Skip to main content

Some Issues on Rough Sets

  • Conference paper
Transactions on Rough Sets I

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3100))

Abstract

The aim of this paper is to give rudiments of rough set theory and present some recent research directions proposed by the author.

Rough set theory is a new mathematical approach to imperfect knowledge.

The problem of imperfect knowledge has been tackled for a long time by philosophers, logicians and mathematicians. Recently it became also a crucial issue for computer scientists, particularly in the area of artificial intelligence. There are many approaches to the problem of how to understand and manipulate imperfect knowledge. The most successful one is, no doubt, the fuzzy set theory proposed by Lotfi Zadeh [1].

Rough set theory proposed by the author in [2] presents still another attempt to this problem. This theory has attracted attention of many researchers and practitioners all over the world, who have contributed essentially to its development and applications. Rough set theory overlaps with many other theories. However we will refrain to discuss these connections here. Despite this, rough set theory may be considered as an independent discipline in its own right.

Rough set theory has found many interesting applications. The rough set approach seems to be of fundamental importance to AI and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, inductive reasoning and pattern recognition.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Polkowski, L., Skowron, A., Zẏtkow, J.: Rough foundations for rough sets. In: [40], pp.55–58

    Google Scholar 

  5. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  6. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Machine Intelligence & Soft-Computing, vol. IV, pp. 17–33. Bookwrights, Raleigh (1997)

    Google Scholar 

  8. Słowiński, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Data and Knowledge Engineering 12(2), 331–336 (2000)

    Article  Google Scholar 

  9. Stepaniuk, J.: Knowledge discovery by application of rough set models. In: [26], pp. 137–233

    Google Scholar 

  10. Skowron, A.: Toward intelligent systems: Calculi of information granules. Bulletin of the International Rough Set Society 5, 9–30 (2001)

    Google Scholar 

  11. Greco, A., Matarazzo, B., Słowiński, R.: Rough approximation by dominance relations. International Journal of Intelligent Systems 17, 153–171 (2002)

    Article  MATH  Google Scholar 

  12. Polkowski, L. (ed.): Rough Sets: Mathematical Foundations. Advances in Soft Computing. Physica-Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  13. Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing. In: [30], pp. 43–84

    Google Scholar 

  14. Skowron, A.: Approximation spaces in rough neurocomputing. In: [29], pp. 13–22

    Google Scholar 

  15. Wróblewski, J.: Adaptive aspects of combining approximation spaces. In: [30], pp. 139–156

    Google Scholar 

  16. Yao, Y.Y.: Informaton granulation and approximation in a decision-theoretical model of rough sets. In: [30], pp. 491–520

    Google Scholar 

  17. Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation (submitted). In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 116–126. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  19. Słowiński, R. (ed.): Intelligent Decision Support - Handbook of Applications and Advances of the Rough Sets Theory. System Theory, Knowledge Engineering and Problem Solving, vol. 11. Kluwer Academic Publishers, Dordrecht (1992)

    MATH  Google Scholar 

  20. Lin, T.Y., Cercone, N. (eds.): Rough Sets and Data Mining - Analysis of Imperfect Data. Kluwer Academic Publishers, Boston (1997)

    Google Scholar 

  21. Orłowska, E. (ed.): Incomplete Information: Rough Set Analysis. Studies in Fuzziness and Soft Computing, vol. 13. Springer, Heidelberg (1997)

    Google Scholar 

  22. Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 1: Methodology and Applications. Studies in Fuzziness and Soft Computing, vol. 18. Physica-Verlag, Heidelberg (1998)

    MATH  Google Scholar 

  23. Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems. Studies in Fuzziness and Soft Computing, vol. 19. Physica-Verlag, Heidelberg (1998)

    MATH  Google Scholar 

  24. Pal, S.K., Skowron, A. (eds.): Rough Fuzzy Hybridization: A New Trend in Decision-Making. Springer, Singapore (1999)

    MATH  Google Scholar 

  25. Duentsch, I., Gediga, G.: Rough set data analysis: A road to non-invasive knowledge discovery. Methodos Publishers, Bangor (2000)

    Google Scholar 

  26. Polkowski, L., Lin, T.Y., Tsumoto, S. (eds.): Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems. Studies in Fuzziness and Soft Computing, vol. 56. Springer, Heidelberg (2000)

    Google Scholar 

  27. Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.): Rough Sets, Granular Computing and Data Mining. Studies in Fuzziness and Soft Computing. Physica-Verlag, Heidelberg (2001)

    Google Scholar 

  28. Demri, S., Orłowska, E. (eds.): Incomplete Information: Structure, Inference, Complexity. Monographs in Theoretical Computer Science. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  29. Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.): Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol. 125. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  30. Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer, Heidelberg (2003)

    Google Scholar 

  31. Słowiński, R., Stefanowski, J. (eds.): Special issue: Proceedings of the First International Workshop on Rough Sets: State of the Art and Perspectives, Kiekrz, Poznań, Poland, September 2–4. Foundations of Computing and Decision Sciences, vol. 18(3-4) (1993)

    Google Scholar 

  32. Ziarko, W. (ed.): Special issue. Computational Intelligence: An International Journal, vol. 11(2) (1995)

    Google Scholar 

  33. Ziarko, W. (ed.): Special issue. Fundamenta Informaticae, vol. 27(2-3) (1996)

    Google Scholar 

  34. Lin, T.Y. (ed.): Special issue. Journal of the Intelligent Automation and Soft Computing, vol. 2(2) (1996)

    Google Scholar 

  35. Peters, J., Skowron, A. (eds.): Special issue on a rough set approach to reasoning about data. International Journal of Intelligent Systems, vol. 16(1) (2001)

    Google Scholar 

  36. Cercone, N., Skowron, A., Zhong, N. (eds.): (Special issue). Computational Intelligence, vol. 17(3) (2001)

    Google Scholar 

  37. Pal, S.K., Pedrycz, W., Skowron, A., Swiniarski, R. (eds.): Special volume: Roughneuro computing. Neurocomputing, vol. 36 (2001)

    Google Scholar 

  38. Skowron, A., Pal, S.K. (eds.): Special volume: Rough sets, pattern recognition and data mining. Pattern Recognition Letters, vol. 24(6) (2003)

    Google Scholar 

  39. Ziarko, W. (ed.): Rough Sets, Fuzzy Sets and Knowledge Discovery: Proceedings of the Second International Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Banff, Alberta, Canada, October 12–15. Workshops in Computing. Springer–Verlag & British Computer Society, London, Berlin (1994)

    Google Scholar 

  40. Lin, T.Y., Wildberger, A.M. (eds.): Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery. Simulation Councils, Inc., San Diego (1995)

    Google Scholar 

  41. Tsumoto, S., Kobayashi, S., Yokomori, T., Tanaka, H., Nakamura, A. (eds.): Proceedings of the The Fourth Internal Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, November 6-8. University of Tokyo, Japan, Tokyo (1996)

    Google Scholar 

  42. Polkowski, L., Skowron, A. (eds.): RSCTC 1998. LNCS (LNAI), vol. 1424. Springer, Heidelberg (1998)

    Google Scholar 

  43. Zhong, N., Skowron, A., Ohsuga, S. (eds.): RSFDGrC 1999. LNCS (LNAI), vol. 1711. Springer, Heidelberg (1999)

    Google Scholar 

  44. Ziarko, W., Yao, Y. (eds.): RSCTC 2000. LNCS (LNAI), vol. 2005. Springer, Heidelberg (2001)

    Google Scholar 

  45. Hirano, S., Inuiguchi, M., Tsumoto, S. (eds.): Proceedings of International Workshop on Rough Set Theory and Granular Computing (RSTGC 2001), Matsue, Shimane, Japan, May 20-22. Bulletin of the International Rough Set Society, vol. 5(1-2). International Rough Set Society, Matsue (2001)

    Google Scholar 

  46. Terano, T., Nishida, T., Namatame, A., Tsumoto, S., Ohsawa, Y., Washio, T. (eds.): JSAI-WS 2001. LNCS (LNAI), vol. 2253. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  47. Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.): RSCTC 2002. LNCS (LNAI), vol. 2475. Springer, Heidelberg (2002)

    Google Scholar 

  48. Skowron, A., Szczuka, M. (eds.): Proceedings of the Workshop on Rough Sets in Knowledge Discovery and Soft Computing at ETAPS 2003 (RSKD 2003), April 12-13. Electronic Notes in Computer Science, vol. 82(4). Elsevier, Amsterdam (2003)

    Google Scholar 

  49. Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.): RSFDGrC 2003. LNCS (LNAI), vol. 2639. Springer, Heidelberg (2003)

    Google Scholar 

  50. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: [24], pp. 3–98

    Google Scholar 

  51. Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets and rough logic: A KDD perspective. In: [26], pp. 583–646

    Google Scholar 

  52. Skowron, A., Pawlak, Z., Komorowski, J., Polkowski, L.: A rough set perspective on data and knowledge. In: Kloesgen, W., Żytkow, J. (eds.) Handbook of KDD, pp. 134–149. Oxford University Press, Oxford (2002)

    Google Scholar 

  53. Pawlak, Z., Polkowski, L., Skowron, A.: Rough set theory. In: Wah, B. (ed.) Ency-Clopedia Of Computer Science and Engineering, Wiley, New York (2004)

    Google Scholar 

  54. Cantor, G.: Grundlagen einer allgemeinen Mannigfaltigkeitslehre, Leipzig, Germany (1883)

    Google Scholar 

  55. Russell, B.: The Principles of Mathematics. George Allen & Unwin Ltd., London (1903)

    MATH  Google Scholar 

  56. Russell, B.: Vagueness. The Australasian Journal of Psychology and Philosophy 1, 84–92 (1923)

    Article  Google Scholar 

  57. Black, M.: Vagueness: An exercise in logical analysis. Philosophy of Science 4(4), 427–455 (1937)

    Article  Google Scholar 

  58. Hempel, C.G.: Vagueness and logic. Philosophy of Science 6, 163–180 (1939)

    Article  Google Scholar 

  59. Fine, K.: Vagueness, truth and logic. Synthese 30, 265–300 (1975)

    Article  MATH  Google Scholar 

  60. Keefe, R., Smith, P.: Vagueness: A Reader. MIT Press, Cambridge (1999)

    Google Scholar 

  61. Keefe, R.: Theories of Vagueness. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  62. Frege, G.: Grundgesetzen der Arithmetik, 2. Verlag von Herman Pohle, Jena (1903)

    Google Scholar 

  63. Read, S.: Thinking about Logic - An Introduction to Philosophy of Logic. Oxford University Press, Oxford (1995)

    Google Scholar 

  64. Leśniewski, S.: Grungzüge eines neuen systems der grundlagen der mathematik. Fundamenta Matematicae 14, 1–81 (1929)

    MATH  Google Scholar 

  65. Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, New York, NY, pp. 251–271. John Wiley & Sons, Chichester (1994)

    Google Scholar 

  66. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: [19], pp. 331–362

    Google Scholar 

  67. Berthold, M., Hand, D.J.: Intelligent Data Analysis. An Introduction. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  68. Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. John Wiley and Sons, Inc., New York (1992)

    MATH  Google Scholar 

  69. Pawlak, Z.: Rough sets and decision algorithms. In: [44], pp. 30–45

    Google Scholar 

  70. Pawlak, Z. In: pursuit of patterns in data reasoning from data – the rough set way. In: [47], pp. 1–9

    Google Scholar 

  71. Pawlak, Z.: Probability, truth and flow graphs. In: [48], pp. 1–9

    Google Scholar 

  72. Wong, S., Ziarko, W.: Algebraic versus probabilistic independence in decision theory. In: Ras, Z.W., Zemankova, M. (eds.) Proceedings of the ACM SIGART First International Symposium on Methodologies for Intelligent Systems Knoxville (ISMIS 1986), Tennessee, USA, October 22-24, pp. 207–212. ACM SIGART, USA (1986)

    Chapter  Google Scholar 

  73. Wong, S., Ziarko, W.: On learning and evaluation of decision rules in the context of rough sets. In: Ras, Z.W., Zemankova, M. (eds.) Proceedings of the ACM SIGART First International Symposium on Methodologies for Intelligent Systems Knoxville (ISMIS 1986), Tennessee, USA, October 22-24, pp. 308–324. ACM SIGART, USA (1986)

    Chapter  Google Scholar 

  74. Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: Probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29(1), 81–95 (1988)

    Article  MATH  Google Scholar 

  75. Yamauchi, Y., Mukaidono, M.: Probabilistic inference and bayeasian theorem based on logical implication. In: [43], pp. 334–342

    Google Scholar 

  76. Intan, R., Y. Y. Yao, M.M.: Generalization of rough sets with alpha-coverings of the universe induced by conditional probability relations. In: [46], pp. 311–315

    Google Scholar 

  77. Ślȩzak, D.: Approximate decision reducts (in Polish). PhD thesis, Warsaw University, Warsaw, Poland (2002)

    Google Scholar 

  78. Ślȩzak, D.: Approximate bayesian networks. In: Bouchon-Meunier, B., Gutierrez- Rios, J., Magdalena, L., Yager, R. (eds.) Technologies for Constructing Intelligent Systems 2: Tools. Studies in Fuzziness and Soft Computing, vol. 90, pp. 313–326. Springer, Heidelberg (2002)

    Google Scholar 

  79. Ślȩzak, D., Wróblewski, J.: Approximate bayesian network classifiers. In: [47], pp. 365–372

    Google Scholar 

  80. Yao, Y.Y.: Information granulation and approximation. In: [30], pp. 491–516

    Google Scholar 

  81. Ślȩzak, D.: Approximate markov boundaries and bayesian networks: Rough set approach. In: [29], pp. 109–121

    Google Scholar 

  82. Ślȩzak, D., Ziarko, W.: Attribute reduction in the bayesian version of variable precision rough set model. In: [48]

    Google Scholar 

  83. Ślȩzak, D., Ziarko, W.: Variable precision bayesian rough set model. In: [49], pp. 312–315

    Google Scholar 

  84. Wong, S.K.M., Wu, D.: A common framework for rough sets, databases, and bayesian networks. In: [49], pp. 99–103

    Google Scholar 

  85. Ślȩzak, D.: The rough bayesian model for distributed decision systems (submitted). In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 384–393. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  86. Swinburne, R.: Bayes Theorem. Proceedings of the British Academy, vol. 113. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  87. Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Chichester (1994)

    Book  MATH  Google Scholar 

  88. Łukasiewicz, J.: Die logischen grundlagen der wahrscheinilchkeitsrechnung, Kraków 1913. In: Borkowski, L. (ed.) Jan Łukasiewicz - Selected Works. North Holland Publishing Company, Polish Scientific Publishers, Amstardam, London, Warsaw (1970)

    Google Scholar 

  89. Adams, E.W.: The Logic of Conditionals. An Application of Probability to Deductive Logic. D. Reidel Publishing Company, Dordrecht (1975)

    MATH  Google Scholar 

  90. Grzymała-Busse, J.W.: LERS - a system for learning from examples based on rough sets. In: [19], pp. 3–18

    Google Scholar 

  91. Skowron, A.: Boolean reasoning for decision rules generation. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 295–305. Springer, Heidelberg (1993)

    Google Scholar 

  92. Pawlak, Z., Skowron, A.: A rough set approach for decision rules generation. In: Thirteenth International Joint Conference on Artificial Intelligence (IJCAI 1993), Chambéry, France, pp. 114–119. Morgan Kaufmann, San Francisco (1993)

    Google Scholar 

  93. Shan, N., Ziarko, W.: An incremental learning algorithm for constructing decision rules. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Berlin, Germany, pp. 326–334. Springer, Heidelberg (1994)

    Google Scholar 

  94. Nguyen, H.S.: Discretization of Real Value Attributes, Boolean Reasoning Approach. PhD thesis, Warsaw University, Warsaw, Poland (1997)

    Google Scholar 

  95. Słowiński, R., Stefanowski, J.: Rough family – software implementation of the rough set theory. In: [23], pp. 581–586

    Google Scholar 

  96. Nguyen, H.S., Nguyen, S.H.: Pattern extraction from data. Fundamenta Informaticae 34, 129–144 (1998)

    MathSciNet  MATH  Google Scholar 

  97. Nguyen, H.S., Nguyen, S.H.: Discretization methods for data mining. In: [22], pp. 451–482

    Google Scholar 

  98. Skowron, A.: Rough sets in KDD - plenary talk. In: Shi, Z., Faltings, B., Musen, M. (eds.) 16-th World Computer Congress (IFIP 2000): Proceedings of Conference on Intelligent Information Processing (IIP 2000), pp. 1–14. Publishing House of Electronic Industry, Beijing (2002)

    Google Scholar 

  99. Bazan, J., Nguyen, H.S., Nguyen, S.H., Synak, P., Wróblewski, J.: Rough set algorithms in classification problems. In: [26], pp. 49–88

    Google Scholar 

  100. Grzymala-Busse, J.W., Shah, P.: A comparison of rule matching methods used in aq15 and lers. In: Ohsuga, S., Raś, Z.W. (eds.) ISMIS 2000. LNCS (LNAI), vol. 1932, pp. 148–156. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  101. Grzymała-Busse, J., Hu, M.: A comparison of several approaches to missing attribute values in data mining. In: [44], pp. 340–347

    Google Scholar 

  102. Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: An algorithm for induction of decision rules consistent with dominance principle. In: [44], pp. 304–313

    Google Scholar 

  103. Skowron, A.: Rough sets and boolean reasoning. In: Pedrycz, W. (ed.) Granular Computing: an Emerging Paradigm. Studies in Fuzziness and Soft Computing, vol. 70, pp. 95–124. Springer-Verlag/Physica-Verlag, Heidelberg, Germany (2001)

    Google Scholar 

  104. Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. European J. of Operational Research 129(1), 1–47 (2001)

    Article  MATH  Google Scholar 

  105. Casti, J.L.: Alternate Realities: Mathematical Models of Nature and Man. John Wiley and Sons, Inc., New York (1989)

    MATH  Google Scholar 

  106. Coombs, C.H., Avruin, G.S.: The Structure of Conflicts. Lawrence Erlbaum, London (1988)

    Google Scholar 

  107. Deja, R.: Conflict analysis, rough set methods and applications. In: [26], pp. 491–520

    Google Scholar 

  108. Maeda, Y., Senoo, K., Tanaka, H.: Interval density function in conflict analysis. In: [43], pp. 382–389

    Google Scholar 

  109. Nakamura, A.: Conflict logic with degrees. In: [24], pp. 136–150

    Google Scholar 

  110. Pawlak, Z.: An inquiry into anatomy of conflicts. Journal of Information Sciences 109, 65–68 (1998)

    Article  MathSciNet  Google Scholar 

  111. Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1973)

    Google Scholar 

  112. Słowiński, R., Greco, S.: A note on dependency factor (2004) (manuscript)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pawlak, Z. (2004). Some Issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds) Transactions on Rough Sets I. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27794-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27794-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22374-0

  • Online ISBN: 978-3-540-27794-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics