Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
alphabet; data source; entropy; fuzziness; information; triangular norm
alphabet; data source; entropy; fuzziness; information; triangular norm
Summary:
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.
References:
[1] Bezdek, J. C.: Analysis of Fuzzy Information. CRC-Press, Boca Raton 1988. Zbl 0648.00013
[2] Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. New Trends and Applications, Physica-Verlag, Heidelberg 2002. MR 1936383 | Zbl 0983.00020
[3] 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. DOI 10.1016/S0019-9958(72)90199-4 | MR 0327383
[4] Dubois, D., Kerre, E., Mesiar, R., Prade, H.: Fuzzy interval analysis. In: Fundamentals of Fuzzy Sets, Kluwer, Dordrecht 2000, pp. 483-581. MR 1890240 | Zbl 0988.26020
[5] Dubois, D., Prade, H.: Possibility Theory. An Approach to Computerized Processing of Uncertainty. Plenum Press, New York 1988. MR 1104217 | Zbl 0703.68004
[6] Feinstein, A.: Foundations of Information Theory. McGraw-Hill, New York 1957. MR 0095087 | Zbl 0082.34602
[7] Giachetti, R. E., Young, R. E.: A parametric representation of fuzzy numbers and their arithmetic operators. Fuzzy Sets and Systems 91 (1997), 185-202. MR 1480045 | Zbl 0920.04008
[8] Hartley, R. V. L.: Transmission of information. Bell System Techn. J. 7 (1928), 3, 535-563.
[9] Havrda, J., Charvát, F.: Quantification method of classifications processes. Concept of structural a-entropy. Kybernetika 3 (1967), 1, 30-35. MR 0209067
[10] Fériet, J. Kampé de: Théories de l'information. Springer, Berlin 1974. MR 0371504
[11] Fériet, J. Kampé de, Forte, B.: Information et probabilité. C. R. Acad. Sci. Paris, Sér. A 265 1967, 110-114; 142-146; 350-353.
[12] Kerre, E. E., Wang, X.: Reasonable properties for the ordering of fuzzy quantities. Part I., Part II. Fuzzy Sets and Systems 118 (2001), 375-385; 387-405.
[13] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht 2000. MR 1790096 | Zbl 1087.20041
[14] Klir, G. J., Folger, T. A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs 1988. MR 0930102 | Zbl 0675.94025
[15] Klir, G. J.: Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems 91 (1997), 2, 165-175. DOI 10.1016/S0165-0114(97)00138-3 | MR 1480043 | Zbl 0920.04007
[16] Kolesárová, A., Vivona, D.: Entropy of T-sums and T-products of $L-R$ fuzzy numbers. Kybernetika 37 (2001), 2, 127-145. MR 1839223 | Zbl 1265.03020
[17] Mareš, M.: Computation Over Fuzzy Quantities. CRC-Press, Boca Raton 1994. MR 1327525 | Zbl 0859.94035
[18] Mareš, M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 143-154. DOI 10.1016/S0165-0114(97)00136-X | MR 1480041
[19] Mareš, M.: Compenzational vagueness. In: Proc. EUSFLAT'2007 (M. Štepnička, V. Novák, and U. Bodenhofer, eds.), Ostrava 2007, pp. 179-184.
[20] Mareš, M., Mesiar, R.: 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. MR 1936394 | Zbl 1039.68128
[21] Mareš, M., Mesiar, R.: 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.
[22] Mesiar, R.: Triangular norms-based addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 73-78. DOI 10.1016/S0165-0114(97)00143-7 | MR 1480048
[23] Mesiar, R., Saminger, S.: Domination of ordered weighted averaging operators over $t$-norms. Soft Computing 8 (2004), 562-570. DOI 10.1007/s00500-003-0315-x | Zbl 1066.68127
[24] Nguyen, H. T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64 (1978), 369-380. DOI 10.1016/0022-247X(78)90045-8 | MR 0480044 | Zbl 0377.04004
[25] and, C. Shannon, Weaver, W.: A mathematical theory of communication. Bell System Techn. J. 27 (1948), 379-423; 623-653. MR 0026286
[26] Sugeno, M.: Theory of Fuzzy Integrals and Its Applications. PhD. Thesis, Tokyo Institute of Technology, 1974.
[27] Vivona, D., Divari, M.: On a conditional information for fuzzy sets. In: Proc. AGOP'2005, Lugano 2005, pp. 147-149.
[28] Winkelbauer, K.: 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. MR 0129056 | Zbl 0161.16904
[29] Zadeh, L. A.: Fuzzy sets. Inform. and Control 8 (1965), 338-353. DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0942.00007
[30] Zadeh, L. A.: 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. DOI 10.1016/0020-0255(75)90017-1 | Zbl 0404.68075
[31] Zadeh, L. A.: Fuzzy logic $=$ Computing with words. IEEE Trans. Fuzzy Systems 2 (1977), 103-111. Zbl 0947.03038
[32] Zadeh, L. A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3-28. DOI 10.1016/0165-0114(78)90029-5 | MR 0480045 | Zbl 0377.04002
[33] Zadeh, L. A.: Yes, no and relatively. Chemtech (1987), June: 340-344; July: 406-410.
[34] Zadeh, L. A.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perception. IEEE Trans. Circuits Systems 45 (1999), 105-119. MR 1683230
[35] Zadeh, L. A.: The concept of cointensive precisation - A key to mechanization of natural language understanding. In: Proc. IPMU, Paris 2006, pp. 13-15.
Search
Partner of
