Abstract
The paper presents a systematic design of information theory based on fuzzy rules of combining evidence. The theory is developed both for discrete and continuous cases, represented respectively by finite distribution of possibility values and by an arbitrary measurable function on the domain of discourse.
Given a fuzzy set its associated uncertainty is expressed by an information function of the corresponding possibility distribution. Some natural properties of information make such expression of uncertainty essentially unique. A further extension is provided by the notion of information distance between two possibility distributions on the same domain of discourse. Finally, information functions and information distances are used to formulate a possibilistic principle of maximum uncertainty.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. Aczel and Z. Daroczy, On measures of information and their characterization, Academic Press, New York 1975.
M. Anvari and G. Rose, Fuzzy relational databases, Analysis of Fuzzy Information, v.II, CRC Press, Boca Raton, FL 1987.
B. Buckles and F. Petry, Generalized database and information systems, Analysis of Fuzzy Information, v.II, CRC Press, Boca Raton, FL 1987.
I.Cziszar, I-divergence geometry of probability distributions and minimization problems, Ann.Prob.,3,1975.
D. Dubois and H. Prade, Possibility theory, Plenum Press, New York 1988.
D. Dubois and H. Prade, Properties of measures of information in evidence and possibility theories, Fuzzy Sets Syst.,2,24,1987.
S. Guiasu, Information Theory and Applications, McGraw Hill, New York 1977.
M.Higashi and G. Klir, On the notion of distance representing information closeness, Int. J. Gen. Sys.,9,1983.
M. Higashi and G.Klir, Measures of uncertainty and information based on possibility distributions Int.J.Gen.Sys., 8,1982.
G. Hardy, J. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge 1934.
E.Jaynes, On the rationale of maximum entropy methods, Proc. IEEE, 70, 1982.
G. Klir and M. Mariano, On the uniqueness of possibilistic measure of uncertainty and information, Fuzzy Sets Syst.,2,24,1987.
A.Ramer, Structure of possibilistic information metrics and distances, Int. J. Gen.Sys., 17,1990.
A.Ramer, A note on defining conditional probability, Am.Math.Monthly, 1990.
A.Ramer, Concepts of fuzzy information measures on continuous domains, Int.J.Gen.Sys., 17,1990.
A.Ramer, Conditional possibility measures, Cybern. Syst.,20,1989.
A. Ramer and L. Lander, Classification of possibilistic uncertainty and information functions, Fuzzy Sets Syst.,2,24,1987.
C.Shannon, A mathematical theory of communication, Bell. Sys. Tech.J.,27,1948.
J.Shore and R.Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Trans. Inf. Theory, IT-26, 1980.
R. Yager, Aspects of possibilistic uncertainty, Int. Man-Machine Stud.,12,1980.
L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst.,1,3,1978.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ramer, A. (1991). Information theory based on fuzzy (possibilistic) rules. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028118
Download citation
DOI: https://doi.org/10.1007/BFb0028118
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54346-6
Online ISBN: 978-3-540-47580-4
eBook Packages: Springer Book Archive