A new rough set theory: Rough soft hemirings

Journal of Intelligent and Fuzzy Systems

Volumn 28, Issue 4, 2015, Pages 1687-1697

  Zhan, Jianming ^a   Liu, Qi ^a   Davvaz, Bijan ^b  

^a HUBEI UNIVERSITY FOR NATIONALITIES   (China)

^b YAZD UNIVERSITY   (Iran)

Author keywords

congruence relation; Rough hemiring; rough soft hemiring; soft hemiring

Indexed keywords

SET THEORY;

APPROXIMATION SPACES; CONGRUENCE RELATION; ROUGH HEMIRING; ROUGH SOFT HEMIRING; SOFT HEMIRING;

ROUGH SET THEORY;

EID: 84924598705     PISSN: 10641246     EISSN: 18758967     Source Type: Journal    
DOI: 10.3233/IFS-141455     Document Type: Article

References (58)

1. H. Aktas and N. C agman. Soft sets and soft groups. Inform Sci 177(13) (2007), 2726-2735.
2. M.I. Ali, Another view on reduction of parameters in soft sets. Applied soft computing 12 (2012), 1814-1821.
3. M.I. Ali, B. Davvaz and M. Shabir, Some properties of generalized rough sets. Inform Sci 224 (2013), 170-179.
4. M.I. Ali, F. Feng, X.Y. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory. Comput Math Appl 57(9) (2009), 1547-1553.
5. M.I. Ali, M. Shabir and S. Tanveer, Roughness in hemirings. Neural Comput & Applic 21 (2012), s171-s180.
6. L.R. Beasley and N.J. Pullman, Linear operators strongly preserving idempotent matrices over semirings, Linear Algebra Appl 160 (1992), 217-229.
7. R. Biswas and S. Nanda, Rough groups and rough subgroups, Bull Polish Acad Sci Math 42 (1994), 251-254.
8. N. C agman and S. Enginoglu. Soft matrix theory and its decision making. Comput Math Appl 59 (2010), 3308-3314.
9. N. C agman and S. Enginoglu. Soft set theory and uni-int decision making, Eur J Oper Res 207(2) (2010), 848-855.
10. D. Chen, C. Wang and Q. Hu, A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inform Sci 177(17) (2007), 3500-3518.
11. B. Davvaz, Roughness in rings. Inform Sci 164(1) (2004), 147-163.
12. B. Davvaz and M. Mahdavipour, Roughness in modules. Inform Sci 176 (2006), 3658-3674.
13. W.A. Dudek, M. Shabir and R. Anjum, Characterizations of hemirings by their h-ideals. Comput Math Appl 59(9) (2010), 3167-3179.
14. F. Feng, X.Z. Zhao and Y.B. Jun, μ-semirings and γ-semirings, Theoret Comput Sci 347(1) (2005), 423-431.
15. F. Feng, Y.B. Jun and X.Z. Zhao. Soft semirings. Comput Math Appl 56(10) (2008), 2621-2628.
16. F. Feng, C. Li, B.Davvaz and M.I. Ali. Soft sets combined with fuzzy sets and rough sets: A tentative approach. Soft Comput 14(9) (2010), 899-911.
17. F. Feng, X.Y. Liu, V. Leoreanu-Fotea and Y.B. Jun. Soft sets and soft rough sets. Inform Sci 181(6) (2011), 1125-1137.
18. S. Ghosh, Matrices over semirings. Inform Sci 90(1) (1996), 221-230.
19. Q. He, C. Wu, D. Chen and S. Zhao, Fuzzy rough set based attribute reduction for information systems with fuzzy decisions. Knowledge-Based Systems 24(5) (2011), 689-696.
20. M. Henriksen, Ideals in semirings with commutative addition, Amer Math Soc Notices 6(1) (1958), 321.
21. B.Q. Hu, Three-way decisions space and three-way decisions. Inform Sci 281 (2014), 21-52.
22. K. Iizuka, On the Jacobson radical of a semiring, Tohoku Math J 11(3) (1959), 409-421.
23. Y.B. Jun, Roughness of ideals in BCK-Algebras, Sci Math Jpn 57(1) (2003), 165-169.
24. Y.B. Jun. Soft BCK/BCI-Algebras. Comput Math Appl 56(5) (2008), 1408-1413.
25. Y.B. Jun, H.S. KimandM.A. Ozturk, Fuzzy κ-ideals in semirings, J Fuzzy Math 13(2) (2005), 351-364.
26. Y.B. Jun, M.A. O zturk and S.Z. Song, On fuzzy h-ideals in hemirings. Inform Sci 162(3) (2004), 211-226.
27. N. Kuroki, Rough ideals in semigroups. Inform Sci 100 (1997), 139-163.
28. T.J. Li, Y. Leung and W.X. Zhang, Generalized fuzzy rough approximation operators based on fuzzy coverings. Int J Approx Reason 48(3) (2008), 836-856.
29. G. Liu and W. Zhu, The algebraic structures of generalized rough set theory. Inform Sci 178(21) (2008), 4105-4113.
30. Q. Liu and J. Zhan, IFP-intuitionistic fuzzy soft h-ideals of hemirings and its decision making. J Appl Math 2014, Article ID 589465, 9 pages.
31. X. Ma, Y. Yin and J. Zhan, Characterizations of h-intraand h-quasi-hemiregular hemirings. Comput Math Appl 63(4) (2012), 783-793.
32. X. Ma and J. Zhan, Fuzzy h-ideals in h-hemiregular and h-semisimple-hemirings. Neural Comput & Applic 19(3) (2010), 477-485.
33. P.K. Maji, R. Biswas and A.R. Roy. Soft set theory. Comput Math Appl 45(4) (2003), 555-562.
34. D. Molodtsov. Soft set theory-first results. Comput Math Appl 37(4) (1999), 19-31.
35. Z. Pawlak, Rough sets, Internat J Comput Inform Sci 11(5) (1982), 341-356.
36. Z. Pawlak, Rough sets: Theoretical aspects of reasoning about data, Kluwer, Dordrecht, 1991.
37. Z. Pawlak and A. Skowron, Rudiments of rough sets. Inform Sci 177(1) (2007), 3-27.
38. A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J Comput Appl Math 203(2) (2007), 412-418.
39. A. Sezgin Sezer, A new view to ring theory via soft unit rings, ideals and bi-ideals. Knowledge-Based Systems 36 (2010), 300-314.
40. L. Sun, J. Xu and Y. Tian, Feature selection using rough entropybased uncertainty measures in incomplete decision systems. Knowledge-Based Systems 36 (2012), 206-216.
41. D.R. La Torre, On h-ideals and κ-ideals in hemirings, Publ Math Debrecen 12(2) (1965), 219-226.
42. W.Z. Wu and W.X. Zhang, Neighborhood operator systems and approximations. Inform Sci 144(1)(2002), 201-217.
43. W.Z. Wu and W.X. Zhang, Constructive and axiomatic approaches of fuzzy approximation operators. Inform Sci 159(3) (2004), 233-254.
44. Q. Xiao, Q. Li and L. Guo, Rough sets induced by ideals in lattices. Inform Sci 271 (2014), 82-92.
45. Y.Y.Yao, Two views of theory of rough sets in finite universes. International Journal of Approximate Reasoning 15 (1996), 291-C317.
46. Y.Y. Yao, Constructive and algebraic methods of the theory of rough sets. Inform Sci 109(1) (1998), 21-47.
47. Y.Y. Yao, Three-way decisions with probabilistic rough sets. Inform Sci 180 (2010), 341-353.
48. Y.Y. Yao and B.X. Yao, Covering based rough set approximations. Inform Sci 200 (2010), 91-107.
49. Y. Yin, Y.B. Jun and J. Zhan, Vague soft hemirings. Comput Math Appl 62(1) (2011), 199-213.
50. Y.Yin and J. Zhan, The characterizations of hemirings in terms of fuzzy soft h-ideals. Neural Comput & Applic 21(1) (2012), 43-57.
51. Y. Yin and J. Wang, Fuzzy Hemirings. Science Press, 2010.
52. L.A. Zadeh. Fuzzy Sets. Information and Control 8(3) (1965), 338-353.
53. J. Zhan andW.A. Dudek, Fuzzy h-ideals of hemirings. Inform Sci 177(3) (2007), 876-886.
54. J. Zhan and Z. Tan, T-fuzzy left κ-ideals of semirings, Sci Math Jpn 58(3) (2003), 597-601.
55. J. Zhan andY.Yin, Anewviewof fuzzy κ-ideals of hemirings, J Intell Fuzzy Systems 23(5) (2012), 169-176.
56. W. Zhu, Generalized rough sets based on relations. Inform Sci 177(22) (2007), 4997-5011.
57. W. Zhu, Relationship between generalized rough sets based on binary relation and covering. Inform Sci 179(3) (2009), 210-225.
58. W. Zhu and S. Wang, Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn & Cyber 2(4) (2011), 273-279.