Vorobyev, Oleg (2009): Eventology versus contemporary theories of uncertainty. Published in: XII International EM'2009 Conference, Program and Abstracts (20. February 2009): pp. 1331.

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Abstract
The development of probability theory together with the Bayesian approach in the three last centuries is caused by two factors: the variability of the physical phenomena and partial ignorance about them. As now it is standard to believe [Dubois, 2007], the nature of these key factors is so various, that their descriptions are required special uncertainty theories, which differ from the probability theory and the Bayesian credo, and provide a better account of the various facets of uncertainty by putting together probabilistic and setvalued representations of information to catch a distinction between variability and ignorance. Eventology [Vorobyev, 2007], a new direction of probability theory and philosophy, offers the original event approach to the description of variability and ignorance, entering an agent, together with his/her beliefs, directly in the frameworks of scientific research in the form of eventological distribution of his/her own events. This allows eventology, by putting together probabilistic and setevent representation of information and philosophical concept of event as cobeing [Bakhtin, 1920], to provide a unified strong account of various aspects of uncertainty catching distinction between variability and ignorance and opening an opportunity to define imprecise probability as a probability of imprecise event in the mathematical frameworks of Kolmogorov's probability theory [Kolmogorov, 1933].
Item Type:  MPRA Paper 

Original Title:  Eventology versus contemporary theories of uncertainty 
English Title:  Eventology versus contemporary theories of uncertainty 
Language:  English 
Keywords:  uncertainty, probability, event, cobeing, eventology, imprecise event 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General 
Item ID:  13961 
Depositing User:  Oleg Vorobyev 
Date Deposited:  12. Mar 2009 07:40 
Last Modified:  12. Feb 2013 18:15 
References:  [1] D. Dubois. Uncertainty theories: a unified view. IEEE Cybernetic Systems Conference, Dublin, Ireland, Invited Paper:49, 2326/09/2007. [2] O. Yu. Vorobyev. Eventology. Siberian Federal University, Krasnoyarsk, Russia, 2007, 435p. [3] M. M. Bakhtin. Speech Genres and Other Late Essays. University of Texas Press, Austin, 1986. [4] A. N. Kolmogorov. Grundbegriffe der Wahrscheinlichkeitrechnung. Ergebnisse der Mathematik, Berlin, 1933. [5] L. A. Zadeh. Fuzzy sets. Information and Control, 8 (3):338353, 1965. [6] L. A. Zadeh. Fuzzy algorithms. Information and Control, 12 (2):94102, 1968. [7] V. Novak, Perfilieva I., and J. Mockor. Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht, 1999. [8] E. Szmidt and J. Kacprzyk. Entropy and intuitionistic fuzzy sets. Proc. of 11th Intern. Conf. IPMU'2006, Paris, Les Cordeliers: EDK:23752382, 2006. [9] L. A. Zadeh. Fuzzy sets as the basis for a theory of possibility. Fuzzy Sets and Systems, 1:328, 1978. [10] D. Dubois and H. Prade. Possibility theory, probability theory and multiplevalued logics: A clarification. Annals of Mathematics and Artificial Intelligence, 32:3566, 2001. [11] D. Dubois. Belief structures, possibility theory and decomposable measures on finite sets. Computers and AI, 5:403416, 1986. [12] D. Dubois and H. Prade. Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, 1988. [13] D. Dubois and H. Prade. Fuzzy Sets and Systems. Academic Press, New York, 1988. [14] D. Dubois, H. Prade, and R. Sabbadin. Decisiontheoretic foundations of possibility theory. Eur. J. Operational Research, 128:459478, 2001. [15] A. P. Dempster. A generalization of bayesian inference. Journal of the Royal Statistical Society, Series B (Methodological), 30:205247, 1968. [16] G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ, 1976. [17] G. Shafer. Belief functions and possibility measures. J. C. Bezdek, ed., Analysis of Fuzzy Information, Boca Raton, FL, CRC Press, I: Mathematics and Logic:5184, 1987. [18] P. Smets and R. Kennes. The transferable belief model. Artifical Intelligence, 66:191234, 1994. [19] P. Smets. Showing why measures of quantified beliefs are belief functions. B. Bouchon and L. Foulloy and R.R. Yager (eds.), Intelligent Systems for Information Processing: From Representation to Applications, Amsterdam, Elsevier:265276, 2002. [20] P. Smets. Belief functions on real numbers. Int. J. Approx. Reasoning, 40 (3):181223, 2005. [21] P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London, 1991. [22] P. Walley. Towards a unified theory of imprecise probability. International Journal of Approximate Reasoning, 24:125148, 2000. [23] I. Couso, S. Moral, and P. Walley. A survey of concepts of independence for imprecise probabilities. Risk Decision and Policy, 5:165181, 2000. [24] G. de Cooman. A behavioural model for vague probability assesssments. Fuzzy Sets and Systems, 154:350358, 2005. [25] G. de Cooman. Imprecise probability models: special instances of belief structures. 3rd Workshop on Combning Probability and logic, Progic'07, England, University of Kent, Invited Lecture, 57 Sept 2007. [26] A. Neumaier. Clouds, fuzzy sets and probability intervals. Reliable Computing, 10:249272, 2004. [27] L. A. Zadeh. Generalized theory of uncertainty  principal concepts and ideas. Computational Statistics & Data Analysis, 51:1546, 2006. [28] Jacob Bernoulli. Ars conjectandi, opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola gallice scripta de ludo pilae reticularis. Thurneysen Brothers, Basel, 1713. [29] P. S. Laplace. A Philosophical Essay on Probabilities. English edition, Dover Publications Inc., New York (1951), 1814. [30] J. Venn. The Logic of Chance, 2nd ed. Macmillan and co, 1876, reprinted, New York, 1962. [31] H. Reichenbach. The Theory of Probability. University of California Press, Berkeley, 1949. [32] R. von Mises. Probability, Statistics and Truth, revised English edition. Macmillan, New York, 1957. [33] Sir R. A. Fisher. Statistical methods and scientific induction. J. R. Statist. Soc. (B), 17:6978, 1955. [34] Sir R. A. Fisher. Statistical Methods and Scientific Inference. Oliver and Boyd, Edinburgh, 1956. [35] J. S. Neyman. L'estimation statistique, traitee comme un probleme classique de probabilite. Actualites scientifiques et industrielles, Hermann et Cie., Paris, 739:2557, 1938. [36] J. S. Neyman and E. S. Pearson. On the problem of the most e±cient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, 231:289337, 1933. [37] K. R. Popper. The propensity interpretation of the calculus of probability and the quantum theory. S. Korner (ed.), The Colston Papers, 9:6570, 1957. [38] K. R. Popper. The propensity interpretation of probability. British Journal of the Philosophy of Science, 10:2542, 1959. [39] D. W. Miller. Critical Rationalism: A Restatement and Defence. Open Court, Chicago and Lasalle, Il, 1994. [40] R. N. Giere. Objective singlecase probabilities and the foundations of statistics. Logic, Methodology and Philosophy of Science, P. Suppes, et al., (eds.), IV, 1973. [41] J. H. Fetzer. Probabilistic explanations. PSA, 2:194207, 1982. [42] J. H. Fetzer. Probability and objectivity in deterministic and indeterministic situations. Synthese, 57:367386, 1983. [43] R. J. Solomonoff. A formal theory of inductive inference: Parts 1 and 2. Information and Control, 7:122; 224254, 1964. [44] R. J. Solomonoff. Complexitybased induction systems: Comparisons and convergence theorems. IEEE Transactions on Information Theory, IT24:422432, 1987. [45] T. Bayes. An essay towards solving a problem in the doctrine of chances. Two Papers by Bayes (1940, 1963); Pearson and Kendall (1970), 1763. [46] F. H. Knight. Risk, Uncertainty and Profit. Houghton Mi²in Company, The Riverside Press Cambridge, Boston and New York, 1921. [47] R. T. Cox. Algebra of Probable Inference. The John Hopkins University Press, 2001. [48] J. M. Keynes. A Treatise on Probability. Macmillan and Co, London, 1921. [49] R. Carnap. Logical Foundations of Probability. University of Chicago Press, Chicago, 1950. [50] F. P. Ramsey. Truth and probability, in foundations of mathematics and other essays. R. B. Braithwaite (ed.), Routledge & P. Kegan (1931), 1926. [51] B. de Finetti. La prevision: ses lois logiques, ses sources subjectives. Ann. lnst. Poineare, 7:168, 1937. [52] B. de Finetti. Theory of probability (2 vols.). J. Wiley & Sons, Inc., New York, 1974. [53] L. J. Savage. The Foundations of Statistics. John Wiley and Sons, New York, 1954. [54] F. J. Anscombe and R. J. Aumann. A definition of subjective probability. Annals of Mathematical Statistics, 34:199205, 1963. [55] D. Kahneman and A. Tversky. Subjective probability: A judgment of representativeness. Cognitive Psychology, 3:430454, 1972. [56] D. Kahneman and A. Tversky. Prospect theory: An analysis of decisions under risk. Econometrica, 47:313327, 1979. [57] D. Kahneman, P. Slovic, and A. Tversky. Judgment Under Uncertainty. Heuristics and Biases. Cambridge University Press, New York, 1982. [58] A. Tversky and D. Kahneman. Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5:297232, 1992. [59] B. O. Koopman. The axioms and algebra of intuitive probability. Ann. Math., 41:269292, 1940. [60] I. J. Good. The interface between statistics and philosophy of science. Statistical Science, 3 (4):386397, 1988. [61] G. L. S. Shackle. Decision, Order and Time in Human Affairs, 2nd edition. Cambridge University Press, UK, 1961. [62] G. L. S. Shackle. Epistemics and Economics: a Critique of Economic Doctrines. Cambridge University Press, UK, 1972. [63] G. L. S. Shackle. Imagination and the Nature of Choice. Edinburgh University Press, Edinburgh, 1979. [64] K. J. Arrow. Functions of a theory of behaviour under uncertainty. Metroeconomica, 11:1220, 1959. [65] G. Debreu. Economics Under Uncertainty. Economie Appliquee, Paris, 1960. [66] K. J. Arrow and L. Hurwicz. Decision making under ignorance. C. F. Carter and J.L. Ford (eds.), Uncertainty and Expectations in Economics. Essays in Honour of G.L.S. Shackle, Oxford: Basil Blackwell, 1972. [67] E. Karni. Probabilities and beliefs. Journal of Risk and Uncertainty, Kluwer Academic Publishers, 13 (3):249262, 1996. [68] E. T. Jaynes. Probability Theory: The Logic of Science. Cambridge University Press, UK, 2003. [69] J. M. Bernardo and A. F. M. Smith. Bayesian Theory, 2nd edition. Wiley, Chichester, 2006. [70] J. C. Harsanyi. Essays on Ethics, Social Behavior, and Scientific Explanation. Reidel Publishing Company, Dordrecht, Holland, 1976. [71] O. Yu. Vorobyev and G. M. Boldyr. On a new notion of conditional event and its application in eventological analysis. Notes of Krasnoyarsk State University, Phys. Math. Series, 1:152159, 2006. [72] G. Bohlmann. Die grundbegriffe der wahrscheinlichkeitsrechnung in ihrer anwendung auf die lebensversicherung. Atti del IV Congresso internazionale dei Matematici (Roma, 611 Aprile, 1908). Roma: Accademia dei Lincei, V.III. Sezione IIb, 1909. [73] S. N. Bernstein. Experience of an axiomatic foundation of probability theory. Messages of the Kharkov Mathematical Society, 15:209274, 1917. [74] R. von Mises. Grun°agen der wahrscheinlichkeitsrechnung. Math. Ztschr., 5:5299, 1919. [75] A. Lomnicki. Nouveaux fondements du calcul des probabilities. Fund. Math., 4:3471, 1923. [76] E. Borel. Sur les probabilities denombrables et leurs applications arithmetiques. Rend. Circ. Mat. Palermo, 26:247271, 1909. [77] M. M. Bakhtin. Toward a Philosophy of the Act. University of Texas Press, Austin (1993), St.Petersburg, 1920. [78] M. Holquist. Dialogism. Bakhtin and his World. 2nd edition. Routledge, Taylor & Francis Group, London and New York, 2002. [79] B. A. W. Russell. History of Western Philosophy and its Connections with Political and Social Circumstances from the Earlist Times to the Present Day. George Allen & Unwin, London, 1946. [80] B. A. W. Russell. Human Knowledge: Its Scope and Limits. George Allen & Unwin, London, 1948. [81] N. O. Lossky. The Intuitive Basis of Knowledge: An Epistemological Inquiry. Macmillan, London (1919), St.Petersburg, 1906. [82] H. Bergson. Matter and Memory. George Allen & Unwin, London, 1911. [83] M. Heidegger. Sein und Zeit. 1949. [84] S. Freud. Group Psychology and the Analysis of the Ego. Bantam Books, New York, 1960. [85] G. Deleuze. Logique du sens. Minuit, Paris, 1969. [86] D. Davidson. Essays on Actions and Events. Oxford University Press, New York, 1980. [87] D. Lewis. Philosophical Papers. Oxford University Press, Oxford, 1983. [88] A. Badiou. L'Etre et l'Evenement. Seuil, coll. L'ordre philosophique, Paris, 1988. [89] J. Kim. Supervenience and Mind: Selected Philosophical Essays. Cambridge University Press, New York, 1993. [90] R. J. Hernstein. Relative and absolute strength of response as a function of frequency of reinforcement. Journal of Experimental Analysis of Behavior, 4:267272, 1961. [91] V. A. Lefebvre. Algebra of Conscience. Kluwer Academic Publishers, Boston, 2003. [92] O. Yu. Vorobyev. Set Probabilistic Modeling. Nauka, Novosibirsk, Russia, 1978. [93] O. Yu. Vorobyev. Mean Measure Modeling. Nauka, Moscow, Russia, 1984. [94] O. Yu. Vorobyev. Set Summation. Nauka, Novosibirsk, Russia, 1993. [95] O. Yu. Vorobyev. Setsummation. Soviet. Math. Dokl., 43:747752, 1991. [96] O. Yu. Vorobyev. The calculus of the setdistributions. Russian Acad. Sci. Dokl. Math., 46:301306, 1993. [97] O. Yu. Vorobyev and A. O. Vorobyev. Summation of the setadditive functions and the mobius inversion formula. Russian Acad. Sci. Dokl. Math., 49 (2):340344, 1994. [98] O. Yu. Vorobyev. Eventological theory of fuzzy events. Proc. of 2nd IASTED Intern. MultiConf. ACITACA'2005, Novosibirsk: Institute of Computational Technologies:356363, 2005. [99] O. Yu. Vorobyev. Eventology of random fuzzy events. Proc. of 11th IFSA2005 World Congress, Beijing: Tsinghua University Press, Springer:330333, 2005. [100] O. Yu. Vorobyev. Eventological theory of random fuzzy events. Proc. of Joint. Intern. Conf. EUSFLATLFA'2005, Barcelona: Universitat Politectica de Catalunya:822831, 2005. [101] O. Yu. Vorobyev. Eventology and generalized theory of uncertainty. Proc. of 11th Intern. Conf. IPMU'2006, Paris, Les Cordeliers: EDK:27442753, 2006. [102] O. Yu. Vorobyev. Statistical eventology and financial and actuarial mathematics. Proc. of the I AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:2549, 2002. [103] O. Yu. Vorobyev and A. O. Vorobyev. On a new notion of setexpectation for a random set of events. Proc. of the II AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:2337, 2003. [104] O. Yu. Vorobyev. Physical foundations of eventology. Proc. of the II AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:3868, 2003. [105] O. Yu. Vorobyev. Theoretical foundations of eventology: structures of symmetric events. Proc. of the II AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:69113, 2003. [106] O. Yu. Vorobyev. Eventological rating reputation. Proc. of the III AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:3348, 2004. [107] O. Yu. Vorobyev. Eventological structures and eventological scoring. Proc. of the III AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:4989, 2004. [108] O. Yu. Vorobyev. Eventology of randomfuzzy events. Proc. of the IV AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:112169, 2005. [109] O. Yu. Vorobyev. Eventology of uncertainty. Proc. of the V AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:2655, 2006. [110] O. Yu. Vorobyev and N. L. Kim. Survey of theory of copula and eventologocal theory of copula. Proc. of the V AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:5694, 2006. [111] O. Yu. Vorobyev. Correlation and regression: eventological approach. Proc. of the VI AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:4671, 2007. [112] O. Yu. Vorobyev. Multivariate discrete distributions: eventological extension. Proc. of the VI AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:7297, 2007. [113] O. Yu. Vorobyev. Insight eventology. Proc. of the VI AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:98142, 2007. [114] O. Yu. Vorobyev. Eventology of choice. Proc. of the VI AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:143158, 2007. [115] O. Yu. Vorobyev. Eventological principles. Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:4046, 2008. [116] O. Yu. Vorobyev. On an eventologial relation "happens as", or "colapses in". Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:4750, 2008. [117] O. Yu. Vorobyev. Eventological htheorem. Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:5158, 2008. [118] O. Yu. Vorobyev. Gibbsean approximation of eventological distributions. Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:5964, 2008. [119] O. Yu. Vorobyev. Dependences of events. Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:6566, 2008. [120] O. Yu. Vorobyev. Multicovariances of events. Proc. of the VII AllRussian FAM Conf. on Financial and Actuarial Mathametics and Related Fields, Krasnoyarsk, Russia, 1:6781, 2008. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/13961 