User:Helgus/ Theory of fuzzy events (Fuzzy mathematical eventology)
Theory of fuzzy events (fuzzy mathematical eventology) is a mathematical language of eventology – a new direction the probability theory; is based on the principle of eventological duality of notion of a set of random events and a random set of events; studying eventological distributions of a set of random events and eventological structures of its dependencies.
Fuzzy mathematical eventology (theory of fuzzy events) studies fuzzy events and sets of fuzzy events, its probability distributions and structures of its dependencies and generalizes fuzzy set theory[1][2][3][4][5], possibility theory[6] and Dempster-Shafer theory of evidence[7];
The basic eventological terms
[edit]- Event, probability and value
- Conditional event, conditional probability and conditional value
- Set of events and random set of events
- Event-terrace
- Eventological duality
- Eventological distribution
- Eventological language
- Eventological glossary
- Additive set-functions and measures
- Set-formulae of Mobius inversing events-terraces
- Formulae of Mobius inversing eventological distributions
- Set-means characteristics of a random set of events
- Eventological Bayes's theorem
- Frechet's covariances and correlations
- The structure of dependencies of a set of events
- Eventological copula
References
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- ^ Dubois D., H.Prade (1988) Possibility theory. - New York: Plenum Press.
- Feynman R.P. (1982) Simulating physics with computers. - International Journal of Theoretical Physics, Vol. 21, nos. 6/7, 467-488.
- ^ Fr'echet M. (1935) G'en'eralisations du th'eor'eme des probabilit'es totales - Fundamenta Mathematica. - 25.
- Hajek, Alan (2003) Interpretations of Probability. - The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N.Zalta (ed.)
- ^ Herrnstein R.J. (1961) Relative and Absolute strength of Response as a Function of Frequency of Reinforcement. - Journal of the Experimental Analysis of Behavior, 4, 267-272.
- ^ Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decisios under risk. - Econometrica, 47, 313-327.
- ^ Lefebvre V.A. (2001) Algebra of conscience. - Kluwer Academic Publishers. Dordrecht, Boston, London.
- ^ Markowitz Harry (1952) Portfolio Selection. - The Journal of Finance. Vol. VII, No. 1, March, 77-91.
- ^ Marshall Alfred A collection of Marshall's published works
- ^ Nelsen R.B. (1999) An Introduction to Copulas. - Lecture Notes in Statistics, Springer-Verlag, New York, v.139.
- ^ Russell Bertrand (1945) A History of Western Philosophy and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day, New York: Simon and Schuster.
- ^ Russell Bertrand (1948) Human Knowledge: Its Scope and Limits, London: George Allen & Unwin.
- Schrodinger Erwin (1959) Mind and Matter. - Cambridge, at the University Press.
- ^ Shafer G. (1976). A Mathematical Theory of Evidence. – Princeton University Press.
- ^ Smith Vernon (2002) Nobel Lecture.
- ^ Stoyan D., and H. Stoyan (1994) Fractals, Random Shapes and Point Fields. - Chichester: John Wiley & Sons.
- ^ Tversky A., Kahneman D. (1992) Advances in prospect theory: cumulative representation of uncertainty. - Journal of Risk and Uncertainty, 5, 297-323.
- ^ Vickrey William Paper on the history of Vickrey auctions in stamp collecting
- ^ Zadeh L.A. (1965) Fuzzy Sets. - Information and Control. - Vol.8. - P.338-353.
- ^ Zadeh L.A. (1968) Probability Measures of Fuzzy Events. - Journal of Mathematical Analysis and Applications. - Vol.10. - P.421-427.
- ^ Zadeh L.A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. – Fuzzy Sets and Systems. - Vol.1. - P.3-28.
- ^ Zadeh L.A. (2005). Toward a Generalized Theory of Uncertainty (GTU) - An Outline. - Information sciences (to appear).
- ^ Zadeh L.A. (2005). Toward a computational theory of precisiation of meaning based on fuzzy logic - the concept of cointensive precisiation. - Proceedings of IFSA-2005 World Congress.} - Beijing: Tsinghua University Press, Springer.