups and normalistic soft groups. Comput Math Appl 62(2):685–698

  36. Shabir M, Ali MI, Shaheen T (2013) Another approach to soft rough sets. Knowl Based Syst 40:72–78

  37. Shabir M, Ayub S, Bashir S (2017) Application of L-fuzzy soft sets in semihypergroups. J Adv Math Stud 10(3):367–385

  38. Shabir M, Ayub S, Bashir S (2017) Prime and semiprime L-fuzzy soft bi-hyperideals. J Hyperstruct 2(6):102–119

  39. Wang C, Chen D (2010) A short note on some properties of rough groups. Comput Math Appl 59(1):431–436

  40. Wang Z, Shu L (2012) The lower and upper approximations in a group. World Acad Sci Eng Technol Int Scholar Sci Res Innovat 6(8):2020–2024

  41. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

  42. Zhan J, Liu Q, Davvaz B (2015) A new rough set theory: rough soft hemirings. J Intell Fuzzy Systems 28(4):1687–1697

  43. Zhan J, Sun B, Alcantud JCR (2019) Covering based multigranulation (I, T)-fuzzy rough set models and applications in multi-attribute group decision-making. Inf Sci 476:290–318

  44. Zhan J, Xu W (2018) Two types of coverings based multigranulation rough fuzzy sets and applications to decision making. Artif Intell Rev. https://doi.org/10.1007/s10462-018-9649-8

  45. Zhang L, Zhan J, Alcantud JCR (2019) Novel classes of fuzzy soft -coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making. Soft Comput 23:5327–5351

  46. Zhang L, Zhan J, Alcantund JCR (2019) Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making. Inf Sci 494:114–140

  47. Zhang K, Zhan J, Wu W-Z (2019) Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making. Fuzzy sets Syst. https://doi.org/10.1016/j.fss.2019.06.019

  48. Zhang L, Zhan J, Xu Z (2019) Covering-based generalized IF rough sets with applications to multi-attribute decision-making. Inf Sci 478:275–302

  49. Zhang K, Zhan J, Yao Y (2019) TOPSIS method based on a fuzzy covering approximation space: an application to biological nano-materials selection. Inf Sci 502:297–329

Download references

Author information

Correspondence to Saba Ayub.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Marcos Eduardo Valle.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ayub, S., Shabir, M. & Mahmood, W. New types of soft rough sets in groups based on normal soft groups. Comp. Appl. Math. 39, 67 (2020). https://doi.org/10.1007/s40314-020-1098-8

Download citation

Keywords

  • Rough sets
  • Soft sets
  • Soft groups
  • Normal soft groups

Mathematics Subject Classification

  • Primary 05C38
  • 15A15
  • Secondary 05A15
  • 15A18