Rough ideals in lattices

Neural Computing and Applications

Volumn 21, Issue SUPPL. 1, 2012, Pages 245-253

  Xiao, Qimei ^a,b   Li, Qingguo ^a   Zhou, Xiangnan ^a  

^a HUNAN UNIVERSITY   (China)

^b CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Homomorphism; Lattice; Rough ideals; Rough set

Indexed keywords

HOMOMORPHISM; LATTICE; ROUGH IDEALS; ROUGH SET;

ROUGH SET THEORY;

EID: 84865746493     PISSN: 09410643     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00521-011-0801-5     Document Type: Article

References (35)

1. Biswas R, Nanda S (1994) Rough groups and rough subgroups. Bull Pol Acad Sci Math 42: 251-254.
2. Bonikowaski Z (1995) Algebraic structures of rough sets. In: Ziarko WP (ed) Rough sets, fuzzy sets and knowledge discovery, Springer, Berlin, pp 242-247.
3. Cattaneo G, Ciucci D (2004) Algebraic structures for rough sets. LNCS 3135: 208-252.
4. Davey BA, Priestley HA (2002) Introduction to lattices and order. Cambridge University Press, Cambridge.
5. Davvaz B, Mahdavipour M (2006) Roughness in modules. Inf Sci 176: 3658-3674.
6. Davvaz B (2006) A new view of approximations in Hv-groups. Soft Comput 10(11): 1043-1046.
7. Davvaz B (2004) Roughness in rings. Inf Sci 164: 147-163.
8. Davvaz B (2006) Roughness based on fuzzy ideals. Inf Sci 176: 2417-2437.
9. Davvaz B (2009) Approximations in hyperrings. J Multiple-Valued Logic Soft Comput 15: 471-488.
10. Davvaz B (2008) Approximations in n-ary algebraic systems. Soft Comput 12: 409-418.
11. Degang C, Wenxiu Z, Yeung D, Tsang ECC (2006) Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf Sci 176: 1829-1848.
12. Ganter B, Wille R (1999) Formal concept analysis. Springer, Berlin.
13. Iwinski T (1987) Algebraic approach to rough sets. Bull Pol Acad Sci Math 35: 673-683.
14. Järvinen J (2002) On the structure of rough approximations. Fundamenta Informaticae 53: 135-153.
15. Kazanci{dotless} O, Davvaz B (2008) On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings. Inf Sci 178: 1343-1354.
16. Kazanci{dotless} O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178: 2349-2359.
17. Kuroki N, Wang PP (1996) The lower and upper approximations in a fuzzy group. Inf Sci 90: 203-220.
18. Kuroki N (1997) Rough ideals in semigroups. Inf Sci 100: 139-63.
19. Leoreanu-Fotea V, Davvaz B (2008) Roughness in n-ary hypergroups. Inf Sci 178: 4114-4124.
20. Leoreanu-Fotea V (2008) The lower and upper approximations in a hypergroup. Inf Sci 178: 3605-3615.
21. Liu G (2008) Generalized rough sets over fuzzy lattices. Inf Sci 178: 1651-1662.
22. Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inf Sci 178: 4105-4113.
23. Mani A (2011) Choice inclusive general rough semantics. Inf Sci 181: 1097-1115.
24. Mordeson N (2001) Rough set theory applied to (fuzzy) ideal theory. Fuzzy Sets Syst 121: 315-324.
25. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11: 341-356.
26. Pomykala J, Pomykala JA (1998) The stone algebra of rough sets. Bull Pol Acad Sci Math 36: 495-508.
27. Polkowski L, Skowron A (1996) Rough mereology: a new paradigm for approximate reasoning. Int J Approx Reason 15: 333-365.
28. Qimei X, Zhenliang Z (2006) Rough prime ideals and rough fuzzy prime ideals in semigroups. Inf Sci 176: 725-733.
29. Rasouli S, Davvaz B (2010) Roughness in MV-algebra. Inf Sci 180: 737-747.
30. Skowron A, Polkowski L (1998) Rough mereological foundations for design, analysis, synthesis, and control in distributed systems. Inf Sci 104: 129-56.
31. Wenxiu Z, Weizhi W (2001) Theory and method of roughness. Science Press, Beijing.
32. Xueyou C, Li Q (2007) Construction of rough approximations in fuzzy setting. Fuzzy Sets Syst 158: 2641-2653.
33. Yamak S, Kazanci{dotless} O, Davvaz B (2010) Generalized lower and upper approximations in a ring. Inf Sci 180: 1759-1768.
34. Yunqiang Y, Jianming Z, Corsini P (2011) L-fuzzy roughness of n-ary polygroups. Acta Mathematica Sinica English Series 27: 97-118.
35. Yunqiang Y, Jianming Z, Corsini P (2011) Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice. Neural Comput Appl 20: 41-57.