# Entropies of vague information sources

Kybernetika (2011)

- Volume: 47, Issue: 3, page 337-355
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

topMareš, Milan. "Entropies of vague information sources." Kybernetika 47.3 (2011): 337-355. <http://eudml.org/doc/196685>.

@article{Mareš2011,

abstract = {The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their rather additive (i. e., probability-like) than monotonous (typical for fuzzy set theoretical models) structure. The main goal of this paper is to describe briefly the existing state of art, and to suggest and analyze alternative, more fuzzy set theoretical, approaches to the fuzzy entropy developed as a significant characteristic of the information sources, in the information-theoretical sense.},

author = {Mareš, Milan},

journal = {Kybernetika},

keywords = {information source; message; uncertainty; fuzzy set; fuzzy entropy; fuzzy information; information source; fuzzy entropy; fuzzy information; additivity; probabilistic model of entropy; measure of uncertainty},

language = {eng},

number = {3},

pages = {337-355},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Entropies of vague information sources},

url = {http://eudml.org/doc/196685},

volume = {47},

year = {2011},

}

TY - JOUR

AU - Mareš, Milan

TI - Entropies of vague information sources

JO - Kybernetika

PY - 2011

PB - Institute of Information Theory and Automation AS CR

VL - 47

IS - 3

SP - 337

EP - 355

AB - The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their rather additive (i. e., probability-like) than monotonous (typical for fuzzy set theoretical models) structure. The main goal of this paper is to describe briefly the existing state of art, and to suggest and analyze alternative, more fuzzy set theoretical, approaches to the fuzzy entropy developed as a significant characteristic of the information sources, in the information-theoretical sense.

LA - eng

KW - information source; message; uncertainty; fuzzy set; fuzzy entropy; fuzzy information; information source; fuzzy entropy; fuzzy information; additivity; probabilistic model of entropy; measure of uncertainty

UR - http://eudml.org/doc/196685

ER -

## References

top- Benvenuti, P., Vivona, D., Divari, M., Order relations for fuzzy sets and entropy measure, In: New Trends in Fuzzy Systems (E. Mancini, M. Squillante and A. Ventre, eds.). World Scientific 1998, pp. 224–232. (1998)
- Bronevich, A., Klir, G. J., 10.1016/j.ijar.2009.11.003, An axiomatic approach. Internat. J. Approx. Reason. 51 (2010), 365–390. (2010) MR2592693DOI10.1016/j.ijar.2009.11.003
- Calvo, T., Mayor, G., (eds.), R. Measiar, Aggregation Operators, Physical-Verlag, Heidelberg 2002. (2002) MR1936383
- Luca, A. De, Termini, S., 10.1016/S0019-9958(72)90199-4, Inform. and Control 20 (1972), 301–312. (1972) MR0327383DOI10.1016/S0019-9958(72)90199-4
- Fisher, R. A., Statistical Methods for Research Workers, Olivier and Boyd, Edinburgh 1932. (1932)
- Forte, B., Measures of Information: The General Axiomatic Theory, RAIRO Information Théory. Appl. 1999, pp. 63–90. (1999) MR0260479
- Hung, W.-L., Yang, M.-S., 10.1002/int.20131, Internat. J. of Intelligent Systems 21 (2006), 443–451. (2006) Zbl1091.94012DOI10.1002/int.20131
- 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. (1974)
- Fériet, J.-M. Kampé dé, Forte, B., Information et probabilité, C. R. Acad. Sci. Paris 265 (1967), 110–114, 142–146, 350–353. (1967)
- Klement, E.-P., Mesiar, R., Pap, E., Triangular Norms, Kluwer, Dordrecht 2000. (2000) Zbl1010.03046MR1790096
- Klir, G. J., Folger, T. A., Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs 1988. (1988) Zbl0675.94025MR0930102
- Klir, G. J., Wang, Z., Generalized Measure Theory, Springer-Verlag, Berlin 2009. (2009) Zbl1184.28002MR2453907
- Kolesárová, A., Vivona, D., Entropy of T-sums and T-products of L-R fuzzy numbers, Kybernetika 37 (2001), 2, 127–145. (2001) Zbl1265.03020MR1839223
- Mareš, M., Computation Over Fuzzy Quantities, CRC-Pres, Boca Raton 1994. (1994) MR1327525
- Mareš, M., 10.1016/S0165-0114(97)00136-X, Fuzzy Sets and Systems 91 (1997), 2, 143–154. (1997) MR1480041DOI10.1016/S0165-0114(97)00136-X
- Mareš, M., Information measures and uncertainty of particular symbols, Kybernetika 47 (2011), 1, 144–163. (2011) Zbl1208.94036MR2807870
- Mareš, M., Mesiar, R., Information in granulated data sources, In: Proc. ICSCCW 2007 (W. Pedrycz, R. Aliev, Mo. Jamshidi, and B. Turksen, eds.), b-Quadrat Verlag, Antalya 2007, pp. 185–194. (2007)
- Ming, Q., Li, T.-R., Some properties and new formulae of fuzzy entropy, In: Proc. 2004 IEEE Internat. Conf. on Networking, Sensing and Control, Vol. I, pp. 401–406. (2004)
- Rathie, P., Generalization of the non-additive measures of uncertainty and information and their axiomatic characterization, Kybernetika 7 (1971), 2, 125–132. (1971) MR0299351
- Rathie, P., On some new measures of uncertainty, inaccuracy and information and their characterizations, Kybernetika 7 (1971), 394–403. (1971) Zbl0224.94035MR0299352
- Rényi, A., On measures of entropy and information, In: Proc. 4th Berkeley Symp. on Math. Statistics and Probability, 1961, Vol. I, pp. 547–561. (1961) MR0132570
- Shannon, C. E., Weawer, W., 10.1002/j.1538-7305.1948.tb01338.x, Bell. Syst. Techn. J. 27 (1948), 379–423, 623–653. (1948) MR0026286DOI10.1002/j.1538-7305.1948.tb01338.x
- Yao, M., Zhang, S., Generalized fuzzy entropy and its applications, In: Proc. 4th Internat. Conf. on Signal Processing 1998, Vol. 2, pp. 1197–1200. (1998)
- Zadeh, L. A., 10.1016/S0019-9958(65)90241-X, Inform. and Control 8 (1965), 3, 338–353. (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X
- Zadeh, L. A., From computing with numbers to computing with words, IEEE Trans. Circuits and Systems 45 (1999), 105–109. (1999) Zbl0954.68513MR1683230

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.