Kybernetika 49 no. 3, 433-445, 2013

Information in vague data source

Milan Mareš and Radko Mesiar

Abstract:

This paper deals with the concept of the "size" or "extent" of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.

Keywords:

entropy, triangular norm, alphabet, information, data source, fuzziness

Classification:

03E72, 94A17

References:

  1. J. C. Bezdek and ed.: Analysis of Fuzzy Information. CRC-Press, Boca Raton 1988.   CrossRef
  2. T. Calvo, G. Mayor, R. Mesiar and eds.: Aggregation Operators. New Trends and Applications, Physica-Verlag, Heidelberg 2002.   CrossRef
  3. A. De Luca and S. Termini: A definition of a non probabilistic entropy in the setting of fuzzy set theory. Inform. and Control 20 (1972), 301-312.   CrossRef
  4. D. Dubois, E. Kerre, R. Mesiar and H. Prade: Fuzzy interval analysis. In: Fundamentals of Fuzzy Sets, Kluwer, Dordrecht 2000, pp. 483-581.   CrossRef
  5. D. Dubois and H. Prade: Possibility Theory. An Approach to Computerized Processing of Uncertainty. Plenum Press, New York 1988.   CrossRef
  6. A. Feinstein: Foundations of Information Theory. McGraw-Hill, New York 1957.   CrossRef
  7. R. E. Giachetti and R. E. Young: A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets and Systems 91 (1997), 185-202.   CrossRef
  8. R. V. L. Hartley: Transmission of information. Bell System Techn. J. 7 (1928), 3, 535-563.   CrossRef
  9. J. Havrda and F. Charvát: Quantification method of classifications processes. Concept of structural a-entropy. Kybernetika 3 (1967), 1, 30-35.   CrossRef
  10. J. Kampé de Fériet: Théories de l'information. Springer, Berlin 1974.   CrossRef
  11. J. Kampé de Fériet and B. Forte: Information et probabilité. C. R. Acad. Sci. Paris, Sér. A 265 1967, 110-114; 142-146; 350-353.   CrossRef
  12. E. E. Kerre and X. Wang: Reasonable properties for the ordering of fuzzy quantities. Part I., Part II. Fuzzy Sets and Systems 118 (2001), 375-385; 387-405.   CrossRef
  13. E. P. Klement, R. Mesiar and E. Pap: Triangular Norms. Kluwer, Dordrecht 2000.   CrossRef
  14. G. J. Klir and T. A. Folger: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs 1988.   CrossRef
  15. G. J. Klir: Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems 91 (1997), 2, 165-175.   CrossRef
  16. A. Kolesárová and D. Vivona: Entropy of T-sums and T-products of $L-R$ fuzzy numbers. Kybernetika 37 (2001), 2, 127-145.   CrossRef
  17. M. Mareš: Computation Over Fuzzy Quantities. CRC-Press, Boca Raton 1994.   CrossRef
  18. M. Mareš: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 143-154.   CrossRef
  19. M. Mareš: Compenzational vagueness. In: Proc. EUSFLAT'2007 (M. Štepnička, V. Novák, and U. Bodenhofer, eds.), Ostrava 2007, pp. 179-184.   CrossRef
  20. M. Mareš and R. Mesiar: Verbally generated fuzzy quantities. In: Aggregation Operators. New Trends and Applications(T. Calvo, G. Mayor, and R. Mesiar (eds.), Physica-Verlag, Heidelberg 2002, pp. 291-353.   CrossRef
  21. M. Mareš and R. Mesiar: Information in granulated data sources. In: Proc. Internat. Conf. on Soft Computing, Computing with Words and Perceptions in Systems (W. Pedrycz, R. Aliev, Mo Jamshidi, and B. Turksen, eds.), Antalya 2007.   CrossRef
  22. R. Mesiar: Triangular norms-based addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 73-78.   CrossRef
  23. R. Mesiar and S. Saminger: Domination of ordered weighted averaging operators over $t$-norms. Soft Computing 8 (2004), 562-570.   CrossRef
  24. H. T. Nguyen: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64 (1978), 369-380.   CrossRef
  25. C. Shannon and and W. Weaver: A mathematical theory of communication. Bell System Techn. J. 27 (1948), 379-423; 623-653.   CrossRef
  26. M. Sugeno: Theory of Fuzzy Integrals and Its Applications. PhD. Thesis, Tokyo Institute of Technology, 1974.   CrossRef
  27. D. Vivona and M. Divari: On a conditional information for fuzzy sets. In: Proc. AGOP'2005, Lugano 2005, pp. 147-149.   CrossRef
  28. K. Winkelbauer: Communication channels with finite past history. In: Trans. Second Prague Conference, Statistical Decision Functions and Random Processes, Prague 1959. Publishing House of the Czechoslovak Academy of Sci., Prague 1960, pp. 685-831.   CrossRef
  29. L. A. Zadeh: Fuzzy sets. Inform. and Control 8 (1965), 338-353.   CrossRef
  30. L. A. Zadeh: The concept of a linguistic variable and its application to approximate reasoning. Inform. Sci. (1975), Part I: 8, 199-249; Part II: 8, 301-357; Part III: 9, 43-80.   CrossRef
  31. L. A. Zadeh: Fuzzy logic $=$ Computing with words. IEEE Trans. Fuzzy Systems 2 (1977), 103-111.   CrossRef
  32. L. A. Zadeh and : Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3-28.   CrossRef
  33. L. A. Zadeh: Yes, no and relatively. Chemtech (1987), June: 340-344; July: 406-410.   CrossRef
  34. L. A. Zadeh: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perception. IEEE Trans. Circuits Systems 45 (1999), 105-119.   CrossRef
  35. L. A. Zadeh: The concept of cointensive precisation - A key to mechanization of natural language understanding. In: Proc. IPMU, Paris 2006, pp. 13-15.   CrossRef