Title:
|
Information Measures and Uncertainty of Particular Symbols (English) |
Author:
|
Mareš, Milan |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
47 |
Issue:
|
1 |
Year:
|
2011 |
Pages:
|
144-163 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
information measure |
Keyword:
|
uncertainty |
Keyword:
|
randomness |
Keyword:
|
vagueness |
Keyword:
|
imprecision |
Keyword:
|
information source |
Keyword:
|
alphabet |
Keyword:
|
message |
MSC:
|
28E10 |
MSC:
|
94A15 |
MSC:
|
94A20 |
MSC:
|
94D05 |
idZBL:
|
Zbl 1208.94036 |
idMR:
|
MR2807870 |
. |
Date available:
|
2011-04-12T13:12:44Z |
Last updated:
|
2013-09-22 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141484 |
. |
Reference:
|
[1] Benvenuti, P.: L’Opera Scientifica.Universitá La Sapienza, Roma 2004. |
Reference:
|
[2] Benvenuti, P., Vivona, D., Divari, M.: 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. |
Reference:
|
[3] Calvo, T., Mayor, G., (eds.), R. Mesiar: Aggregation Operators.Physica-Verlag, Heidelberg 2002. Zbl 0983.00020, MR 1936383 |
Reference:
|
[4] Luca, A. De, Termini, S.: A definition of a non probabilistic entropy in the setting of fuzzy set theory.Inform. and Control 20 (1972), 301–312. MR 0327383, 10.1016/S0019-9958(72)90199-4 |
Reference:
|
[5] Dubois, D., Kerre, E., Mesiar, R., Prade, H.: Fuzzy interval analysis.In: Fundamentals of Fuzzy Sets. Kluwer, Dordrecht 2000, pp. 483–581. Zbl 0988.26020, MR 1890240 |
Reference:
|
[6] Feinstein, A.: Foundations of Information Theory.McGraw-Hill, New York 1957. MR 0095087 |
Reference:
|
[7] Fisher, R. A.: Statistical Methods for Research Workers.Olivier and Boyd, Edinburgh 1932. |
Reference:
|
[8] Gintis, H.: Game Theory Evolving.Princeton Univ. Press, Princenton 2009. Zbl 1161.91005 |
Reference:
|
[9] Gura, Ein-Ya, Maschler, M. B.: Insight Into Game Theory.Cabridge Univ. Press, Cambridge 2009. MR 2469283 |
Reference:
|
[10] Hung, W.-L., Yang, M-S.: Fuzzy entropy on intuicionistic fuzzy sets.Internat. J. Intelligent Systems 21 (2006), 443–451. 10.1002/int.20131 |
Reference:
|
[11] Fériet, J.-M. Kampé de: La théorie general de l’information et la mesure subjective de l’information.In: Lecture Notes in Math. 398, Springer-Verlag, Heidelberg 1974, pp. 1–35. |
Reference:
|
[12] Fériet, J.-M. Kampé de, Forte, B.: Information et probabilité.C. R. Acad. Sci. Paris 265 (1967), 110–114, 142–146, 350–353. |
Reference:
|
[13] Klir, G. J., Folger, T. A.: Fuzzy Sets, Uncertainty and Information.Prentice Hall, Englewood Cliffs, 1988. Zbl 0675.94025, MR 0930102 |
Reference:
|
[14] Klir, G. J., Wang, Zhenyuan: Generalized Measure Theory.Springer, Berlin 2009. Zbl 1184.28002, MR 2453907 |
Reference:
|
[15] Kolesárová, A., Vivona, D.: Entropy of T-sums and T-products of L-R fuzzy numbers.Kybernetika 37 (2001), 2, 127–145. Zbl 1265.03020, MR 1839223 |
Reference:
|
[16] Mareš, M.: Computation Over Fuzzy Quantities.CRC-Press, Boca Raton 1994. MR 1327525 |
Reference:
|
[17] Mareš, M.: Weak arithmetics of fuzzy numbers.Fuzzy Sets and Systems 91 (1997), 2, 143–154. MR 1480041, 10.1016/S0165-0114(97)00136-X |
Reference:
|
[18] Mareš, M.: 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. |
Reference:
|
[19] Mareš, M., Mesiar, R.: 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. |
Reference:
|
[20] Quing, Ming, Li, Tian-Rui: Some properties and new formulae of fuzzy entropy.In: Proc. 2004 IEEE Internat. Conf. on Networking, Sensing and Control, Vol. I, pp. 401–406. |
Reference:
|
[21] Narens, L.: Abstract Measurement Theory.MIT Press, London 1985. Zbl 0607.00021, MR 0776041 |
Reference:
|
[22] Nelsen, R. B.: An Introduction to Copulas.Springer, New York 2006. Zbl 1152.62030, MR 2197664 |
Reference:
|
[23] Neumann, J. von, Morgenstern, O.: Theory of Games and Economic Behaviour.Princeton Univ. Press, Princeton 1944. MR 0011937 |
Reference:
|
[24] Pawlak, Z.: Rough Sets.Kluwer, Dordrecht 1991. Zbl 0758.68054 |
Reference:
|
[25] Rényi, A.: On measures of entropy and information.In: Proc. Fourth Berkeley Symp. on Math. Statistics and Probability 1961, Vol. 1, pp. 547–561. MR 0132570 |
Reference:
|
[26] Shannon, C., Weaver, W.: A mathematical theory of communication.Bell Systems Technical Journal 27 (1948), 379–423, 623–653. MR 0026286, 10.1002/j.1538-7305.1948.tb01338.x |
Reference:
|
[27] Wiener, N.: Cybernetics or Control and Communication in the Animal and the Machine.Cambridge Univ. Press, Cambridge 1948. MR 0025096 |
Reference:
|
[28] Wiener, N., Rosenblueth, A., Bigelow, J.: Behaviour, purpose and teleology.Philosophy of Science 10 (1943), 1, 18–24. 10.1086/286788 |
Reference:
|
[29] Winkelbauer, K.: Communication channels with finite past history.In: Trans. Second Prague Conference on Information Theory etc., Publ. House of ČSAV, Prague 1960. Zbl 0161.16904, MR 0129056 |
Reference:
|
[30] Min, Yao, Sen, Zhang: Generalized fuzzy entropy and its applications.In: Proc. 4th Internat. Conf. on Signal Processing 1998, Vol. 2, pp. 1197–1200. |
Reference:
|
[31] Zadeh, L. A.: Fuzzy sets.Inform. and Control 8 (1965), 3, 338–353. Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
Reference:
|
[32] Zadeh, L. A.: From computing with numbers to computing with words.IEEE Trans. Circuits and Systems 45 (1999), 105–109. Zbl 0954.68513, MR 1683230 |
. |