Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
information measure; system of functional equations
information measure; system of functional equations
Summary:
In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.
References:
[1] Aczél J., Forte, B., Ng C. T.: L’equation fonctionelle et la théorie de l’Information sans probabilité. C. R. Acad. Sci. Paris 275 (1972), 727–729
[2] Aczél J., Forte, B., Ng C. T.: On a triangular functional equation and some application, in particular to the generalized theory of information. Aequationes Math. XI (1974), 11–30 MR 0352760
[3] Baker J. A., Forte, B., Lam L. F.: On the existence of a collector for a class of information measures. Utilitas Math. 1 (1972), 219–239 MR 0329765 | Zbl 0256.94025
[4] Benvenuti P., Divari, M., Pandolfi M.: Su un sistema di equazioni funzionali proveniente dalla teoria soggettiva della informazione. Rend. Mat. 3 (1972), 5, 529–540 MR 0323446 | Zbl 0249.94006
[5] Benvenuti P., Vivona, D., Divari M.: A general information for fuzzy sets. In: Uncertainty in Knowledge Bases (B. Bouchon-Meunier, R. R. Yager, and L. A. Zadeh, eds., Lectures Notes in Computer Sciences 521), Springer–Verlag, Heidelberg 1999, pp. 307–316 MR 1252472
[6] Bertoluzza C.: Compositive information measures of a fuzzy set. In: Fuzzy logic and soft computing 4 (B. Bouchon-Meunier, R. R. Yager, and L. A. Zadeh, eds.), World Scientific 1995, pp. 353–359 MR 1391014
[7] Forte B.: Information and probability: Collectors and Shannon compositivity. J. Deutsch. Math.-Verein 75 (1973), 42–49 MR 0689197 | Zbl 0258.94015
[8] Forte B.: Information and probability: Collectors and compositivity. Symps. Math. IX (1972), 121–129 MR 0368938 | Zbl 0241.94019
[9] Forte B.: Measures of information: the general axiomatic theory. RAIRO Inform. Théor. Appl. xxx (1969), 63–90 MR 0260479 | Zbl 0192.56001
[10] Fériet J. Kampé de, Forte B.: Information et probabilité. C. R. Acad. Sci. Paris 265 (1967), 110–114, 142–146, 350–353
[11] Fériet J. Kampé de: Mesures de l’information par un ensemble d’observateurs. C. R. Acad. Sci. Paris 269 (1969), 1081–1085, 271 (1970), 1017–1021 MR 0274199
[12] Fériet J. Kampé de: La Theorie Generale de L’Information et La Misure Subjective de L’Information. In: Lectures Notes in Mathematics 398, Springer–Verlag, Heidelberg 1974, pp. 1–35
[13] Fériet J. Kampé de, Forte, B., Benvenuti P.: Forme générale de l’opération de composition continue d’une information. C. R. Acad. Sci. Paris 269 (1969), 529–534 MR 0252110
[14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[15] Maschio G.: Note di teoria dell’informazione. In: Quaderno dei gruppi di ricerca del C.N.R. 97 (1972)
[16] Vivona D., Divari M.: On a collector of $\wedge $-compositive informations. In: Proc. IPMU’04, 2004, pp. 1199–1203
[17] Zadeh L. A.: Fuzzy sets. Inform. and Control 8 (1965), 338–353 DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606
Search
Partner of
