Kybernetika 47 no. 1, 144-163, 2011

Information measures and uncertainty of particular symbols

Milan Mareš

Abstract:

The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced by sources of the considered type.

Keywords:

information measure, uncertainty, randomness, vagueness, imprecision, information source, alphabet, message

Classification:

94A20, 94A15, 94D05, 28E10

References:

  1. P. Benvenuti: L'Opera Scientifica. Universit\'{a} La Sapienza, Roma 2004.   CrossRef
  2. P. Benvenuti, D. Vivona and M. Divari: Order relations for fuzzy sets and entropy measure. In: New Trends in Fuzzy Systems (D. Mancini, M. Squillante, and A. Ventre, eds.). World Scientific 1998, pp. 224-232.   CrossRef
  3. T. Calvo, G. Mayor and R. Mesiar (eds.): Aggregation Operators. Physica-Verlag, Heidelberg 2002.   CrossRef
  4. A. De Luca and S. Termini: A definition of a non probabilistic entropy in the setting of fuzzy set theory. Inform. and Control {\si 20} (1972), 301-312.   CrossRef
  5. D. Dubois, E. Kerre, R. Mesiar and H. Prade: Fuzzy interval analysis. In: Fundamentals of Fuzzy Sets. Kluwer, Dordrecht 2000, pp. 483-581.   CrossRef
  6. A. Feinstein: Foundations of Information Theory. McGraw-Hill, New York 1957.   CrossRef
  7. R. A. Fisher: Statistical Methods for Research Workers. Olivier and Boyd, Edinburgh 1932.   CrossRef
  8. H. Gintis: Game Theory Evolving. Princeton Univ. Press, Princenton 2009.   CrossRef
  9. Ein-Ya Gura and M. B. Maschler: Insight Into Game Theory. Cabridge Univ. Press, Cambridge 2009.   CrossRef
  10. W.-L. Hung and M-S. Yang: Fuzzy entropy on intuicionistic fuzzy sets. Internat. J. Intelligent Systems {\si 21} (2006), 443-451.   CrossRef
  11. G. J. Klir and T. A. Folger: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs, 1988.   CrossRef
  12. G. J. Klir and Zhenyuan Wang: Generalized Measure Theory. Springer, Berlin 2009.   CrossRef
  13. A. Koles\'{a}rov\'{a} and D. Vivona: Entropy of T-sums and T-products of L-R fuzzy numbers. Kybernetika {\si 37} (2001), 2, 127-145.   CrossRef
  14. M. Mare\v{s}: Computation Over Fuzzy Quantities. CRC-Press, Boca Raton 1994.   CrossRef
  15. M. Mare\v{s}: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems {\si 91} (1997), 2, 143-154.   CrossRef
  16. M. Mare\v{s}: Fuzzy components of cooperative market. In: Perception-Based Data Mining and Decision Making in Economics and Finance. (I. Batyrshin and J. Kacprzyk, eds.), Physica-Verlag, Heidelberg 2007.   CrossRef
  17. M. Mare\v{s} and R. Mesiar: Information in granulated data source. In: Proc. ICSCCW-2007 (W. Pedrycz, R. Aliev, Mo. Jamshidi, and B. Turksen, eds.), b-Quadrat Verlag, Antalya 2007, pp. 185-194.   CrossRef
  18. Ming Quing and Tian-Rui Li: Some properties and new formulae of fuzzy entropy. In: Proc. 2004 IEEE Internat. Conf. on Networking, Sensing and Control, Vol. I, pp. 401-406.   CrossRef
  19. L. Narens: Abstract Measurement Theory. MIT Press, London 1985.   CrossRef
  20. R. B. Nelsen: An Introduction to Copulas. Springer, New York 2006.   CrossRef
  21. J. von Neumann and O. Morgenstern: Theory of Games and Economic Behaviour. Princeton Univ. Press, Princeton 1944.   CrossRef
  22. Z. Pawlak: Rough Sets. Kluwer, Dordrecht 1991.   CrossRef
  23. A. R\'{e}nyi: On measures of entropy and information. In: Proc. Fourth Berkeley Symp. on Math. Statistics and Probability 1961, Vol. 1, pp. 547-561.   CrossRef
  24. C. Shannon and W. Weaver: A mathematical theory of communication. Bell Systems Technical Journal {\si 27} (1948), 379-423, 623-653.   CrossRef
  25. N. Wiener: Cybernetics or Control and Communication in the Animal and the Machine. Cambridge Univ. Press, Cambridge 1948.   CrossRef
  26. N. Wiener, A. Rosenblueth and J. Bigelow: Behaviour, purpose and teleology. Philosophy of Science {\si 10} (1943), 1, 18-24.   CrossRef
  27. K. Winkelbauer: Communication channels with finite past history. In: Trans. Second Prague Conference on Information Theory etc., Publ. House of \v{C}SAV, Prague 1960.   CrossRef
  28. Yao Min and Zhang Sen: Generalized fuzzy entropy and its applications. In: Proc. 4th Internat. Conf. on Signal Processing 1998, Vol. 2, pp. 1197-1200.   CrossRef
  29. L. A. Zadeh: Fuzzy sets. Inform. and Control {\si 8} (1965), 3, 338-353.   CrossRef
  30. L. A. Zadeh: From computing with numbers to computing with words. IEEE Trans. Circuits and Systems {\si 45} (1999), 105-109.   CrossRef