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A Study of Multiple-Source Approximation Systems

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Transactions on Rough Sets XII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6190))

Abstract

The article continues an investigation of multiple-source ap- proximation systems (MSASs) [1,2]. These are collections of Pawlak approximation spaces over the same domain, and embody the situation where information arrives from a collection of sources. Notions of strong/weak lower and upper approximations of a subset of the domain were introduced in [1]. These result in a division of the domain into five mutually disjoint sets. Different kinds of definability of a set are then defined. In this paper, we study further properties of all these concepts in a structure called multiple-source approximation system with group knowledge base (MSAS G), where we also have equivalence relations representing the combined knowledge base of each group of sources. Some of the properties of combined knowledge base are presented and its relationship with the strong/weak lower and upper approximation is explored. Specifically, ordered structures that arise from these concepts are studied in some detail. In this context, notions of dependency, that reflect how much the information provided by a MSAS G depends on an individual source or group of sources, are introduced. Membership functions for MSASs were investigated in [2]. These are also studied afresh here.

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References

  1. Khan, M.A., Banerjee, M.: Formal reasoning with rough sets in multiple-source approximation systems. International Journal of Approximate Reasoning 49(2), 466–477 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Khan, M.A., Banerjee, M.: Multiple-source approximation systems: membership functions and indiscernibility. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 80–87. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  4. Ras, Z., Dardzinska, A.: Ontology-based distributed autonomous knowledge systems. Information Systems 29, 47–58 (2004)

    Article  Google Scholar 

  5. Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  6. Farinas Del Cerro, L., Orłowska, E.: DAL – a logic for data analysis. Theoretical Computer Science 36, 251–264 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wong, S.K.M.: A rough set model for reasoning about knowledge. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications, pp. 276–285. Physica, Heidelberg (1998)

    Google Scholar 

  8. Liau, C.J.: An overview of rough set semantics for modal and quantifier logics. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8(1), 93–118 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rasiowa, H.: Mechanical proof systems for logic of reaching consensus by groups of intelligent agents. Int. J. Approximate Reasoning 5(4), 415–432 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rauszer, C.M.: Knowledge representation systems for groups of agents. In: Woleński, J. (ed.) Philosophical Logic in Poland, pp. 217–238. Kluwer, Dordrecht (1994)

    Chapter  Google Scholar 

  11. Rauszer, C.M.: Rough logic for multiagent systems. In: Masuch, M., Polos, L. (eds.) Logic at Work 1992. LNCS (LNAI), vol. 808, pp. 161–181. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  12. Pagliani, P., Chakraborty, M.K.: Information quanta and approximation spaces I: non-classical approximation operators. In: Proc. 2005 IEEE Conf. on Granular Computing, pp. 605–610. IEEE Press, Los Alamitos (2005)

    Chapter  Google Scholar 

  13. Skowron, A.: Approximate reasoning in MAS: rough set approach. In: Proc. 2006 IEEE/WIC/ACM Conf. on Intelligent Agent Technology, pp. 12–18. IEEE Computer Society, Washington (2006)

    Chapter  Google Scholar 

  14. Banerjee, M., Khan, M.A.: Propositional logics from rough set theory. Transactions on Rough Sets VI, 1–25 (2007)

    Google Scholar 

  15. Pagliani, P.: Pretopologies and dynamic spaces. Fundamenta Informaticae 59(2-3), 221–239 (2004)

    MathSciNet  MATH  Google Scholar 

  16. Orłowska, E.: Kripke semantics for knowledge representation logics. Studia Logica XLIX, 255–272 (1990)

    Google Scholar 

  17. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in Decision-Making, pp. 3–98. Springer, Singapore (1999)

    Google Scholar 

  18. Birkhoff, G.: Lattice theory. American Mathematical Society Colloquium Publications, New York (1967)

    MATH  Google Scholar 

  19. Rasiowa, H.: An Algebraic Approach to Non-classical Logics. North Holland, Amsterdam (1974)

    MATH  Google Scholar 

  20. Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and fuzzy set model. Fuzzy Sets and Systems 21, 357–362 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  21. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 47–75. Kluwer, Boston (1997)

    Chapter  Google Scholar 

  24. Ślȩzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49(2), 255–271 (2008)

    Article  MATH  Google Scholar 

  26. Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49(2), 272–284 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Greco, S., Matarazzo, B., Słowiński, R.: Parametrized rough set model using rough membership and Bayesian confirmation measures. International Journal of Approximate Reasoning 49(2), 285–300 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wong, S.K.M., Ziarko, W., Li Ye, R., Li, R.: Comparison of rough-set and statistical methods in inductive learning. International Journal of Man-Machine Studies 24, 53–72 (1986)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  32. Intan, R., Mukaidono, M.: Generalization of rough membership function based on α−coverings of the universe. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002. LNCS (LNAI), vol. 2275, pp. 129–135. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208 016, India

    Md. Aquil Khan & Mohua Banerjee

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  1. Md. Aquil Khan
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  2. Mohua Banerjee
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, R3T 5V6, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Insitute of Computing Science, Laboratory of Intelligent Decision Support Systems, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  4. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  5. School of Electronics and Information Engineering, Tongji University, 201804, Shanghai, P.R. China

    Duoqian Miao

  6. Faculty of Medicine, Department of Medical Informatics, 89-1 Enya-cho, Shimane University, 693-8501, Izumo, Japan

    Shusaku Tsumoto

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Khan, M.A., Banerjee, M. (2010). A Study of Multiple-Source Approximation Systems. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds) Transactions on Rough Sets XII. Lecture Notes in Computer Science, vol 6190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14467-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-14467-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14466-0

  • Online ISBN: 978-3-642-14467-7

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