×

zbMATH — the first resource for mathematics

Rudiments of rough sets. (English) Zbl 1142.68549
Summary: Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, knowledge discovery, decision analysis, and expert systems. In the article, we present the basic concepts of rough set theory and point out some rough set-based research directions and applications.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ()
[2] A. An, Y. Huang, X. Huang, N. Cercone, Feature selection with rough sets for web page classification. In: Peters et al. [228], pp. 1-13. · Zbl 1108.68607
[3] P. Apostoli, A. Kanda, Parts of the continuum: Towards a modern ontology of sciences, Technical Reports in Philosophical Logic, vol. 96 (1). The University of Toronto, Department of Philosophy, Toronto, Canada, 1999, Revised March, 1999.
[4] ()
[5] Balbiani, P.; Vakarelov, D., A modal logic for indiscernibility and complementarity in information systems, Fundamenta informaticae, 50, 3-4, 243-263, (2002) · Zbl 1016.03026
[6] Banerjee, M., Logic for rough truth, Fundamenta informaticae, 71, 2-3, 139-151, (2006) · Zbl 1094.03015
[7] M. Banerjee, M.K. Chakraborty, Rough set algebras. In: Pal et al. [194], pp. 157-184.
[8] Banerjee, M.; Pal, S.K., Roughness of a fuzzy set, Information sciences, 93, 3-4, 235-246, (1996) · Zbl 0879.04004
[9] J. Bazan, H.S. Nguyen, S.H. Nguyen, P. Synak, J. Wróblewski, Rough set algorithms in classification problems. In: Polkowski et al. [241], pp. 49-88. · Zbl 0992.68197
[10] J. Bazan, A. Osmólski, A. Skowron, D. Śle¸zak, M. Szczuka, J. Wróblewski, Rough set approach to the survival analysis. In: Alpigini et al. [1], pp. 522-529.
[11] J. Bazan, A. Skowron, On-line elimination of non-relevant parts of complex objects in behavioral pattern identification. In: Pal et al. [189], pp. 720-725.
[12] J.G. Bazan, A comparison of dynamic and non-dynamic rough set methods for extracting laws from decision tables. In: Polkowski and Skowron [244], pp. 321-365. · Zbl 1067.68711
[13] J.G. Bazan, H.S. Nguyen, A. Skowron, M. Szczuka, A view on rough set concept approximation. In: Wang et al. [350], pp. 181-188. · Zbl 1026.68615
[14] J.G. Bazan, J.F. Peters, A. Skowron, Behavioral pattern identification through rough set modelling. In: Śle¸zak et al. [301], pp. 688-697.
[15] Black, M., Vagueness: an exercise in logical analysis, Philosophy of science, 4, 4, 427-455, (1937)
[16] Brown, F., Boolean reasoning, (1990), Kluwer Academic Publishers Dordrecht
[17] E. Bryniarski, U. Wybraniec-Skardowska, Generalized rough sets in contextual spaces. In: Rough Sets and Data Mining - Analysis of Imperfect Data. pp. 339-354.
[18] Cantor, G., Über eine eigenschaft des inbegriffes aller reellen algebraischen zahlen, Crelle’s journal für Mathematik, 77, 258-263, (1874) · JFM 06.0057.01
[19] Cantor, G., Grundlagen einer allgemeinen mannigfaltigkeitslehre, (1883), B.G. Teubner Leipzig · JFM 15.0453.01
[20] ()
[21] G. Cattaneo, Abstract approximation spaces for rough theories. In: Polkowski and Skowron [244], pp. 59-98. · Zbl 0927.68087
[22] G. Cattaneo, D. Ciucci, Algebraic structures for rough sets. In: Peters et al. [228], pp. 208-252. · Zbl 1109.68115
[23] Cattaneo, G.; Ciucci, D.; Giuntini, R.; Konig, M., Algebraic structures related to many valued logical systems. part I: heyting – wajsberg algebras, Fundamenta informaticae, 63, 4, 331-355, (2004) · Zbl 1090.03035
[24] Cattaneo, G.; Ciucci, D.; Giuntini, R.; Konig, M., Algebraic structures related to many valued logical systems. part II: equivalence among some widespread structures, Fundamenta informaticae, 63, 4, 357-373, (2004) · Zbl 1092.03035
[25] Cercone, N.; Skowron, A.; Zhong, N., Computational intelligence: an international journal, vol. 17, 3, (2001), (Special issue)
[26] B.S. Chlebus, S.H. Nguyen, On finding optimal discretizations for two attributes. In: Polkowski and Skowron [243], pp. 537-544.
[27] Chmielewski, M.R.; Grzymała-Busse, J.W., Global discretization of continuous attributes as preprocessing for machine learning, International journal of approximate reasoning, 15, 4, 319-331, (1996) · Zbl 0949.68560
[28] Cios, K.; Pedrycz, W.; Swiniarski, R., Data mining methods for knowledge discovery, (1998), Kluwer Norwell, MA · Zbl 0912.68199
[29] Comer, S.D., An algebraic approach to the approximation of information, Fundamenta informaticae, 14, 4, 495-502, (1991) · Zbl 0727.68114
[30] Czyżewski, A., Automatic identification of sound source position employing neural networks and rough sets, Pattern recognition letters, 24, 6, 921-933, (2003)
[31] Czyżewski, A.; Królikowski, R., Neuro-rough control of masking thresholds for audio signal enhancement, Neurocomputing, 36, 5-27, (2001) · Zbl 1003.68639
[32] A. Czyżewski, M. Szczerba, B. Kostek, Musical phrase representation and recognition by means of neural networks and rough sets. In: Peters and Skowron [225], pp. 254-278. · Zbl 1104.68758
[33] ()
[34] Demri, S.; Sattler, U., Automata-theoretic decision procedures for information logics, Fundamenta informaticae, 53, 1, 1-22, (2002) · Zbl 1025.03021
[35] Demri, S.; Stepaniuk, J., Computational complexity of multimodal logics based on rough sets, Fundamenta informaticae, 44, 4, 373-396, (2000) · Zbl 0971.03023
[36] J. Deogun, V.V. Raghavan, A. Sarkar, H. Sever, Data mining: trends in research and development. In: Rough Sets and Data Mining - Analysis of Imperfect Data, pp. 9-46.
[37] P. Doherty, W. Łukaszewicz, A. Skowron, A. Szałas, Approximation transducers and trees: a technique for combining rough and crisp knowledge. In: Knowledge Engineering: A Rough Set Approach [38], pp. 189-218.
[38] Doherty, P.; Łukaszewicz, W.; Skowron, A.; Szałas, A., Knowledge engineering: A rough set approach, Studies in fizziness and soft computing, vol. 202, (2006), Springer Heidelberg
[39] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Fuzzy sets and systems, 23, 3-18, (1987) · Zbl 0633.68099
[40] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International journal of general systems, 17, 191-209, (1990) · Zbl 0715.04006
[41] D. Dubois, H. Prade, Foreword. In: Rough Sets: Theoretical Aspects of Reasoning about Data [206].
[42] V. Dubois, M. Quafafou, Concept learning with approximation: rough version spaces. In: Alpigini et al. [1], pp. 239-246. · Zbl 1013.68574
[43] Duda, R.; Hart, P.; Stork, R., Pattern classification, (2002), John Wiley & Sons New York, NY
[44] ()
[45] Düntsch, I., A logic for rough sets, Theoretical computer science, 179, 427-436, (1997) · Zbl 0896.03050
[46] Düntsch, I.; Gediga, G., Uncertainty measures of rough set prediction, Artificial intelligence, 106, 1, 77-107, (1998)
[47] Düntsch, I.; Gediga, G., Rough set data analysis, (), 281-301 · Zbl 0983.68194
[48] Düntsch, I.; Gediga, G., Rough set data analysis: A road to non-invasive knowledge discovery, (2000), Methodos Publishers Bangor, UK
[49] Düntsch, I.; Orlowska, E.; Wang, H., Algebras of approximating regions, Fundamenta informaticae, 46, 1-2, 71-82, (2001) · Zbl 0987.03058
[50] Fan, T.-F.; Liau, C.-J.; Yao, Y., On modal and fuzzy decision logics based on rough set theory, Fundamenta informaticae, 52, 4, 323-344, (2002) · Zbl 1016.03027
[51] K. Farion, W. Michalowski, R. Słowiński, S. Wilk, S. Rubin, Rough set methodology in clinical practice: Controlled hospital trial of the MET system. In: Tsumoto et al. [337], pp. 805-814. · Zbl 1103.68844
[52] Filip, H., Nominal and verbal semantic structure: analogies and interactions, Language sciences, 23, 453-501, (2000)
[53] Fine, K., Vagueness, truth and logic, Synthese, 30, 265-300, (1975) · Zbl 0311.02011
[54] Forrest, P., Sets as mereological tropes, Metaphysical, 3, 5-10, (2002)
[55] Frege, G., Grundgesetzen der arithmetik, 2, (1903), Verlag von Hermann Pohle Jena · JFM 34.0071.05
[56] Friedman, J.H.; Hastie, T.; Tibshirani, R., The elements of statistical learning: data mining, inference, and prediction, (2001), Springer-Verlag Heidelberg · Zbl 0973.62007
[57] ()
[58] Garcia-Molina, H.; Ullman, J.; Widom, J., Database systems: the complete book, (2002), Prentice Hall Upper Saddle River, New Jersey
[59] Gediga, G.; Düntsch, I., Rough approximation quality revisited, Artificial intelligence, 132, 219-234, (2001) · Zbl 0983.68194
[60] Gediga, G.; Düntsch, I., Maximum consistency of incomplete data via non-invasive imputation, Artificial intelligence review, 19, 93-107, (2003)
[61] G. Gediga, I. Düntsch, On model evaluation, indices of importance, and interaction values in rough set analysis. In: Pal et al. [194], pp. 251-276.
[62] Gomolińska, A., A comparative study of some generalized rough approximations, Fundamenta informaticae, 51, 1-2, 103-119, (2002) · Zbl 1023.03050
[63] Gomolińska, A., A graded meaning of formulas in approximation spaces, Fundamenta informaticae, 60, 1-4, 159-172, (2004) · Zbl 1083.68119
[64] A. Gomolińska, Rough validity, confidence, and coverage of rules in approximation spaces. In: Peters and Skowron [226], pp. 57-81.
[65] Góra, G.; Wojna, A.G., RIONA: A new classification system combining rule induction and instance-based learning, Fundamenta informaticae, 51, 4, 369-390, (2002) · Zbl 1011.68114
[66] S. Greco, M. Inuiguchi, R. Słowiński, A new proposal for fuzzy rough approximations and gradual decision rule representation. In: Peters et al. [228], pp. 319-342. · Zbl 1108.68609
[67] Greco, S.; Inuiguchi, M.; Słowiński, R., Fuzzy rough sets and multiple-premise gradual decision rules, International journal of approximate reasoning, 41, 2, 179-211, (2006) · Zbl 1093.68114
[68] Greco, S.; Matarazzo, B.; Słowiński, R., Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems, (), 295-316
[69] 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
[70] Greco, S.; Matarazzo, B.; Słowiński, R., Data mining tasks and methods: classification: multicriteria classification, (), 318-328
[71] S. Greco, B. Matarazzo, R. Słowiński, Dominance-based rough set approach to knowledge discovery (I) - general perspective, (ii) - extensions and applications. In: Zhong and Liu [374], pp. 513-552, 553-612.
[72] Greco, S.; Pawlak, Z.; Słowiński, R., Can Bayesian confirmation measures be useful for rough set decision rules?, Engineering applications of artificial intelligence, 17, 4, 345-361, (2004)
[73] S. Greco, R. Słowiński, J. Stefanowski, M. Zurawski, Incremental versus non-incremental rule induction for multicriteria classification. In: Peters et al. [228], pp. 54-62.
[74] Grzymała-Busse, J.W., Managing uncertainty in expert systems, (1990), Kluwer Academic Publishers Norwell, MA · Zbl 0751.68069
[75] J.W. Grzymała-Busse, LERS - A system for learning from examples based on rough sets. In: Słowiński [305], pp. 3-18.
[76] Grzymała-Busse, J.W., Selected algorithms of machine learning from examples, Fundamenta informaticae, 18, 193-207, (1993) · Zbl 0781.68094
[77] Grzymała-Busse, J.W., Classification of unseen examples under uncertainty, Fundamenta informaticae, 30, 3-4, 255-267, (1997)
[78] Grzymała-Busse, J.W., A new version of the rule induction system LERS, Fundamenta informaticae, 31, 1, 27-39, (1997) · Zbl 0882.68122
[79] J.W. Grzymała-Busse, Three strategies to rule induction from data with numerical attributes. In: Peters et al. [228], pp. 54-62. · Zbl 1108.68611
[80] J.W. Grzymała-Busse, LERS - A data mining system. In: Maimon and Rokach [138], pp. 1347-1351.
[81] J.W. Grzymała-Busse, Rule induction. In: Maimon and Rokach [138], pp. 277-294. · Zbl 1091.68531
[82] J.W. Grzymała-Busse, W.J. Grzymała-Busse, Handling missing attribute values. In: Maimon and Rokach [138], pp. 37-57. · Zbl 1156.68583
[83] Grzymała-Busse, J.W.; Grzymała-Busse, W.J.; Goodwin, L.K., Coping with missing attribute values based on closest fit in preterm birth data: a rough set approach, Computational intelligence: an international journal, 17, 3, 425-434, (2001)
[84] J.W. Grzymaa-Busse, Z.S. Hippe, Data mining methods supporting diagnosis of melanoma, In: 18th IEEE Symposium on Computer-Based Medical Systems (CBMS 2005), 23-24 June 2005, Dublin, Ireland, IEEE Computer Society, 2005, pp. 371-373.
[85] Grzymała-Busse, J.W.; Ziarko, W., Data mining and rough set theory, Communications of the ACM, 43, 108-109, (2000)
[86] Han, S.; Wang, J., Reduct and attribute order, Journal of computer science and technology, 19, 4, 429-449, (2004)
[87] Hempel, C.G., Vagueness and logic, Philosophy of science, 6, 163-180, (1939)
[88] S. Hirano, M. Inuiguchi, S. Tsumoto (Eds.). Proceedings of International Workshop on Rough Set Theory and Granular Computing (RSTGC’2001), Matsue, Shimane, Japan, May 20-22, 2001, Bulletin of the International Rough Set Society, vol. 5(1-2). International Rough Set Society, Matsue, Shimane, 2001.
[89] Hirano, S.; Tsumoto, S., Rough representation of a region of interest in medical images, International journal of approximate reasoning, 40, 1-2, 23-34, (2005)
[90] Hu, X.; Cercone, N., Learning in relational databases: a rough set approach, Computational intelligence: an international journal, 11, 2, 323-338, (1995)
[91] Hu, X.; Cercone, N., Data mining via discretization, generalization and rough set feature selection, Knowledge and information systems: an international journal, 1, 1, 33-60, (1999)
[92] Hu, X.; Cercone, N., Discovering maximal generalized decision rules through horizontal and vertical data reduction, Computational intelligence: an international journal, 17, 4, 685-702, (2001)
[93] Hu, X.; Cercone, N.; Shan, N., A rough set approach to compute all maximal generalized rules, Journal of computing and information, 1, 1, 1078-1089, (1995)
[94] Hu, X.; Lin, T.Y.; Han, J., A new rough set model based on database systems, Journal of fundamental informatics, 59, 2-3, 135-152, (2004) · Zbl 1098.68127
[95] Hvidsten, T.R.; Wilczyński, B.; Kryshtafovych, A.; Tiuryn, J.; Komorowski, J.; Fidelis, K., Discovering regulatory binding-site modules using rule-based learning, Genome research, 6, 15, 856-866, (2005)
[96] M. Inuiguchi, Generalizations of rough sets: from crisp to fuzzy cases. In: Tsumoto et al. [337], pp. 26-37 (plenary talk). · Zbl 1103.03048
[97] ()
[98] T. Iwiński, Rough analysis of lattices, Working papers, vol. 23. University of Carlos III, Madrid, 1991.
[99] J. Järvinen, Representation of information systems and dependence spaces, and some basic algorithms. Licentiate’s thesis. Ph.D. thesis, University of Turku, Department of Mathematics, Turku, Finland, 1997.
[100] Järvinen, J., On the structure of rough approximations, Fundamenta informaticae, 53, 2, 135-153, (2002) · Zbl 1012.68200
[101] Jech, T., Set theory, (1997), Springer Verlag New York · Zbl 0882.03045
[102] Jelonek, J.; Stefanowski, J., Feature subset selection for classification of histological images, Artificial intelligence in medicine, 9, 3, 227-239, (1997)
[103] Jensen, R.; Shen, Q., Semantics-preserving dimensionality reduction: rough and fuzzy-rough approaches, IEEE transactions on knowledge and data engineering, 16, 2, 1457-1471, (2004)
[104] R. Jensen, Q. Shen, A. Tuso, Finding rough set reducts with SAT. In: Śle¸zak et al. [300], pp. 194-203. · Zbl 1134.68538
[105] R. Keefe, Theories of Vagueness. Cambridge Studies in Philosophy, Cambridge, UK, 2000.
[106] Keefe, R.; Smith, P., Vagueness: A reader, (1997), MIT Press Massachusetts, MA
[107] Kim, D., Data classification based on tolerant rough set, Pattern recognition, 34, 8, 1613-1624, (2001) · Zbl 0984.68520
[108] Kim, D.; Bang, S.Y., A handwritten numeral character classification using tolerant rough set, IEEE transactions on pattern analysis and machine intelligence, 22, 9, 923-937, (2000)
[109] ()
[110] J. Komorowski, Z. Pawlak, L. Polkowski, A. Skowron, Rough sets: a tutorial. In: Pal and Skowron [195], pp. 3-98.
[111] B. Kostek, Soft computing-based recognition of musical sounds. In: Polkowski and Skowron [245], pp. 193-213.
[112] Kostek, B., Soft computing in acoustics, applications of neural networks, fuzzy logic and rough sets to physical acoustics, Studies in fuzziness and soft computing, vol. 31, (1999), Physica-Verlag Heidelberg · Zbl 1044.68919
[113] Kostek, B., Perception-based data processing in acoustics: applications to music information retrieval and psychophysiology of hearing, Studies in computational intelligence, vol. 3, (2005), Springer Heidelberg
[114] B. Kostek, A. Czyżewski, Processing of musical metadata employing Pawlak’s flow graphs. In: Peters and Skowron [225], pp. 279-298. · Zbl 1104.68763
[115] B. Kostek, P. Szczuko, P. Żwan, P. Dalka, Processing of musical data employing rough sets and artificial neural networks. In: Peters and Skowron [226], pp. 112-133. · Zbl 1116.68584
[116] M. Kryszkiewicz, Maintenance of reducts in the varable precision rough set model. In: Rough Sets and Data Mining - Analysis of Imperfect Data. pp. 355-372.
[117] M. Kryszkiewicz, Properties of incomplete information systems in the framework of rough sets. In: Polkowski and Skowron [244], pp. 422-450. · Zbl 0940.68138
[118] Kryszkiewicz, M., Rough set approach to incomplete information systems, Information sciences, 112, 1-4, 39-49, (1998) · Zbl 0951.68548
[119] Kryszkiewicz, M., Rules in incomplete information systems, Information sciences, 113, 3-4, 271-292, (1999) · Zbl 0948.68214
[120] M. Kryszkiewicz, K. Cichoń, Towards scalable algorithms for discovering rough set reducts. In: Peters et al. [228], pp. 120-143. · Zbl 1104.68764
[121] Lægreid, A.; Hvidsten, T.R.; Midelfart, H.; Komorowski, J.; Sandvik, A.K., Discovering regulatory binding-site modules using rule-based learning, Genome researche, 5, 13, 965-979, (2003)
[122] Latkowski, R., On decomposition for incomplete data, Fundamenta informaticae, 54, 1, 1-16, (2003) · Zbl 1146.68460
[123] Latkowski, R., Flexible indiscernibility relations for missing attribute values, Fundamenta informaticae, 67, 1-3, 131-147, (2005) · Zbl 1096.68149
[124] A.O.V. Le Blanc, Lesniewski’s Computative Protothetic. Report (Ph.D. thesis), University of Manchester, Manchester, UK, 2003.
[125] G.W. Leibniz, Discourse on metaphysics. In: Ariew and Garber [4], pp. 35-68.
[126] Leśniewski, S., Grungzüge eines neuen systems der grundlagen der Mathematik, Fundamenta mathematicae, 14, 1-81, (1929) · JFM 55.0626.03
[127] Li, Y.; Shiu, S.C.-K.; Pal, S.K.; Liu, J.N.-K., A rough set-based case-based reasoner for text categorization, International journal of approximate reasoning, 41, 2, 229-255, (2006)
[128] Lin, T.Y., Neighborhood systems and approximation in database and knowledge base systems, (), 75-86
[129] Lin, T.Y., Journal of the intelligent automation and soft computing, vol. 2, 2, (1996), (Special issue)
[130] ()
[131] ()
[132] Lingras, P., Fuzzy – rough and rough – fuzzy serial combinations in neuro-computing, Neurocomputing, 36, 1-4, 29-44, (2001) · Zbl 1003.68637
[133] Lingras, P., Unsupervised rough set classification using gas, Journal of intelligent information systems, 16, 3, 215-228, (2001) · Zbl 1016.68112
[134] Lingras, P.; Davies, C., Application of rough genetic algorithms, Computational intelligence: an international journal, 17, 3, 435-445, (2001)
[135] Lingras, P.; West, C., Interval set clustering of web users with rough K-means, Journal of intelligent information systems, 23, 1, 5-16, (2004) · Zbl 1074.68586
[136] Liu, C.; Zhong, N., Rough problem settings for ILP dealing with imperfect data, Computational intelligence: an international journal, 17, 3, 446-459, (2001)
[137] Łukasiewicz, J., Die logischen grundlagen der wahrscheinlichkeitsrechnung, 1913, (), 16-63
[138] ()
[139] J. Małuszyński, A. Vitória, Toward rough datalog. In: Pal et al. [194], pp. 297-332.
[140] S. Marcus, The paradox of the heap of grains, in respect to roughness, fuzziness and negligibility. In: Polkowski and Skowron [243], pp. 19-23. · Zbl 0907.03006
[141] Marek, V.W.; Rasiowa, H., Approximating sets with equivalence relations, Theoretical computer science, 48, 3, 145-152, (1986) · Zbl 0638.68066
[142] Marek, V.W.; Truszczyński, M., Contributions to the theory of rough sets, Fundamenta informaticae, 39, 4, 389-409, (1999) · Zbl 0944.68051
[143] Menasalvas, E.; Wasilewska, A., Data mining as generalization: a formal model, (), 99-126
[144] H. Midelfart, Supervised learning in the gene ontology. Part I: rough set framework. Part II: a bottom-up algorithm. In: Peters and Skowron [227], pp. 69-97, 98-124. · Zbl 1136.68493
[145] Midelfart, H.; Komorowski, J.; Nørsett, K.; Yadetie, F.; Sandvik, A.K.; Lægreid, A., Learning rough set classifiers from gene expression and clinical data, Fundamenta informaticae, 2, 53, 155-183, (2004) · Zbl 1011.92025
[146] Mill, J.S., Ratiocinative and inductive, being a connected view of the principles of evidence, and the methods of scientific investigation, (1862), Parker, Son, and Bourn West Strand London
[147] Mitchel, T.M., Machine learning, Computer science, (1999), McGraw-Hill Boston, MA
[148] P. Mitra, S. Mitra, S.K. Pal, Modular rough fuzzy mlp: Evolutionary design. In: Skowron et al. [280], pp. 128-136.
[149] Mitra, P.; Pal, S.K.; Siddiqi, M.A., Non-convex clustering using expectation maximization algorithm with rough set initialization, Pattern recognition letters, 24, 6, 863-873, (2003) · Zbl 1053.68098
[150] S. Mitra, Computational intelligence in bioinformatics. In: Peters and Skowron [226], pp. 134-152. · Zbl 1116.68572
[151] Mitra, S.; Acharya, T., Data mining. multimedia, soft computing, and bioinformatics, (2003), John Wiley & Sons New York, NY
[152] Miyamoto, S., Application of rough sets to information retrieval, Journal of the American society for information science, 49, 3, 195-220, (1998)
[153] Miyamoto, S., Generalizations of multisets and rough approximations, International journal of intelligent systems, 19, 7, 639-652, (2004) · Zbl 1101.68524
[154] M.J. Moshkov, Time complexity of decision trees. In: Peters and Skowron [226], pp. 244-459. · Zbl 1117.68071
[155] M.J. Moshkov, M. Piliszczuk, On partial tests and partial reducts for decision tables. In: Śle¸zak et al. [300], pp. 149-155. · Zbl 1134.68498
[156] A. Mrózek, Rough sets in computer implementation of rule-based control of industrial processes. In: Słowiński [305], pp. 19-31.
[157] T. Munakata, Rough control: a perspective. In: Rough Sets and Data Mining - Analysis of Imperfect Data, pp. 77-88.
[158] M. Muraszkiewicz, H. Rybiński, Towards a parallel rough sets computer. In: Ziarko [376], pp. 434-443. · Zbl 0941.68569
[159] Nakamura, A., Fuzzy quantifiers and rough quantifiers, (), 111-131
[160] A. Nakamura, On a logic of information for reasoning about knowledge. In: Ziarko [376], pp. 186-195. · Zbl 0939.68835
[161] Nakamura, A., A rough logic based on incomplete information and its application, International journal of approximate reasoning, 15, 4, 367-378, (1996) · Zbl 0935.03045
[162] Nguyen, H.S., On the decision table with maximal number of reducts, Electronic notes in theoretical computer science, 82, 4, (2003) · Zbl 1270.68319
[163] H.S. Nguyen, Approximate boolean reasoning approach to rough sets and data mining. In: Śle¸zak et al. [301], pp. 12-22 (plenary talk). · Zbl 1155.68532
[164] Nguyen, H.S.; Nguyen, S.H., Rough sets and association rule generation, Fundamenta informaticae, 40, 4, 383-405, (1999) · Zbl 0946.68153
[165] H.S. Nguyen, D. Śle¸zak. Approximate reducts and association rules – correspondence and complexity results. In: Skowron et al. [280], pp. 137-145. · Zbl 0954.68129
[166] S.H. Nguyen, Regularity analysis and its applications in data mining. In: Polkowski et al. [241], pp. 289-378. · Zbl 0992.68049
[167] S.H. Nguyen, J. Bazan, A. Skowron, H.S. Nguyen, Layered learning for concept synthesis. In: Peters and Skowron [225], pp. 187-208. · Zbl 1104.68565
[168] S.H. Nguyen, H.S. Nguyen, Some efficient algorithms for rough set methods. In: Sixth International Conference on Information Processing and Management of Uncertainty on Knowledge Based Systems IPMU’1996, Granada, Spain, 1996, vol. III, pp. 1451-1456.
[169] T.T. Nguyen, Eliciting domain knowledge in handwritten digit recognition. In: Pal et al. [189], pp. 762-767.
[170] T.T. Nguyen, A. Skowron, Rough set approach to domain knowledge approximation. In: Wang et al. [350], pp. 221-228. · Zbl 1026.68644
[171] T. Nishino, M. Nagamachi, H. Tanaka, Variable precision Bayesian rough set model and its application to human evaluation data. In: Śle¸zak et al. [300], pp. 294-303. · Zbl 1134.68549
[172] Norsett, K.G.; Lægreid, A.; Midelfart, H.; Yadetie, F.; Erlandsen, S.E.; Falkmer, S.; Gronbech, J.E.; Waldum, H.L.; Komorowski, J.; Sandvik, A.K., Gene expression based classification of gastric carcinoma, Cancer letters, 2, 210, 227-237, (2004)
[173] Novotný, M.; Pawlak, Z., Algebraic theory of independence in information systems, Fundamenta informaticae, 14, 4, 454-476, (1991) · Zbl 0727.68118
[174] Novotný, M.; Pawlak, Z., Algebraic theory of independence in information systems, Fundamenta informaticae, 14, 454-476, (1991) · Zbl 0727.68118
[175] Novotný, M.; Pawlak, Z., On a problem concerning dependence space, Fundamenta informaticae, 16, 275-287, (1992) · Zbl 0762.68059
[176] C.-S. Ong, J.-J. Huang, G.-H. Tzeng, Using rough set theory for detecting the interaction terms in a generalized logit model. In: Tsumoto et al. [337], pp. 624-629. · Zbl 1103.68866
[177] Orłowska, E., Semantics of vague concepts, (), 465-482
[178] E. Orłowska, Rough concept logic. In: Skowron [272], pp. 177-186.
[179] Orłowska, E., Reasoning about vague concepts, Bulletin of the Polish Academy of sciences, mathematics, 35, 643-652, (1987) · Zbl 0641.68160
[180] Orłowska, E., Logic for reasoning about knowledge, Zeitschrift für mathematische logik und grundlagen der Mathematik, 35, 559-572, (1989) · Zbl 0711.03008
[181] Orłowska, E., Kripke semantics for knowledge representation logics, Studia logica, 49, 2, 255-272, (1990) · Zbl 0726.03023
[182] ()
[183] E. Orłowska, Z. Pawlak, Expressive power of knowledge representation system. Technical Report, Institute of Computer Science, Polish Academy of Sciences 432. · Zbl 0541.68070
[184] Orłowska, E.; Pawlak, Z., Representation of non – deterministic information, Theoretical computer science, 29, 27-39, (1984) · Zbl 0537.68098
[185] Pagliani, P., From concept lattices to approximation spaces: algebraic structures of some spaces of partial objects, Fundamenta informaticae, 18, 1-25, (1993) · Zbl 0776.06005
[186] Pagliani, P., Rough sets and Nelson algebras, Fundamenta informaticae, 27, 2-3, 205-219, (1996) · Zbl 0858.68110
[187] Pagliani, P., Pretopologies and dynamic spaces, Fundamenta informaticae, 59, 2-3, 221-239, (2004) · Zbl 1098.68131
[188] Pal, S.K., Soft data mining, computational theory of perceptions, and rough-fuzzy approach, Information sciences, 163, 1-3, 5-12, (2004)
[189] ()
[190] Pal, S.K.; Dasgupta, B.; Mitra, P., Rough self organizing map, Applied intelligence, 21, 289-299, (2004) · Zbl 1101.68825
[191] Pal, S.K.; Mitra, P., Case generation using rough sets with fuzzy representation, IEEE transactions on knowledge and data engineering, 16, 3, 292-300, (2004)
[192] Pal, S.K.; Mitra, P., Pattern recognition algorithms for data mining, (2004), CRC Press Boca Raton, Florida · Zbl 1099.68091
[193] Pal, S.K.; Pedrycz, W.; Skowron, A.; Swiniarski, R., Rough-neuro computing, neurocomputing, 36, (2001), (Special volume)
[194] ()
[195] ()
[196] Pancerz, K.; Suraj, Z., Discovering concurrent models from data tables with the ROSECON system, Fundamenta informaticae, 60, 1-4, 251-268, (2004) · Zbl 1086.68560
[197] Paun, G.; Polkowski, L.; Skowron, A., Rough set approximation of languages, Fundamenta informaticae, 32, 149-162, (1997) · Zbl 0891.68054
[198] Z. Pawlak, Rough real functions and rough controllers. In: Rough Sets and Data Mining - Analysis of Imperfect Data, pp. 139-147. · Zbl 0866.93063
[199] Z. Pawlak, Classification of Objects by Means of Attributes, Reports, vol. 429. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, 1981.
[200] Pawlak, Z., Information systems – theoretical foundations, Information systems, 6, 205-218, (1981) · Zbl 0462.68078
[201] Z. Pawlak, Rough Relations, Reports, vol. 435. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, 1981.
[202] Pawlak, Z., Rough sets, International journal of computer and information sciences, 11, 341-356, (1982) · Zbl 0501.68053
[203] Pawlak, Z., Rough classification, International journal of man-machine studies, 20, 5, 469-483, (1984) · Zbl 0541.68077
[204] Pawlak, Z., Rough logic, Bulletin of the Polish Academy of sciences, technical sciences, 35, 5-6, 253-258, (1987) · Zbl 0645.03019
[205] Pawlak, Z., Decision logic, Bulletin of the EATCS, 44, 201-225, (1991) · Zbl 0744.68118
[206] 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
[207] Pawlak, Z., Concurrent versus sequential – the rough sets perspective, Bulletin of the EATCS, 48, 178-190, (1992) · Zbl 1023.68640
[208] Z. Pawlak, Decision rules, Bayes’ rule and rough sets. In: Skowron et al. [280], pp. 1-9. · Zbl 0948.03026
[209] Z. Pawlak, A treatise on rough sets. In: Peters and Skowron [227], pp. 1-17. · Zbl 1136.68535
[210] Z. Pawlak, A. Skowron, Rough sets: Some extensions, Information Sciences, in press, doi:10.1016/j.ins.2006.06.006. · Zbl 1142.68550
[211] Z. Pawlak, L. Polkowski, A. Skowron, Rough sets and rough logic: a KDD perspective. In: Polkowski et al. [241], pp. 583-646. · Zbl 1009.68159
[212] Pawlak, Z.; Skowron, A., A rough set approach for decision rules generation, (), 114-119
[213] Pawlak, Z.; Skowron, A., Rough membership functions, (), 251-271 · Zbl 0794.03045
[214] Z. Pawlak, A. Skowron, Rough sets and boolean reasoning, Information Sciences, in press, doi:10.1016/j.ins.2006.06.007. · Zbl 1142.68551
[215] Pawlak, Z.; Słowiński, K.; Słowiński, R., Rough classification of patients after highly selective vagotomy for duodenal ulcer, International journal of man-machine studies, 24, 5, 413-433, (1986)
[216] Pawlak, Z.; Wong, S.K.M.; Ziarko, W., Rough sets: probabilistic versus deterministic approach, (), 227-242
[217] Pedrycz, W.; Han, L.; Peters, J.F.; Ramanna, S.; Zhai, R., Calibration of software quality: fuzzy neural and rough neural computing approaches, Neurocomputing, 36, 1-4, 149-170, (2001) · Zbl 1003.68635
[218] Peters, J.; Skowron, A., A rough set approach to reasoning about data, International journal of intelligent systems, vol. 16, 1, (2001), (Special issue) · Zbl 0967.00024
[219] J.F. Peters, Rough ethology: Towards a biologically-inspired study of collective behavior in intelligent systems with approximation spaces. In: Peters and Skowron [226], pp. 153-174. · Zbl 1116.68574
[220] Peters, J.F.; Han, L.; Ramanna, S., Rough neural computing in signal analysis, Computational intelligence: an international journal, 17, 3, 493-513, (2001)
[221] Peters, J.F.; Henry, C., Reinforcement learning with approximation spaces, Fundamenta informaticae, 71, 1-27, (2006)
[222] Peters, J.F.; Ramanna, S., Towards a software change classification system: A rough set approach, Software quality journal, 11, 2, 121-147, (2003)
[223] J.F. Peters, S. Ramanna, Approximation space for software models. In: Peters et al. [228], pp. 338-355. · Zbl 1104.68770
[224] J.F. Peters, S. Ramanna, M.S. Szczuka, Towards a line-crawling robot obstacle classification system: a rough set approach. In: Wang et al. [350], pp. 303-307. · Zbl 1026.68647
[225] ()
[226] ()
[227] ()
[228] ()
[229] Peters, J.F.; Skowron, A.; Suraj, Z., An application of rough set methods in control design, Fundamenta informaticae, 43, 1-4, 269-290, (2000) · Zbl 0971.93052
[230] Peters, J.F.; Skowron, A.; Synak, P.; Ramanna, S., Rough sets and information granulation, (), 370-377 · Zbl 1037.68753
[231] Peters, J.F.; Suraj, Z.; Shan, S.; Ramanna, S.; Pedrycz, W.; Pizzi, N.J., Classification of meteorological volumetric radar data using rough set methods, Pattern recognition letters, 24, 6, 911-920, (2003)
[232] J.F. Peters, M.S. Szczuka, Rough neurocomputing: A survey of basic models of neurocomputation. In: Alpigini et al. [1], pp. 308-315. · Zbl 1013.68521
[233] J.F. Peters, K. Ziaei, S. Ramanna, Approximate time rough control: Concepts and application to satellite attitude control. In: Polkowski and Skowron [243], pp. 491-498.
[234] Pindur, R.; Susmaga, R.; Stefanowski, J., Hyperplane aggregation of dominance decision rules, Fundamenta informaticae, 61, 2, 117-137, (2004) · Zbl 1083.68121
[235] L. Polkowski, On convergence of rough sets. In: Słowiński [305], pp. 305-311. · Zbl 1012.68218
[236] Polkowski, L., On fractal dimension in information systems. toward exact sets in infinite information systems, Fundamenta informaticae, 50, 3-4, 305-314, (2002) · Zbl 1012.68218
[237] Polkowski, L., Rough sets: mathematical foundations, Advances in soft computing, (2002), Physica-Verlag Heidelberg
[238] 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
[239] Polkowski, L., A note on 3-valued rough logic accepting decision rules, Fundamenta informaticae, 61, 1, 37-45, (2004) · Zbl 1083.68116
[240] L. Polkowski, Toward rough set foundations. mereological approach. In: Tsumoto et al. [337], pp. 8-25. (plenary talk). · Zbl 1103.03049
[241] ()
[242] 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
[243] ()
[244] ()
[245] ()
[246] L. Polkowski, A. Skowron, Rough mereology in information systems. a case study: Qualitative spatial reasoning. In: Polkowski et al. [241], pp. 89-135. · Zbl 0992.68198
[247] 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)
[248] Pomykała, J.; Pomykała, J.A., The stone algebra of rough sets, Bulletin of the Polish Academy of sciences, mathematics, 36, 495-508, (1988) · Zbl 0786.04008
[249] G.-F. Qiu, W.-X. Zhang, W.-Z. Wu, Characterizations of attributes in generalized approximation representation spaces. In: Śle¸zak et al. [300], pp. 84-93.
[250] Quafafou, M.; Boussouf, M., Generalized rough sets based feature selection, Intelligent data analysis, 4, 1, 3-17, (2000) · Zbl 1055.68560
[251] Radzikowska, A.; Kerre, E.E., A comparative study of fuzzy rough sets, Fuzzy sets and systems, 126, 2, 137-155, (2002) · Zbl 1004.03043
[252] A. Radzikowska, E.E. Kerre, Fuzzy rough sets based on residuated lattices. In: Peters et al. [228], pp. 278-296. · Zbl 1109.68118
[253] Ras, Z.W., Reducts-driven query answering for distributed autonomous knowledge systems, International journal of intelligent systems, 17, 2, 113-124, (2002) · Zbl 1012.68014
[254] Z.W. Ras, A. Dardzinska, Collaborative query processing in DKS controlled by reducts. In: Alpigini et al. [1], pp. 189-196. · Zbl 1013.68573
[255] Rasiowa, H., Axiomatization and completeness of uncountably valued approximation logic, Studia logica, 53, 1, 137-160, (1994) · Zbl 0787.03015
[256] Rasiowa, H.; Skowron, A., Approximation logic, (), 123-139
[257] H. Rasiowa, A. Skowron, Rough concept logic. In: Skowron [272], pp. 288-297. · Zbl 0611.68006
[258] C. Rauszer, An equivalence between indiscernibility relations in information systems and a fragment of intuitionistic logic. In: Skowron [272], pp. 298-317. · Zbl 0609.68076
[259] Rauszer, C., An equivalence between theory of functional dependence and a fragment of intuitionistic logic, Bulletin of the Polish Academy of sciences, mathematics, 33, 571-579, (1985) · Zbl 0583.68054
[260] Rauszer, C., Logic for information systems, Fundamenta informaticae, 16, 371-382, (1992) · Zbl 0768.68199
[261] Rauszer, C., Knowledge representation systems for groups of agents, (), 217-238
[262] Read, S., Thinking about logic: an introduction to the philosophy of logic, (1994), Oxford University Press Oxford, New York
[263] Rissanen, J., Modeling by shortes data description, Automatica, 14, 465-471, (1978) · Zbl 0418.93079
[264] Rissanen, J., Minimum-description-length principle, (), 523-527
[265] Roy, A.; Pal, S.K., Fuzzy discretization of feature space for a rough set classifier, Pattern recognition letters, 24, 6, 895-902, (2003) · Zbl 1053.68091
[266] Russell, B., The principles of mathematics, (1903), George Allen & Unwin Ltd. London, Great Britain, (2nd Edition in 1937) · JFM 34.0062.14
[267] Russell, B., Vagueness, The Australian journal of psychology and philosophy, 1, 84-92, (1923)
[268] Russell, B., An inquiry into meaning and truth, (1940), George Allen & Unwin Ltd. and W.W. Norton, London and New York
[269] Sever, H.; Raghavan, V.V.; Johnsten, T.D., The status of research on rough sets for knowledge discovery in databases, (), 673-680
[270] Shan, N.; Ziarko, W., An incremental learning algorithm for constructing decision rules, (), 326-334 · Zbl 0941.68698
[271] Simons, P., A study in ontology, (1987), Oxford University Press Oxford, UK
[272] ()
[273] Skowron, A., Boolean reasoning for decision rules generation, (), 295-305
[274] Skowron, A., Extracting laws from decision tables, Computational intelligence: an international journal, 11, 371-388, (1995)
[275] Skowron, A., Rough sets in KDD - plenary talk, (), 1-14
[276] Skowron, A., Rough sets and Boolean reasoning, (), 95-124 · Zbl 0986.68143
[277] A. Skowron, Approximate reasoning in distributed environments. In: Zhong and Liu [374], pp. 433-474.
[278] Skowron, A., Rough sets and vague concepts, Fundamenta informaticae, 64, 1-4, 417-431, (2005) · Zbl 1102.68131
[279] Skowron, A.; Grzymała-Busse, J.W., From rough set theory to evidence theory, (), 193-236
[280] A. Skowron, S. Ohsuga, N. Zhong (Eds.). Proceedings of the 7th International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing (RSFDGrC’99), Yamaguchi, November 9-11, 1999, Lecture Notes in Artificial Intelligence, vol. 1711, Springer-Verlag, Heidelberg, 1999.
[281] Skowron, A.; Pal, S.K., Rough sets, pattern recognition and data mining, Pattern recognition letters, vol. 24, 6, (2003), (Special volume)
[282] Skowron, A.; Pawlak, Z.; Komorowski, J.; Polkowski, L., A rough set perspective on data and knowledge, (), 134-149
[283] A. Skowron, J. Peters, Rough sets: trends and challenges. In: Wang et al. [350], pp. 25-34 (plenary talk). · Zbl 1026.68653
[284] A. Skowron, C. Rauszer, The discernibility matrices and functions in information systems. In: Słowiński [305], pp. 331-362.
[285] Skowron, A.; Stepaniuk, J., Tolerance approximation spaces, Fundamenta informaticae, 27, 2-3, 245-253, (1996) · Zbl 0868.68103
[286] A. Skowron, J. Stepaniuk, Information granules and rough-neural computing. In: Pal et al. [194], pp. 43-84. · Zbl 0969.68078
[287] A. Skowron, J. Stepaniuk, Ontological framework for approximation. In: Śle¸zak et al. [300], pp. 718-727. · Zbl 1134.68514
[288] Skowron, A.; Stepaniuk, J.; Peters, J.F., Rough sets and infomorphisms: towards approximation of relations in distributed environments, Fundamenta informaticae, 54, 1-2, 263-277, (2003) · Zbl 1111.68706
[289] A. Skowron, R. Swiniarski, Rough sets and higher order vagueness. In: Śle¸zak et al. [300], pp. 33-42. · Zbl 1134.68558
[290] A. Skowron, R. Swiniarski, P. Synak, Approximation spaces and information granulation. In: Peters and Skowron [226], pp. 175-189. · Zbl 1116.68602
[291] Skowron, A.; Synak, P., Complex patterns, Fundamenta informaticae, 60, 1-4, 351-366, (2004) · Zbl 1083.68122
[292] Skowron, A.; Synak, P., Reasoning in information maps, Fundamenta informaticae, 59, 2-3, 241-259, (2004) · Zbl 1098.68132
[293] (), Available from:
[294] D. Śle¸zak, Approximate reducts in decision tables. In: Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU’1996. Granada, Spain, 1996, vol. III, pp. 1159-1164.
[295] D. Śle¸zak, Approximate Markov boundaries and Bayesian networks. In: Inuiguchi et al. [97], pp. 109-121.
[296] Śle¸zak, D., Normalized decision functions and measures for inconsistent decision tables analysis, Fundamenta informaticae, 44, 291-319, (2000) · Zbl 0970.68171
[297] D. Śle¸zak, Various approaches to reasoning with frequency-based decision reducts: A survey. In: Polkowski et al. [241], pp. 235-285.
[298] Śle¸zak, D., Approximate entropy reducts, Fundamenta informaticae, 53, 365-387, (2002) · Zbl 1092.68676
[299] D. Śle¸zak, Rough sets and Bayes factor. In: Peters and Skowron [226], pp. 202-229.
[300] ()
[301] ()
[302] 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
[303] Słowiński, K.; Słowiński, R.; Stefanowski, J., Rough sets approach to analysis of data from peritoneal lavage in acute pancreatitis, Medical informatics, 13, 3, 143-159, (1998)
[304] K. Słowiński, J. Stefanowski, Medical information systems – problems with analysis and way of solution. In: Pal and Skowron [195], pp. 301-315.
[305] ()
[306] R. Słowiński, J. Stefanowski (Eds.). Special issue: Proceedings of the First International Workshop on Rough Sets: State of the Art and Perspectives, Kiekrz, Poznań, Poland, September 2-4 (1992). In: Foundations of Computing and Decision Sciences, vol. 18(3-4). 1993.
[307] Słowiński, R.; Stefanowski, J., Rough set reasoning about uncertain data, Fundamenta informaticae, 27, 229-244, (1996) · Zbl 0854.68098
[308] Słowiński, R.; Stefanowski, J.; Greco, S.; Matarazzo, B., Rough sets processing of inconsistent information, Control and cybernetics, 29, 379-404, (2000) · Zbl 1030.90045
[309] Słowiński, R.; Stefanowski, J.; Siwiński, D., Application of rule induction and rough sets to verification of magnetic resonance diagnosis, Fundamenta informaticae, 53, 345-363, (2002) · Zbl 1045.68918
[310] Słowiński, R.; Vanderpooten, D., Similarity relation as a basis for rough approximations, (), 17-33
[311] Smith, B., Formal ontology, common sense and cognitive science, International journal of human-computer studies, 43, 641-667, (1995)
[312] Stefanowski, J.; Tsoukiàs, A., Incomplete information tables and rough classification, Computational intelligence, 17, 3, 545-566, (2001)
[313] Stefanowski, J.; Wilk, S., Minimizing business credit risk by means of approach integrating decision rules and case based learning, Journal of intelligent systems in accounting, finance and management, 10, 97-114, (2001)
[314] Stell, J.G., Boolean connection algebras: A new approach to the region-connection calculus, Artificial intelligence, 122, 111-136, (2000) · Zbl 0948.68142
[315] J. Stepaniuk, Approximation spaces, reducts and representatives. In: Polkowski and Skowron [245], pp. 109-126. · Zbl 0943.68158
[316] J. Stepaniuk, Knowledge discovery by application of rough set models. In: Polkowski et al. [241], pp. 137-233. · Zbl 0992.68199
[317] K. Sugihara, Y. Maeda, H. Tanaka, Interval evaluation by AHP with rough set concept. In: Skowron et al. [280], pp. 375-381.
[318] Z. Suraj, Rough set methods for the synthesis and analysis of concurrent processes. In: Polkowski et al. [241], pp. 379-488. · Zbl 0992.68201
[319] J. Swift. Gulliver’s Travels into Several Remote Nations of the World. (ananymous publisher), London, M, DCC, XXVI, 1726.
[320] R. Swiniarski, Rough sets and Bayesian methods applied to cancer detection. In: Polkowski and Skowron [243], pp. 609-616.
[321] R. Swiniarski, Rough sets and principal component analysis and their applications. data model building and classification. In: Pal and Skowron [195], pp. 275-300.
[322] R. Swiniarski, An application of rough sets and Haar wavelets to face recognition. In: Ziarko and Yao [380], pp. 561-568. · Zbl 1013.68261
[323] R. Swiniarski, L. Hargis, A new halftoning method based on error diffusion with rough set filterin. In: Polkowski and Skowron [245], pp. 336-342.
[324] Swiniarski, R.; Hargis, L., Rough sets as a front end of neural networks texture classifiers, Neurocomputing, 36, 1-4, 85-103, (2001) · Zbl 1003.68642
[325] R.W. Swiniarski, A. Skowron, Independent component analysis, principal component analysis and rough sets in face recognition. In: Peters and Skowron [225], pp. 392-404. · Zbl 1104.68772
[326] Szczuka, M., Refining classifiers with neural networks, International journal of intelligent systems, 16, 39-55, (2001) · Zbl 0969.68140
[327] Szczuka, M.; Wojdyłło, P., Neuro-wavelet classifiers for EEG signals based on rough set methods, Neurocomputing, 36, 103-122, (2001) · Zbl 1003.68640
[328] H. Tanaka, Dual mathematical models based on rough approximations in data analysis. In: Wang et al. [350], pp. 52-59. · Zbl 1026.68658
[329] Tanaka, H.; Lee, H., Interval regression analysis with polynomials and its similarity to rough sets concept, Fundamenta informaticae, 37, 1-2, 71-87, (1999) · Zbl 0930.68043
[330] Tarski, A., Logic, semantics, metamathematics, (1983), Oxford University Press Oxford, UK, [translated by J.H. Woodger]
[331] ()
[332] Tsumoto, S., Automated induction of medical expert system rules from clinical databases based on rough set theory, Information sciences, 112, 67-84, (1998)
[333] S. Tsumoto, Empirical induction on medical system expert rules based on rough set theory. In: Polkowski and Skowron [243], pp. 307-323.
[334] Tsumoto, S., Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model, Information sciences, 162, 2, 65-80, (2004)
[335] Tsumoto, S.; Hirano, S., Automated discovery of chronological patterns in long time-series medical datasets, International journal of intelligent systems, 20, 6, 737-757, (2005)
[336] S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka, A. Nakamura (Eds.). Proceedings of the The Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, November 6-8, University of Tokyo, Japan. The University of Tokyo, Tokyo, 1996.
[337] ()
[338] Tsumoto, S.; Tanaka, H., PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods, Computational intelligence: an international journal, 11, 389-405, (1995)
[339] Tsumoto, S.; Ziarko, W., The application of rough sets-based data mining technique to differential diagnosis of meningoenchepahlitis, (), 438-447
[340] Vakarelov, D., A modal logic for similarity relations in pawlak knowledge representation systems, Fundamenta informaticae, 15, 1, 61-79, (1991) · Zbl 0737.68078
[341] Vakarelov, D., Modal logics for knowledge representation systems, Theoretical computer science, 90, 2, 433-456, (1991) · Zbl 0755.68131
[342] Vakarelov, D., A duality between pawlak’s knowledge representation systems and bi-consequence systems, Studia logica, 55, 1, 205-228, (1995) · Zbl 0839.68098
[343] D. Vakarelov, A modal characterization of indiscernibility and similarity relations in Pawlak’s information systems. In: Śle¸zak et al. [300], pp. 12-22 (plenary talk). · Zbl 1134.68505
[344] J.J. Valdés, A.J. Barton, Relevant attribute discovery in high dimensional data based on rough sets and unsupervised classification: Application to leukemia gene expression. In: Śle¸zak et al. [301], pp. 362-371.
[345] Varzi, A.C., Change, temporal parts, and the argument from vagueness, Dialectica, 59, 4, 485-498, (2005)
[346] A. Vitória, A framework for reasoning with rough sets. Licentiate Thesis, Linköping University 2004. In: Peters and Skowron [227], pp. 178-276.
[347] Vopenka, P., Mathematics in the alternative set theory, (1979), Teubner Leipzig · Zbl 0499.03042
[348] Wakulicz-Deja, A.; Paszek, P., Diagnose progressive encephalopathy applying the rough set theory, International journal of medical informatics, 46, 2, 119-127, (1997)
[349] Wakulicz-Deja, A.; Paszek, P., Applying rough set theory to multi stage medical diagnosing, Fundamenta informaticae, 54, 4, 387-408, (2003) · Zbl 1039.92023
[350] ()
[351] Wang, J.; Jia, C.; Zhao, K., Investigation on AQ11, ID3 and the principle of discernibility matrix, Journal of computer science and technology, 16, 1, 1-12, (2001) · Zbl 0974.68175
[352] Wang, J.; Ju, W., Reduction algorithms based on discernibility matrix: the ordered attributes method, Journal of computer science and technology, 16, 6, 489-504, (2001) · Zbl 1014.68160
[353] A. Wasilewska, Topological rough algebras. In: Rough Sets and Data Mining - Analysis of Imperfect Data. pp. 411-425. · Zbl 0860.03042
[354] Wasilewska, A.; Vigneron, L., Rough equality algebras, (), 26-30
[355] A. Wasilewska, L. Vigneron, Rough algebras and automated deduction. In: Polkowski and Skowron [244], pp. 261-275. · Zbl 0926.03081
[356] Wieczorkowska, A.; Wróblewski, J.; Synak, P.; Śle¸zak, D., Application of temporal descriptors to musical instrument sound recognition, Journal of intelligent information systems, 21, 1, 71-93, (2003)
[357] A. Wojna, Analogy based reasoning in classifier construction. In: Peters and Skowron [227], pp. 277-374. · Zbl 1136.68508
[358] Wong, S.K.M.; Ziarko, W., Comparison of the probabilistic approximate classification and the fuzzy model, Fuzzy sets and systems, 21, 357-362, (1987) · Zbl 0618.60002
[359] Wróblewski, J., Theoretical foundations of order-based genetic algorithms, Fundamenta informaticae, 28, 423-430, (1996) · Zbl 0866.68043
[360] J. Wróblewski, Genetic algorithms in decomposition and classification problem. In: Polkowski and Skowron [245], pp. 471-487.
[361] J. Wróblewski, Adaptive aspects of combining approximation spaces. In: Pal et al. [194], pp. 139-156.
[362] Wu, W.-Z.; Mi, J.-S.; Zhang, W.-X., Generalized fuzzy rough sets, Information sciences, 151, 263-282, (2003) · Zbl 1019.03037
[363] Wu, W.-Z.; Zhang, W.-X., Constructive and axiomatic approaches of fuzzy approximation operators, Information sciences, 159, 2, 233-254, (2004) · Zbl 1071.68095
[364] Y.Y. Yao, Generalized rough set models. In: Polkowski and Skowron [244], pp. 286-318. · Zbl 0946.68137
[365] Yao, Y.Y., Information granulation and rough set approximation, International journal of intelligent systems, 16, 87-104, (2001) · Zbl 0969.68079
[366] Y.Y. Yao, On generalizing rough set theory. In: Wang et al. [350], pp. 44-51. · Zbl 1026.68669
[367] Yao, Y.Y., Probabilistic approaches to rough sets, Expert systems, 20, 287-297, (2003)
[368] Yao, Y.Y.; Lingras, P., Interpretation of belief functions in the theory of rough sets, Information sciences, 104, 1-2, 81-106, (1998) · Zbl 0923.04007
[369] Y.Y. Yao, S.K.M. Wong, T.Y. Lin, A review of rough set models. In: Rough Sets and Data Mining - Analysis of Imperfect Data, pp. 47-75. · Zbl 0861.68101
[370] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
[371] Zhang, W.-X.; Mi, J.-S.; Wu, W.-Z., Approaches to knowledge reductions in inconsistent systems, International journal of intelligent systtems, 18, 9, 989-1000, (2003) · Zbl 1069.68606
[372] Zheng, Z.; Wang, G., RRIA: A rough set and rule tree based incremental knowledge acquisition algorithm, Fundamenta informaticae, 59, 2-3, 299-313, (2004) · Zbl 1098.68711
[373] Zhong, N.; Dong, J.; Ohsuga, S., Meningitis data mining by cooperatively using GDT-RS and RSBR, Pattern recognition letters, 24, 6, 887-894, (2003) · Zbl 1053.68099
[374] ()
[375] Ziarko, W., Variable precision rough set model, Journal of computer and system sciences, 46, 39-59, (1993) · Zbl 0764.68162
[376] ()
[377] Ziarko, W., Computational intelligence, An international journal, 11, 2, (1995), Special issue
[378] Ziarko, W., Fundamenta informaticae, 27, 2-3, (1996), Special issue
[379] Ziarko, W., Probabilistic decision tables in the variable precision rough set model, Computational intelligence, 17, 593-603, (2001)
[380] ()
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.