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Polish Information Processing Society
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Annals of Computer Science and Information Systems, Volume 18

Proceedings of the 2019 Federated Conference on Computer Science and Information Systems

Information granule system induced by a perceptual system

DOI: http://dx.doi.org/10.15439/2019F147

Citation: Proceedings of the 2019 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 18, pages 1927 ()

Full text

Abstract. Knowledge represented in the semantic network, especially in the Semantic Web, can be expressed in attributive language AL. Expressions of this language are interpreted in different theories of information granules: set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy sets or rough sets. In order to unify the interpretations of expressions for different theories, it is assumed that expressions of the AL language can be interpreted in a chosen relational system called a granule system. In this paper, it is proposed to use information granule database and it is also demonstrated that this database can be induced by the measurement system of the adequacy of information retrieval, called a perceptual system. It can simplify previous formal description of the information granule system significantly. This paper also shows some examples of inducing rough and fuzzy granule databases by some perceptual systems.

References

  1. Baader F., Calvanese D., McGuinness D., Nardi D., Patel-Schneider P. (eds.): The Description Logic. Handbook Theory, Implementation and Application. Cambridge University Press, Cambridge, 2003.
  2. Blizard W, D.: Multiset Theory. Notre Dame Journal of Formal Logic, vol. 30, Number 1, pp. 36-66, 1989.
  3. Blass, A. C., Childs D. L.: Axioms and Models for an Extended Set Theory. University of Michigan, Mathematics Dept: 2011.
  4. Bobillo F., Straccia U.: Fuzzy Description Logics with general t-norms and datatypes, Fuzzy Sets Systems, vol. 160(23), pp. 3382-3402, 2009.
  5. Bryniarska, A.: The Paradox of the Fuzzy Disambiguation in the Infor mation Retrieval. (IJARAI) International Journal of Advanced Research in Artificial Intelligence, pp. 55-58, Volume 2 No 9, 2013.
  6. Bryniarska A.: The Model of Possible Web Data Retrieval. Proceedings of 2nd IEEE International Conference on Cybernetics CYBCONF 2015, pp. 348-353, 2015.
  7. Bryniarska A., Bryniarski E.: Rough search of vague knowledge. In: G. Wang, A. Skowron, Y. Yao, D. Slezak, L. Polkowski (eds.), Thriving Rough Sets-10th Anniversary - Honoring Professor Zdzislaw Pawlak’s Life and Legacy & 35 years of Rough Sets, Studies in Computational Intelligence, Springer , Berlin Heidelberg New York, pp.283-310, 2017.
  8. Bryniarska A.: Autodiagnosis of Information Retrieval on the Web as a Simulation of Selected Processes of Consciousness in the Human Brain. In: Biomedical Engineering and Neuroscience, W. P. Hunek, S. Paszkiel eds., Advances in Intelligent Systems and Computing 720, pp. 111-120, Springer, 2018.
  9. Bryniarska A.: Certain information granule system as a result of sets approximation by fuzzy context, International Journal of Approximate Reasoning, Volume 111, pp. 1-20, August 2019, in press.
  10. Bryniarski E.: A calculus of rough sets of the first order. Bull. Pol. Ac.: Math. 37, pp. 109-136, 1989.
  11. Bryniarski E.: Formal conception of rough sets. Fund. Infor. 27(2-3), pp.103-108, 1996.
  12. Fahle M., Poggio T.: Perceptual Learning. Cambridge, MA: The MIT Press, 2002.
  13. Merleau-Ponty M.: Phenomenology of Perception. Paris and New York: Smith, Callimard, Paris and Routledge & Kegan Paul, 1945.
  14. Moore R.: Interval Analysis, Prentice-Hall, Englewood Clifis, NJ, 1966.
  15. Pawlak Z.: Rough sets. Intern. J. Comp. Inform. Sci. 11, pp. 341-356, 1982.
  16. Pawlak Z.: Rough Sets. Theoretical Aspects of Reasoning about. Data. Kluwer Academic Publishers, Dordrecht, 1991.
  17. Pawlak Z, Skowron A.: Rough membership function, in: R. E Yeager, M. Fedrizzi and J. Kacprzyk (eds.), Advaces in the Dempster-Schafer of Evidence, Wiley, New York, 251-271, 1994.
  18. Pawlak Z., Skowron A.: Rudiments of rough sets. Information Sciences, 177,1, 1, pp. 3-27, 2007.
  19. Pawlak Z., Skowron. A.: Rough sets and Boolean reasoning. Information Sciences, 177, 1, pp. 41-73, 2007.
  20. Pedrycz W.: Shadowed sets: representing and processing fuzzy sets, IEEE Transactions on Systems, Man, and Cybernetics - Part B 28 pp. 103-109, 1998.
  21. Pedrycz W.: Knowledge-Based Clustering: From Data to Information Granules, J. Wiley, Hoboken, NJ, 2005.
  22. Pedrycz W.: Allocation of information granularity in optimization and decision-making models: towards building the foundations of Granular Computing. Eur J Oper Res 232(1),pp. 137-145, 2014. http://dx.doi.org/10.1016/j.ejor.2012.03.038
  23. Peters J. F., Skowron A., Stepaniuk J.: Nearness of objects: Extension of approximation space model. Fundamenta Informaticae, vol. 79, no. 3-4, pp. 497–512, 2007.
  24. Peters J. F.: Discovery of perceptually near information granules. In: Novel Developments in Granular Computing: Applications of Advanced Human Reasoning and Soft Computation, J. T. Yao, Ed. Hersey, N.Y., USA: Information Science Reference, 2009.
  25. Peters J. F. , Ramanna S.: Affinities between perceptual granules: Foun- dations and Perspectives. In: Human-Centric Information Processing Through Granular Modelling, A. Bargiela and W. Pedrycz, Eds. Berlin: Springer-Verlag, pp. 49–66, 2009.
  26. Peters J. F. , Wasilewski P.: Foundations of near sets. Elsevier Science, vol. 179, no. 1, pp. 3091–3109, 2009.
  27. Tsichritzis D. C., Lochovsky F.: Data models, Published by Prentice Hall, Inc. Englewood Clis, New Jersey, USA, 1982.
  28. Vopenka P.: Mathematics in the Alternative Set Theory. Leipzig: Teubner, 1979.
  29. Zadeh L.A.: Fuzzy sets. Inf Control 8(3): pp. 338-353, 1965.
  30. Zadeh L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems 90, pp. 111-117, 1997.
  31. Zadeh L.A.: Toward a generalized theory of uncertainty (GTU) an outline, Information Sciences 172, pp. 1-40, 2005.