Roughness based on fuzzy ideals

Information Sciences

Volumn 176, Issue 16, 2006, Pages 2417-2437

  Davvaz, B ^a  

^a YAZD UNIVERSITY   (Iran)

Author keywords

Fuzzy ideal; Fuzzy set; Ideal; Lower approximation; Ring; Rough set; Upper approximation

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; GRAPH THEORY;

CLASSICAL SET THEORY; FUZZY IDEALS; IDEAL; LOWER APPROXIMATIONS; RING; ROUGH SET; UPPER APPROXIMATIONS;

FUZZY SETS;

EID: 33646912283     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2005.10.001     Document Type: Article

References (57)

1. Anderson F.W., and Fuller K.R. Rings and Categories of Modules. second ed. (1992), Springer-Verlag, USA
2. Biswas R., and Nanda S. Rough groups and rough subgroups. Bull. Polish Acad. Sci. Math. 42 (1994) 251-254
3. Banerjee M., and Pal S.K. Roughness of a fuzzy set. Inform. Sci. 93 3-4 (1996) 235-246
4. Bonikowaski Z. Algebraic structures of rough sets. In: Ziarko W.P. (Ed). Rough Sets Fuzzy Sets, and Knowledge Discovery (1995), Springer-Verlag, Berlin 242-247
5. Bonikowaski Z., Bryniarski E., and Wybraniec-Skardowska U. Extensions and intentions in the rough set theory. Inform. Sci. 107 (1998) 149-167
6. Chakrabarty K., Biswas R., and Nanda S. Fuzziness in rough sets. Fuzzy Sets Syst. 110 (2000) 247-251
7. Comer S.D. On connections between information systems, rough sets and algebraic logic. Algebraic Methods in Logic and Computer Science Vol. 28 (1993), Banach Center Publications 117-124
8. P. Corsini, Rough sets, fuzzy sets and join spaces, Honorary volume dedicated to Prof. Emeritus J. Mittas, Aristotle Univ. of Thessaloniki, 1999-2000.
9. Corsini P., and Leoreanu V. Applications of Hyperstructure Theory. Advanced in Mathematics Vol. 5 (2003), Kluwer Academic Publisher
10. P. Corsini, V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rendiconti del Circolo Matematico di Palermo, Series II, Tomo LI, 2002, pp. 527-536.
11. B. Davvaz, M. Mahdavipour, Roughness in modules, submitted.
12. Davvaz B. Roughness in rings. Inform. Sci. 164 (2004) 147-163
13. Davvaz B. Rough sets in a fundamental ring. Bull. Iranian Math. Soc. 24 2 (1998) 49-61
14. v-groups. Ratio Math. 13 (1999) 71-86
15. v-modules. Taiwanese J. Math. 6 4 (2002) 499-505
16. Davvaz B. Fuzzy sets and probabilistic rough sets. Int. J. Sci. & Technol. Univ. Kashan 1 (2000) 23-28
17. Davvaz B. Rough polygroups. Italian J. Pure Appl. Math. 12 (2002) 91-96
18. Davvaz B., and Iranshahi S. Empty interior and empty exterior subsets in an approximation space. Jour. Inst. Math. & Comp. Sci. (Math. Ser.) 16 2 (2003) 101-103
19. Dubois D., and Prade H. Rough fuzzy sets and fuzzy rough sets. Int. J. General Syst. 17 2-3 (1990) 191-209
20. Fernandez Salido J.M., and Murakami S. Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations. Fuzzy Sets Syst. 139 (2003) 635-660
21. Iwinski T. Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math. 35 (1987) 673-683
22. Jarvinen J. On the structure of rough approximations. Fundamental Informatica 53 (2002) 135-153
23. Jun Y.B. Roughness of ideals in BCK-algebras. Scientiae Math. Japonica 57 1 (2003) 165-169
24. Jun Y.B. Roughness of gamma-subsemigroups/ideals in gamma-semigroups. Bull. Korean Math. Soc. 40 3 (2003) 531-536
25. Kondo M. On the structure of generalized rough sets. Inform. Sci. 176 5 (2006) 589-600
26. Kuroki N. Rough ideals in semigroups. Inform. Sci. 100 (1997) 139-163
27. Kuroki N., and Mordeson J.N. Structure of rough sets and rough groups. J. Fuzzy Math. 5 1 (1997) 183-191
28. Kuroki N., and Wang P.P. The lower and upper approximations in a fuzzy group. Inform. Sci. 90 (1996) 203-220
29. V. Leoreanu, Direct limits and products of join spaces associated with rough sets, Honorary volume dedicated to Prof. Emeritus J. Mittas, Aristotle University of Thessaloniki, 1999-2000.
30. Liu W.J. Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets Syst. 8 (1982) 133-139
31. Liu W.J. Operations on fuzzy ideals. Fuzzy Sets Syst. 11 (1983) 31-41
32. Mi J.-S., and Zhang W.-X. An axiomatic characterization of a fuzzy generalization of rough sets. Inform. Sci. 160 (2004) 235-249
33. Mordeson J.N. Rough set theory applied to (fuzzy) ideal theory. Fuzzy Sets and Systems 121 (2001) 315-324
34. Mukherjee T.K., and Sen M.K. On fuzzy ideals in rings 1. Fuzzy Sets Syst. 21 (1987) 99-104
35. Pawlak Z. Rough sets. Int. J. Inf. Comp. Sci. 11 (1982) 341-356
36. Pawlak Z. Rough Sets-Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic Publishing, Dordrecht
37. Polkowski L., and Skowron A. Rough Sets in Knowledge Discovery 1. Methodology and Applications, Studies in Fuzziness and Soft Computing Vol. 18 (1998), Physica-Verlag, Heidelberg
38. Polkowski L., and Skowron A. Rough Sets in Knowledge Discovery 2. Applications. Studies in Fuzziness and Soft Computing Vol. 19 (1998), Physica-Verlag, Heidelberg
39. Pomykala J., and Pomykala J.A. The stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36 (1988) 495-508
40. Qin K., and Pei Z. On the topological properties of fuzzy rough sets. Fuzzy Sets Syst. 151 3 (2005) 601-613
41. Quafafou M. α-RST: a generalization of rough set theory. Inform. Sci. 124 (2000) 301-316
42. Rady E.A., Kozae A.M., and Abd El-Monsef M.M.E. Generalized rough sets. Chaos, Solitons and Fractals 21 (2004) 49-53
43. Radzikowska A.M., and Kerre E.E. A comprative study of fuzzy rough sets. Fuzzy Sets and Systems 126 (2002) 137-155
44. Rosenfeld A. Fuzzy groups. J. Math. Anal. Appl. 35 (1971) 512-517
45. Sarkar M. Rough-fuzzy functions in classification. Fuzzy Sets Syst. 132 (2002) 353-369
46. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press
47. Wong S.K.M., and Nie X.P. Rough sets, a special case of interval structures. In: Ziarco W.P. (Ed). Proceedings of the International Workshop on Rough Sets, Fuzzy Sets and Knowledge Discovery, Banff 1993 (1994), Springer
48. Wu W.-Z., and Zhang W.-X. Neighborhood operator systems and approximations. Inform. Sci. 144 (2002) 201-217
49. Q.M. Xiao, Z.-L. Zhang, Rough prime ideals and rough fuzzy prime ideals in semigroups, Inform. Sci., in press, doi:10.1016/j.ins.2004.12.010.
50. Yao Y.Y., and Lingras P.J. Interpretations of belief functions in the theory of rough sets. Inform. Sci. 104 (1998) 81-106
51. Yao Y.Y. Relational interpretation of neighborhood operators and rough set approximation operator. Inform. Sci. 111 (1998) 239-259
52. Zadeh L.A. Fuzzy sets. Inform. Cont. 8 (1965) 338-353
53. Zadeh L.A. The concept of linguistic variable and its applications to approximate reasoning. Part I, Inform. Sci. 8 (1975) 199-249
54. Part II, Inform. Sci. 8 (1975) 301-357
55. Part III, Inform. Sci. 9 (1976) 43-80
56. Zhang H., Liang H., and Liu D. Two new operators in rough set theory with applications to fuzzy sets. Inform. Sci. 166 (2004) 147-165
57. Zhu W., and Wang F.-Y. Reduction and axiomization of covering generalized rough sets. Inform. Sci. 152 (2003) 217-230