×

Rough sets: some extensions. (English) Zbl 1142.68550

Summary: We present some extensions of the rough set approach and we outline a challenge for the rough set based research.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation

Software:

ElemStatLearn
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] ()
[2] ()
[3] Barsalou, L.W., Perceptual symbol systems, Behavioral and brain sciences, 22, 577-660, (1999)
[4] J. Bazan, H.S. Nguyen, S.H. Nguyen, P. Synak, J. Wróblewski, Rough set algorithms in classification problems, in: Polkowski et al. [55], pp. 49-88. · Zbl 0992.68197
[5] J. Bazan, A. Skowron, On-line elimination of non-relevant parts of complex objects in behavioral pattern identification, in: Pal et al. [40], pp. 720-725.
[6] J.G. Bazan, H.S. Nguyen, J.F. Peters, A. Skowron, M. Szczuka, Rough set approach to pattern extraction from classifiers, in: Skowron and Szczuka [78], pp. 20-29. Available from: <http://www.elsevier.nl/locate/entcs/volume82.html>. · Zbl 1270.68306
[7] J.G. Bazan, H.S. Nguyen, A. Skowron, M. Szczuka, A view on rough set concept approximation, in: Wang et al. [93], pp. 181-188. · Zbl 1026.68615
[8] J.G. Bazan, J.F. Peters, A. Skowron, Behavioral pattern identification through rough set modelling, in: Śle¸zak et al. [84], pp. 688-697.
[9] J.G. Bazan, A. Skowron, Classifiers based on approximate reasoning schemes, in: Dunin-Ke¸plicz et al. [12], pp. 191-202. · Zbl 1082.68832
[10] Behnke, S., Hierarchical neural networks for image interpretation, Lecture notes in computer science, vol. 2766, (2003), Springer Heidelberg
[11] Breiman, L., Statistical modeling: the two cultures, Statistical science, 16, 3, 199-231, (2001) · Zbl 1059.62505
[12] ()
[13] Düntsch, I.; Gediga, G., Rough set data analysis: A road to non-invasive knowledge discovery, (2000), Methodos Publishers Bangor, UK
[14] Fahle, M.; Poggio, T., Perceptual learning, (2002), MIT Press Cambridge
[15] Friedman, J.H.; Hastie, T.; Tibshirani, R., The elements of statistical learning: data mining, inference and prediction, (2001), Springer-Verlag Heidelberg · Zbl 0973.62007
[16] Gell-Mann, M., The quark and the jaguar – adventures in the simple and the complex, (1994), Brown and Co. London · Zbl 0833.00011
[17] Greco, S.; Matarazzo, B.; Słowiński, R., Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems, (), 295-316
[18] Greco, S.; Matarazzo, B.; Słowiński, R., Rough set theory for multicriteria decision analysis, European journal of operational research, 129, 1, 1-47, (2001) · Zbl 1008.91016
[19] Greco, S.; Matarazzo, B.; Słowiński, R., Data mining tasks and methods: classification: multicriteria classification, (), 318-328
[20] S. Greco, B. Matarazzo, R. Słowiński, Dominance-based rough set approach to knowledge discovery (I) - general perspective, in: Zhong and Liu [99], pp. 513-552.
[21] S. Greco, B. Matarazzo, R. Słowiński, Dominance-based rough set approach to knowledge discovery (II) - extensions and applications, in: Zhong and Liu [99], pp. 553-612.
[22] S. Greco, R. Słowiński, J. Stefanowski, M. Zurawski, Incremental versus non-incremental rule induction for multicriteria classification, in: Peters et al. [49], pp. 54-62.
[23] Grzymała-Busse, J.W., Managing uncertainty in expert systems, (1990), Kluwer Academic Publishers Norwell, MA · Zbl 0751.68069
[24] Harnad, S., Categorical perception: the groundwork of cognition, (1987), Cambridge University Press New York, NY
[25] Huhns, M.N.; Singh, M.P., Readings in agents, (1998), Morgan Kaufman San Mateo
[26] R. Keefe, Theories of Vagueness, Cambridge Studies in Philosophy, Cambridge, UK, 2000.
[27] ()
[28] G.W. Leibniz, Discourse on metaphysics, in: Ariew and Garber [2], pp. 35-68.
[29] Leśniewski, S., Grungzüge eines neuen systems der grundlagen der Mathematik, Fundamenta mathematicae, 14, 1-81, (1929) · JFM 55.0626.03
[30] Leśniewski, S., On the foundations of mathematics, Topoi, 2, 7-52, (1982)
[31] Lin, T.Y., Neighborhood systems and approximation in database and knowledge base systems, (), 75-86
[32] Lin, T.Y., The discovery analysis and representation of data dependencies in databases, (), 107-121 · Zbl 0927.68089
[33] ()
[34] S. Marcus, The paradox of the heap of grains, in respect to roughness, fuzziness and negligibility, in: Polkowski and Skowron [57], pp. 19-23. · Zbl 0907.03006
[35] T.M. Mitchel, Machine Learning, McGraw-Hill Series in Computer Science Boston, MA, 1999.
[36] Nguyen, S.H.; Bazan, J.; Skowron, A.; Nguyen, H.S., Layered learning for concept synthesis, (), 187-208 · Zbl 1104.68565
[37] T.T. Nguyen, A. Skowron, Rough set approach to domain knowledge approximation, in: Wang et al. [93], pp. 221-228. · Zbl 1026.68644
[38] Orłowska, E., Semantics of vague conepts, (), 465-482
[39] Orłowska, E., Reasoning about vague concepts, Bulletin of the Polish Academy of sciences, mathematics, 35, 643-652, (1987) · Zbl 0641.68160
[40] ()
[41] ()
[42] Z. Pawlak, Classification of Objects by Means of Attributes, Reports, vol. 429, Institute of Computer Science, Polish Academy of Sciences Warsaw, Poland, 1981.
[43] Z. Pawlak, Rough Relations, Reports, vol. 435, Institute of Computer Science, Polish Academy of Sciences Warsaw, Poland, 1981.
[44] Pawlak, Z., Rough sets, International journal of computer and information sciences, 11, 341-356, (1982) · Zbl 0501.68053
[45] Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, system theory, knowledge engineering and problem solving, vol. 9, (1991), Kluwer Academic Publishers Dordrecht, The Netherlands
[46] Pawlak, Z., Decision rules, bayes’ rule and rough sets, (), 1-9 · Zbl 0948.03026
[47] Z. Pawlak, A. Skowron, Rudiments of rough sets, Information Sciences, in press, doi:10.1016/j.ins.2006.06.003. · Zbl 1142.68549
[48] ()
[49] ()
[50] Pindur, R.; Susmaga, R.; Stefanowski, J., Hyperplane aggregation of dominance decision rules, Fundamenta informaticae, 61, 2, 117-137, (2004) · Zbl 1083.68121
[51] Poggio, T.; Smale, S., The mathematics of learning: dealing with data, Notices of the AMS, 50, 5, 537-544, (2003) · Zbl 1083.68100
[52] Polkowski, L., Rough sets: mathematical foundations, Advances in soft computing, (2002), Physica-Verlag Heidelberg
[53] Polkowski, L., Rough mereology: a rough set paradigm for unifying rough set theory and fuzzy set theory, Fundamenta informaticae, 54, 67-88, (2003) · Zbl 1031.03069
[54] L. Polkowski, Toward rough set foundations. Mereological approach, in: Tsumoto et al. [91], pp. 8-25. · Zbl 1103.03049
[55] ()
[56] Polkowski, L.; Skowron, A., Rough mereology: A new paradigm for approximate reasoning, International journal of approximate reasoning, 15, 4, 333-365, (1996) · Zbl 0938.68860
[57] ()
[58] ()
[59] Polkowski, L.; Skowron, A., Towards adaptive calculus of granules, (), 201-227 · Zbl 0949.68143
[60] L. Polkowski, A. Skowron, Rough mereology in information systems. a case study: qualitative spatial reasoning, in: Polkowski et al. [55], pp. 89-135. · Zbl 0992.68198
[61] Polkowski, L.; Skowron, A., Rough mereological calculi of granules: A rough set approach to computation, Computational intelligence: an international journal, 17, 3, 472-492, (2001)
[62] Polkowski, L.; Skowron, A.; Żytkow, J., Rough foundations for rough sets, (), 55-58
[63] Read, S., Thinking about logic: an introduction to the philosophy of logic, (1994), Oxford University Press Oxford, New York
[64] Skowron, A., Rough sets in KDD - plenary talk, (), 1-14
[65] Skowron, A., Toward intelligent systems: calculi of information granules, Bulletin of the international rough set society, 5, 1-2, 9-30, (2001) · Zbl 1054.68692
[66] A. Skowron, Approximate reasoning in distributed environments, in: Zhong and Liu [99], pp. 433-474.
[67] Skowron, A., Perception logic in intelligent systems (keynote talk), (), 1-5
[68] Skowron, A., Rough sets and vague concepts, Fundamenta informaticae, 64, 1-4, 417-431, (2005) · Zbl 1102.68131
[69] A. Skowron, Rough sets in perception-based computing (keynote talk), in: Pal et al. [40], pp. 21-29.
[70] A. Skowron, J. Peters, Rough sets: Trends and challenges, in: Wang et al. [93], pp. 25-34 (plenary talk). · Zbl 1026.68653
[71] Skowron, A.; Stepaniuk, J., Tolerance approximation spaces, Fundamenta informaticae, 27, 2-3, 245-253, (1996) · Zbl 0868.68103
[72] Skowron, A.; Stepaniuk, J., Information granules: towards foundations of granular computing, International journal of intelligent systems, 16, 1, 57-86, (2001) · Zbl 0969.68078
[73] A. Skowron, J. Stepaniuk, Information granules and rough-neural computing, in: Pal et al. [41], pp. 43-84.
[74] A. Skowron, J. Stepaniuk, Ontological framework for approximation, in: Śle¸zak et al. [83], pp. 718-727. · Zbl 1134.68514
[75] A. Skowron, R. Swiniarski, Rough sets and higher order vagueness, in: Śle¸zak et al. [83], pp. 33-42. · Zbl 1134.68558
[76] A. Skowron, R. Swiniarski, P. Synak, Approximation spaces and information granulation, in: Peters and Skowron [48], pp. 175-189. · Zbl 1116.68602
[77] Skowron, A.; Synak, P., Complex patterns, Fundamenta informaticae, 60, 1-4, 351-366, (2004) · Zbl 1083.68122
[78] (), Available from:
[79] D. Śle¸zak, M. Szczuka, J. Wróblewski, Feedforward concept networks, in: Dunin-Ke¸plicz et al. [12], pp. 281-292.
[80] Śle¸zak, D., Normalized decision functions and measures for inconsistent decision tables analysis, Fundamenta informaticae, 44, 291-319, (2000) · Zbl 0970.68171
[81] D. Śle¸zak, Various approaches to reasoning with frequency-based decision reducts: a survey, in: Polkowski et al. [55], pp. 235-285.
[82] D. Śle¸zak, Rough sets and Bayes factor, in: Peters and Skowron [48], pp. 202-229.
[83] (), (Part I)
[84] (), (Part II)
[85] Śle¸zak, D.; Ziarko, W., The investigation of the Bayesian rough set model, International journal of approximate reasoning, 40, 81-91, (2005) · Zbl 1099.68089
[86] R. Słowiński, S. Greco, B. Matarazzo, Rough set analysis of preference-ordered data, in: Alpigini et al. [1], pp. 44-59. · Zbl 1013.68599
[87] Słowiński, R.; Vanderpooten, D., Similarity relation as a basis for rough approximations, (), 17-33
[88] ()
[89] Stepaniuk, J., Approximation spaces, reducts and representatives, (), 109-126 · Zbl 0943.68158
[90] Stone, P., Layered learning in multi-agent systems: A winning approach to robotic soccer, (2000), The MIT Press Cambridge, MA
[91] ()
[92] Vapnik, V., Statistical learning theory, (1998), John Wiley & Sons New York, NY · Zbl 0935.62007
[93] ()
[94] Y.Y. Yao, Generalized rough set models, in: Polkowski and Skowron [58], pp. 286-318.
[95] Yao, Y.Y., Information granulation and rough set approximation, International journal of intelligent systems, 16, 87-104, (2001) · Zbl 0969.68079
[96] Y.Y. Yao, On generalizing rough set theory, in: Wang et al. [93], pp. 44-51. · Zbl 1026.68669
[97] Y.Y. Yao, S.K.M. Wong, T.Y. Lin, A review of rough set models, in: Lin and Cercone [33], pp. 47-75. · Zbl 0861.68101
[98] Zadeh, L.A., A new direction in AI: toward a computational theory of perceptions, AI magazine, 22, 1, 73-84, (2001)
[99] ()
[100] Ziarko, W., Variable precision rough set model, Journal of computer and system sciences, 46, 39-59, (1993) · Zbl 0764.68162
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.