On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings

Information Sciences

Volumn 178, Issue 5, 2008, Pages 1343-1354

  Kazanci, Osman ^a   Davvaz, B ^b  

^a KARADENIZ TECHNICAL UNIVERSITY   (Turkey)

^b YAZD UNIVERSITY   (Iran)

Author keywords

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

Indexed keywords

APPROXIMATION THEORY; IMAGE ANALYSIS; ROUGH SET THEORY;

COMMUTATIVE RINGS; FUZZY IDEALS; PRIME IDEALS;

FUZZY SETS;

EID: 37249037694     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2007.10.005     Document Type: Article

References (44)

1. Bakhshi M., and Borzooei R.A. Lattice structure on fuzzy congruence relations of a hypergroupoid. Inform. Sci. 177 (2007) 3305-3313
2. Biswas R., and Nanda S. Rough groups and rough subgroups. Bull. Polish Acad. Sci. Math. 42 (1994) 251-254
3. Corsini P., and Leoreanu V. Fuzzy sets and join spaces associated with rough sets. Rendiconti Circ. Mat. Palermo, Ser. II LI (2002) 527-536
4. Davvaz B., and Mahdavipour M. Roughness in modules. Inform. Sci. 176 (2006) 3658-3674
5. Davvaz B. Roughness in rings. Inform. Sci. 164 (2004) 147-163
6. v-groups. Soft Comput. 10 11 (2006) 1043-1046
7. v-modules. Taiwanese J. Math. 6 4 (2002) 499-505
8. Davvaz B. Roughness based on fuzzy ideals. Inform. Sci. 176 (2006) 2417-2437
9. Davvaz B. Rough subpolygroups in a factor polygroup. J. Intell. Fuzzy Syst. 17 6 (2006) 613-621
10. v-submodules and many valued implications. Inform. Sci. 177 (2007) 865-875
11. v-submodules. Inform. Sci. 176 (2006) 285-300
12. Degang C., Wenxiu Z., Yeung D., and Tsang E.C.C. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inform. Sci. 176 (2006) 1829-1848
13. Deng T., Chen Y., Xu W., and Dai Q. A novel approach to fuzzy rough sets based on a fuzzy covering. Inform. Sci. 177 (2007) 2308-2326
14. Dudek W.A., Davvaz B., and Jun Y.B. On intuitionistic fuzzy subhyperquasigroups of hyperquasigroups. Inform. Sci. 170 (2005) 251-262
15. Jun Y.B. Quotient structures of intuitionistic fuzzy finite state machines. Inform. Sci. 177 (2007) 4977-4986
16. Jun Y.B. Roughness of ideals in BCK-algebras. Sci. Math. Japonica 57 1 (2003) 165-169
17. Jun Y.B. Roughness of Γ-subsemigroups/Ideals in Γ-semigroups. Bull. Korean Math. Soc. 40 3 (2003) 531-536
18. Jun Y.B., and Song S.Z. Generalized fuzzy interior ideals in semigroups. Inform. Sci. 176 (2006) 3079-3093
19. Jun Y.B., Öztürk M.A., and Park C.H. Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings. Inform. Sci. 177 (2007) 4662-4677
20. Kondo M. On the structure of generalized rough sets. Inform. Sci. 176 (2006) 589-600
21. Kumbhojkar H.V., and Bapat M.S. On prime and primary fuzzy ideals and their radicals. Fuzzy Sets Syst. 53 (1993) 203-216
22. Kuroki N. Rough ideals in semigroups. Inform. Sci. 100 (1997) 139-163
23. Kuroki N., and Wang P.P. The lower and upper approximations in a fuzzy group. Inform. Sci. 90 (1996) 203-220
24. Lingras P., and Butz C. Rough set based 1-v-1 and 1-v-r approaches to support vector machine multi-classification. Inform. Sci. 177 (2007) 3782-3798
25. Liu W.J. Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets Syst. 8 (1982) 133-139
26. Mi J.-S., and Zhang W.-X. An axiomatic characterization of a fuzzy generalization of rough sets. Inform. Sci. 160 (2004) 235-249
27. Mukherjee T.K., and Sen M.K. Primary fuzzy ideals and radical of fuzzy ideals. Fuzzy Sets Syst. 56 (1993) 97-101
28. Ozkan I., and Turksen I.B. Upper and lower values for the level of fuzziness in FCM. Inform. Sci. 177 (2007) 5143-5152
29. Pawlak Z. Rough sets. Int. J. Inf. Comp. Sci. 11 (1982) 341-356
30. Pawlak Z., and Skowron A. Rudiments of rough sets. Inform. Sci. 177 (2007) 3-27
31. Pei D. On definable concepts of rough set models. Inform. Sci. 177 (2007) 4230-4239
32. Rosenfeld A. Fuzzy groups. J. Math. Anal. Appl. 35 (1971) 512-517
33. Wu W.-Z., and Zhang W.-X. Neighborhood operator systems and approximations. Inform. Sci. 144 (2002) 201-217
34. Xiao Q.M., and Zhang Z.-L. Rough prime ideals and rough fuzzy prime ideals in semigroups. Inform. Sci. 176 (2006) 725-733
35. Yang X.-P. Minimization of axiom sets on fuzzy approximation operators. Inform. Sci. 177 (2007) 3840-3854
36. Yang Y., and John R. Roughness bounds in rough set operations. Inform. Sci. 176 (2006) 3256-3267
37. Yao Y.Y. Relational interpretation of neighborhood operators and rough set approximation operator. Inform. Sci. 111 (1998) 239-259
38. Li F., Yin Y., and Lu L. (θ, T)-fuzzy rough approximation operators and TL- fuzzy rough ideals on a ring. Inform. Sci. 177 (2007) 4711-4726
39. Zadeh L.A. Fuzzy sets. Inform. Control 8 (1965) 338-353
40. Zhan J., Davvaz B., and Shum K.P. A new view of fuzzy hypernear-rings. Inform. Sci. 178 (2008) 425-438
41. 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
42. Zhang W.-X., Ma J.-M., and Fan S.-Q. Variable threshold concept lattices. Inform. Sci. 177 (2007) 4883-4892
43. Zhu W. Generalized rough sets based on relations. Inform. Sci. 177 (2007) 4997-5011
44. Zhu W. Topological approaches to covering rough sets. Inform. Sci. 177 (2007) 1499-1508