User:Helgus/ Eventology and its applications
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The basic achievements of mathematical eventology in actual fileds of application are:
- eventological portfolio analysis (statement and the decision of inverse eventological Markowitz’s problems (Harry Markovitz, the Nobel Prize on economy, 1990);
- eventological models of supply and demand (eventological substantiation and expanded interpretation of classical market «Marchall’s cross» - «supply and demand cross»);
- eventological interpretation of Herrnstein’s experiment with pigeons (1961) in psychology («The mind appears there and then, where and when there is an ability to make a probabilistic choice» - Vladimir Lefebvre, University of California at Irvin, 2003);
- eventological models of «Vickrey auctions» (William Vickrey, the Nobel Prize on economy, 1996);
- eventological basis and expansion of prospect theory (Daniel Kahneman and Amos Tversky) (Daniel Kahneman, the Nobel Prize on economy, 2002);
- eventological generalization of methods of experimental economics (Vernon Smith, the Nobel Prize on economy, 2002); and also in
- statistical geometry (Dietrich Stoyan): the new notion of set-means for random sets (1975).
Following fields have been developed recently:
- eventological theory of dependencies of random events including theory of eventological copula;
- eventological system analysis,
- eventological decision theory and
- eventological theory of set-preferences (eventological explanation for a long time known Blyth’s paradox in preference theory).
[edit] Applications of eventological theory
- Eventological theory of fuzzy events
- Eventological foundation of Kahneman and Tversky theory
- Eventological portfolio analysis
- Eventological system analysis
- Eventology of making decision
- Eventological theory of set-preferences
- Eventological foundation of economics
- Eventological scoring
- Eventological direct and inverse Markowitz's problems
- Eventological market "Marshall's Cross"
- Eventological explaination of K.Blayh's paradox in theory of preferences
[edit] References
- ^ Blyth C.R. (1972) On Simpson's Paradox and the Sure --- Thing Principle. - Journal of the American Statistical Association, June, 67, P.367-381.
- ^ 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.
