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Eventology

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Eventology (from lat. eventum, eventusevent, outcome, success, destiny and + logos) [20] is a scientific theory that studies eventful nature of a mind [14] and a matter [14]; a huge event variety of subjects (mind) and objects (matter); an event structure and event-valued functions; an origin, expansion, and development of sets of events; connections of events with each other; establishes the general and particular laws of eventful existence of a mind and a matter in all event occurrences and event properties.


In a basis of eventology lays remarks, which now seems obvious: «the matter and the mind is simply convenient way of linkage of events together» (Russell [12, 13], 1946; Vorob’ov, 2001) and «the mind appears there and then, where and when there is an ability to make a probabilistic choice» (Lefebvre [6, 8], 2003). Using these remarks as initial axioms and also well-developed apparatus of mathematical eventology (crisp and fuzzy), eventology introduces mind directly as an eventological distribution of set of events in scientific and mathematical research and understands an eventological movement of events (movement of a matter or a mind) as changing the eventological distributions.


From the point of eventology view, the probability is a property of an event: an event has a probability the same as the probability has an event; subjective probability [5] is a property of a subjective event. Such point of view allows to develop the eventological theory of fuzzy events which exclusively from positions of Kolmogorov’s axiomatics of probability theory offers the strictly proved general approach to the eventological description of various kinds of fuzziness and uncertainty, including those kinds to which possibility theory [2], Dempster-Shafer theory of evidence [15], fuzzy sets and fuzzy logic of Zadeh [21, 22, 23, 24, 25], etc. are devoted.

Alongside with philosophical questions, eventology also mentions economic, social and other questions in different applied fields of natural and human sciences (see «Eventology and its applications»).


Historical survey

The first isolated attempts to cognize a mind and a matter from the point of view of an event, have been made during antique times (Aristotle, Plato, Sokrat). Elaborated through Renaissance antique ideas initiated modern scientific knowledge. Rapt observations upon event occurrence laid the foundation of probability theory in the 16th century (Pascal, Ferma). In the beginning of the 20th century it has turned into the scientific discipline, which leaned over mathematical definition of event as a subset of space of elementary events (Kolmogorov, 1933); basically it was intended for «calculating probabilities of events from probabilities of other events» («Mathematical encyclopedic dictionary» (ed. Yu.V.Prokhorov), MED, 1988; Encyclopedia «Probability and Mathematical Statistics» (ed. Yu.V.Prokhorov), PMS, 1995). During the 19-20 c. experimental methods of observing upon events was thriving, as the result mathematical statistics arose – the scientific discipline focused on the solving problems, which are in the certain sense inverse to problems of probability theory, – estimation of probability distributions by results of observations upon events.


The further development of probability theory has expanded the known eventful world of subjects and objects; has deepened the conception of it's eventful structure. At the same time speculative theories of eventful development and properties of a mind and a matter still prevailed. Sharply increased number of studied eventful objects (new eventful methods, penetration eventful techniques in various areas of knowledge), accumulation and differentiation of eventful knowledge formed a variety of application fields for eventful methodology.


One of the main achievements on a boundary of millenia is an association of separated eventful approaches and methods by the general name – «eventology» (the scientific theory directed on studying sets of events), and also creation of mathematical eventology (crisp and fuzzy) – the new branch, which has arisen within the probability theory. It studies eventological distributions of sets of events, structures of its dependences and leans over the new principle of eventological duality of notion «a set of random events» and «a random set of events»


The development of eventology in 21 century has two characteristic and interconnected tendencies. On the one hand, mathematical eventology develops; it has reached amazing successes, since 90th years of the last century has opened and isolated mathematical bases of the theory of dependences of sets of events. On the other hand, the aspiration to complete synthetic eventful knowledge of a mind and a matter has incited the eventological branches studying eventful properties of a mind and a matter at all structural levels of it's organization.


Among the last achievements of eventology are: – the eventological portfolio analysis, which allowed to put and solve so-called inverse eventological Markowitz’s problem (Harry Markowitz [9], the Nobel Prize, 1990) - unknown before. Discovering eventological basis of market «Marshall’s cross» [10] («supply and demand cross») in economics; theory «William Vickrey auctions» (William Vickrey [19], the Nobel Prize, 1994); the modern prospect theory (Daniel Kahneman [7] [18], the Nobel Prize, 2002), and, at last, the eventological system analysis with an object of research - sets of events – theoretical models of complex systems of events, which describes structures of system connections of any complexity with exhaustive completeness, resulted into fundamental eventological changes.


In each of the areas named above these eventological discoveries have allowed to look at problems with new eventful points of view. This has immediately led to new unexpected statements of problems, which became solvable with eventological methods, adding and improving each of the theories.

Practical significance of eventological researches and methods for a number of the most urgent applied areas, and also penetration into these researches of mathematical ideas and methods of the theory of random events have advanced eventology and the mathematical eventology from the beginning 21 century to the foremost boundaries of natural sciences and human sciences.


Eventological sections on International conferences

  • (2003, Moscow University, Moscow, chairman. prof. A.N.Shiryaev) International Conference "Kolmogorov and contemporary mathematics";
  • (2005, IASTED'2005, Novosibirsk) II International Conference "Automation, Control and Information Technology"
    (session “Eventology of random-fuzzy events”, chairman prof. O.Yu.Vorob’ov)
  • (2005, IFSA'2005, Beijing, chairman prof. L.A.Zadeh) XI International Fuzzy Systems Association World Congress
    (session “Eventology of fuzzy events”, chairman prof. O.Yu.Vorob’ov)
  • (2005, EUSFLAT'2005, Barselona, chairman prof. L.A.Zadeh) IV International Conference of European Society for Fuzzy Logic and Technology
    (session “Eventological theory of fuzzy events”, chairman prof. O.Yu.Vorob’ov)
  • (2006, IPMU'2006, Paris, chairman prof. L.A.Zadeh, keynote speaker D.Kahneman) XI International Conference “Information Processing and Management of Uncertainty”
    (session E22 “Eventology and Unceratainty”, chairman prof. O.Yu.Vorob’ov)

PhD theses on eventology (phys.-math. sciences, in Russian)

  • Vorob'ov Alexei (1998) Direct and inverse problems for models of spreading space risks. Krasnoyarsk: ICM of RAS
  • Goldenok Ellen (2002) Modeling dependence and interaction structures of random events in statistical systems. Krasnoyarsk: KGTEI
  • Kupriyanova Tatyana (2002) A problem of classification of subsets of random set and its application. Krasnoyarsk: Krasnoyarsk University
  • Semenova Daria (2002) Methods of constructing statistical dependencies of portfolio operations in market systems. Krasnoyarsk: ICM of RAS
  • Fomin Andrew (2002) Set-regressional analysis of dependencies of random events in statistical systems. Krasnoyarsk: ICM of RAS
  • Klochkov Svyatoslav (2006) Eventological models of distributing and filling resources. Krasnoyarsk: KGTEI
  • Baranova Iren (2006) Methods of bipartitional sets of events in eventological analysis of complicated systems. Krasnoyarsk: Krasnoyarsk University
  • Tyaglova Hellena (2006) Game theory methods of analysis of random sets of events. Krasnoyarsk: ICM of RAS
  • Tarasova Olga (2007) Grid and regression algorithms for approximation of complicated systems of events. Krasnoyarsk: ICM of RAS


Bibliography (in English)

  • Vorob'ov O.Yu. (1991) Set-summation. Soviet Math. Dokl. 1991, Vol.43,p.747-752
  • Vorob'ov O.Yu. (1993) The calculus of set-distribution. Rissian Acad. Sci., Dokl. Math., 1993, Vol.46, 301-306.
  • Vorob'ov O.Yu., A.O.Vorob'ov (1994) Summation of set-additive functions anf the Mobius inversion formula. Russian Acad. Sci. Dokl. Math., vol. 49, No. 2, 340-344.
  • Stoyan Dietrich, and Helga Stoyan (1994) Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. John Wiley and Sons. Chichester, New York
    (pp.107-116: Vorob'ov's means of a random set)
  • Vorob'ov O.Yu., A.O.Vorob'ov (1996) Inverse problems for generalized Richardson's model of spread. Computational Fluid Dynamics'96, John Wiley & Sons, 104-110.
  • Vorob'ov O.Yu. (1996) A random set analysis of fire spread. Fire Technology, NFPA (USA), v.32, N 2, 137--173.
  • Vorob'ov Oleg Yu., Arcady A. Novosyolov, Konstantin V. Simonov, and Andrew Yu. Fomin (2001) Portfolio Analysis of Financial Market Risks by Random Set Tools. Risks in Investment Accumulation Products of Financial Institutions. Simposium Proceedings held in January 1999, New York. Schaumburg, USA: The Society of Actuaries, 43--66.

Bibliography (in Russian)

  • Vorob'ov Oleg (1978) Probabilistic set modeling. — Novosibirsk: Nauka. — 131 p.
  • Vorob'ov Oleg (1984) Mean measure modeling. — Moscow: Nauka. — 133 p.
  • Vorob'ov Oleg (1993) Set-summation. — Novosibirsk: Nauka. — 137 p.
  • Kovyazin S.A. (1999) Mean measure set. — Probability and Mathematical Statistics. Encyclopaedia. Ed. Yu.V.Prokhorov. Moscow: BRE.
    (Mean measure set: Vorob’ov’s means. – p.644.)
  • Vorob'ov Oleg (2006) Introduction to eventology. — Krasnoyarsk: ICM of RAS, Krasnoyarsk University. — 466 p.
  • Vorob'ov Oleg (2006) Eventology. — Krasnoyarsk: ICM of RAS, Krasnoyarsk University. — 347 p.
  • Vorob'ov Oleg (2007, to appear) Eventology and its applications. — Krasnoyarsk: ICM of RAS, Krasnoyarsk University. — 512 p.

References

  • [1] Blyth C.R. (1972) On Simpson's Paradox and the Sure --- Thing Principle. - Journal of the American Statistical Association, June, 67, P.367-381.
  • [2] Dubois D., H.Prade (1988) Possibility theory. - New York: Plenum Press.
  • [3] Feynman R.P. (1982) Simulating physics with computers. - International Journal of Theoretical Physics, Vol. 21, nos. 6/7, 467-488.
  • [4] Fr'echet M. (1935) G'en'eralisations du th'eor'eme des probabilit'es totales - Fundamenta Mathematica. - 25.
  • [5] Hajek, Alan (2003) Interpretations of Probability. - The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N.Zalta (ed.)
  • [6] 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.
  • [7] Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decisios under risk. - Econometrica, 47, 313-327.
  • [8] Lefebvre V.A. (2001) Algebra of conscience. - Kluwer Academic Publishers. Dordrecht, Boston, London.
  • [9] Markowitz Harry (1952) Portfolio Selection. - The Journal of Finance. Vol. VII, No. 1, March, 77-91.
  • [10] Marshall Alfred A collection of Marshall's published works
  • [11] Nelsen R.B. (1999) An Introduction to Copulas. - Lecture Notes in Statistics, Springer-Verlag, New York, v.139.
  • [12] 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.
  • [13] Russell Bertrand (1948) Human Knowledge: Its Scope and Limits, London: George Allen & Unwin.
  • [14] Schrodinger Erwin (1959) Mind and Matter. - Cambridge, at the University Press.
  • [15] Shafer G. (1976). A Mathematical Theory of Evidence. – Princeton University Press.
  • [16] Smith Vernon (2002) Nobel Lecture.
  • [17] Stoyan D., and H. Stoyan (1994) Fractals, Random Shapes and Point Fields. - Chichester: John Wiley & Sons.
  • [18] Tversky A., Kahneman D. (1992) Advances in prospect theory: cumulative representation of uncertainty. - Journal of Risk and Uncertainty, 5, 297-323.
  • [19] Vickrey William Paper on the history of Vickrey auctions in stamp collecting
  • [20] Vorob'ov O.Yu. Eventology. - Krasnoyarsk: Siberian Federal University. - 2007. - 435pp.
  • [21] Zadeh L.A. (1965) Fuzzy Sets. - Information and Control. - Vol.8. - P.338-353.
  • [22] Zadeh L.A. (1968) Probability Measures of Fuzzy Events. - Journal of Mathematical Analysis and Applications. - Vol.10. - P.421-427.
  • [23] Zadeh L.A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. – Fuzzy Sets and Systems. - Vol.1. - P.3-28.
  • [24] Zadeh L.A. (2005). Toward a Generalized Theory of Uncertainty (GTU) - An Outline. - Information sciences (to appear).
  • [25] 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.

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