×

zbMATH — the first resource for mathematics

Generalized rough sets over fuzzy lattices. (English) Zbl 1136.03328
Summary: This paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches. From the viewpoint of the constructive approach, the basic properties of generalized rough sets over fuzzy lattices are obtained. The matrix representation of the lower and upper approximations is given. According to this matrix view, a simple algorithm is obtained for computing the lower and upper approximations. As for the axiomatic approach, a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices.

MSC:
03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
06D72 Fuzzy lattices (soft algebras) and related topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Banerjee, M.; Pal, S.K., Roughness of a fuzzy set, Information sciences, 93, 235-246, (1996) · Zbl 0879.04004
[2] Chen, D.; Zhang, W.; Yeung, D.; Tsang, E.C.C., Rough approximations on a complete completely distributive lattice with applications to generalized rough sets, Information sciences, 176, 1829-1848, (2006) · Zbl 1104.03053
[3] Cock, M.D.; Cornelis, C.; Kerre, E.E., Fuzzy rough sets: the forgotten step, IEEE transactions on fuzzy systems, 15, 121-130, (2007)
[4] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International journal of general system, 17, 191-208, (1990) · Zbl 0715.04006
[5] Goguen, J.A., L-fuzzy sets, Journal of mathematical analysis and applications, 18, 145-174, (1967) · Zbl 0145.24404
[6] Jensen, R.; Shen, Q., Fuzzy rough sets assisted attribute selection, IEEE transactions on fuzzy systems, 15, 73-89, (2007)
[7] Lin, T.Y.; Liu, Q., Rough approximate operators: axiomatic rough set theory, (), 256-260 · Zbl 0818.03028
[8] Liu, G.L., The axiomatization of the rough set upper approximation operations, Fundamenta informaticae, 69, 331-342, (2006) · Zbl 1096.68150
[9] Mi, J.S.; Zhang, W.X., An axiomatic characterization of a fuzzy generalization of rough sets, Information sciences, 160, 1-4, 235-249, (2004) · Zbl 1041.03038
[10] Morsi, N.N.; Yakout, M.M., Axiomatics for fuzzy rough sets, Fuzzy sets and systems, 100, 327-342, (1998) · Zbl 0938.03085
[11] Nanda, S.; Majumdar, S., Fuzzy rough sets, Fuzzy sets and systems, 45, 157-160, (1992) · Zbl 0749.04004
[12] Pal, S.; Mitra, P., Case generation using rough sets with fuzzy representation, IEEE transactions on knowledge and data engineering, 16, 3, 292C300, (2004)
[13] Pawlak, Z., Rough sets, International journal of computer and information sciences, 11, 341-356, (1982) · Zbl 0501.68053
[14] Pawlak, Z., Rough sets – theoretical aspects of reasoning about data, (1991), Kluwer Academic Publishers Boston, MA · Zbl 0758.68054
[15] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information sciences, 177, 1, 3-27, (2007) · Zbl 1142.68549
[16] Pawlak, Z.; Skowron, A., Rough sets: some extensions, Information sciences, 177, 1, 28-40, (2007) · Zbl 1142.68550
[17] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Information sciences, 177, 1, 41-73, (2007) · Zbl 1142.68551
[18] ()
[19] ()
[20] Pei, D., A generalized model of fuzzy rough sets, International journal of general system, 34, 603-613, (2005) · Zbl 1082.03047
[21] Qi, G.; Liu, W., Rough operations on Boolean algebras, Information sciences, 173, 49-63, (2005) · Zbl 1074.03025
[22] Radzikowska, A.M.; Kerre, E.E., Fuzzy rough sets based on residuated lattices, Transactions on rough sets, lecture notes in computer sciences, 3135, 278-296, (2004) · Zbl 1109.68118
[23] Radzikowska, A.M.; Kerre, E.E., A comparative study of fuzzy rough sets, Fuzzy sets and systems, 126, 137-155, (2001) · Zbl 1004.03043
[24] Slezak, D.; Ziarko, W., The investigation of the Bayesian rough set model, International journal of approximate reasoning, 40, 81-91, (2005) · Zbl 1099.68089
[25] Slowinski, R.; Vanderpooten, D., A generalized definition of rough approximation based on similarity, IEEE transactions on knowledge and data engineering, 12, 331-336, (2000)
[26] Wang, G.J., Theory of L-fuzzy topological space, (1988), Shaanxi Normal University Press Xi’an, (in Chinese)
[27] Wu, W.Z.; Mi, J.S.; Zhang, W.X., Generalized fuzzy rough sets, Information sciences, 151, 263-282, (2003) · Zbl 1019.03037
[28] Wu, W.Z.; Zhang, W.X., Constructive and axiomatic approaches of fuzzy approximation operators, Information sciences, 159, 233-254, (2004) · Zbl 1071.68095
[29] Wu, W.Z.; Leung, Y.; Zhang, W.X., On generalized rough fuzzy approximation operators, Transactions on rough sets, lecture notes in computer sciences, 4100, 263-284, (2006) · Zbl 1136.68538
[30] Yang, X.P.; Li, T.J., The minimization of axiom sets characterizing generalized approximation operators, Information sciences, 176, 887-899, (2006) · Zbl 1094.03042
[31] Yao, Y.Y., Constructive and algebraic methods of the theory of rough sets, Information sciences, 109, 21-47, (1998) · Zbl 0934.03071
[32] Yao, Y.Y., Two views of the theory of rough sets in finite universes, International journal of approximation reasoning, 15, 291-317, (1996) · Zbl 0935.03063
[33] Yao, Y.Y., Relational interpretations of neighborhood operators and rough set approximation operators, Information sciences, 111, 239-259, (1998) · Zbl 0949.68144
[34] Yao, Y., Neighborhood systems and approximate retrieval, Information sciences, 176, 3431-3452, (2007) · Zbl 1119.68074
[35] Yao, Y.Y.; Lin, T.Y., Generalization of rough sets using modal logic, Intelligent automation and soft computing, an international journal, 2, 103-120, (1996)
[36] Yeung, D.S.; Chen, D.; Tsang, E.C.C.; Lee, J.W.T.; Wang, X., On the generalization of fuzzy rough sets, IEEE transaction on fuzzy systems, 13, 343-361, (2005)
[37] Zhu, W.; Wang, F.Y., Reduction and axiomization of covering generalized rough sets, Information sciences, 152, 217-230, (2003) · Zbl 1069.68613
[38] Zhu, W., Topological approaches to covering rough sets, Information sciences, 177, 1499-1508, (2007) · Zbl 1109.68121
[39] Zhu, W.; Wang, F.Y., On three types of covering rough sets, IEEE transactions on knowledge and data engineering, 19, 8, 1131-1144, (2007)
[40] Zhu, W., Generalized rough sets based on relations, Information sciences, 177, 22, 4997-5011, (2007) · Zbl 1129.68088
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.