Geodesic
Postulating the theory of experience and chance
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 705-717.

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of the paper is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory in a number of general concepts of the theory of experience and chance. The main result of this work is the axiom of co$\sim$event, intended for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating the theory of experience and chance can be imagined, however, in this work a preference is given to a system of postulates that is able to describe in the most simple manner the results of what I call an experienced-random experiment.
Keywords: eventology, event, co$\sim$event, experience, to experience, to happen, to occur, theory of experience and chance, theory of co$\sim$events, axiom of co$\sim$event, probability, believability, certainty, probability theory, believability theory, certainty theory.
Mots-clés : chance 
@article{JSFU_2019_12_6_a6,
     author = {Oleg Yu. Vorobyev},
     title = {Postulating the theory of experience and chance},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {705--717},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a6/}
}
TY  - JOUR
AU  - Oleg Yu. Vorobyev
TI  - Postulating the theory of experience and chance
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 705
EP  - 717
VL  - 12
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a6/
LA  - en
ID  - JSFU_2019_12_6_a6
ER  - 
%0 Journal Article
%A Oleg Yu. Vorobyev
%T Postulating the theory of experience and chance
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 705-717
%V 12
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a6/
%G en
%F JSFU_2019_12_6_a6
Oleg Yu. Vorobyev. Postulating the theory of experience and chance. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 705-717. http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a6/

[1] P.A.M. Dirac, “A new notation for quantum mechanics”, Proceedings of the Cambridge Philosophical Society, 35 (1939), 416–418 | DOI | MR

[2] P.A.M. Dirac, The principles of quantum mechanics, Yeshiva University, New York, 1964 | MR

[3] D. Dubois, H. Prade, “Possibility theory, probability theory and multiple-valued logics: A clarification”, Annals of Mathematics and Artificial Intelligence, 32 (2001), 35–66 | DOI | MR | Zbl

[4] G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton, NJ, 1976 | MR | Zbl

[5] O. Yu.Vorobyev, Eventology, Siberian Federal University Press, Krasnoyarsk, Russia, 2007

[6] O. Yu.Vorobyev, “Contemporary uncertainty theories: An eventological view”, Proc. of the VIII Intern. FAM Conf. on Financial and Actuarial Mathematics and Related Fields, v. 1, SFU, Krasnoyarsk, 2009, 26–34

[7] O. Yu. Vorobyev, “Eventology versus contemporary theories of uncertainty”, Proc. of the XII Intern. EM conference on eventological mathematics and related fields, SFU, Krasnoyarsk, 2009, 13–27

[8] O. Yu. Vorobyev, “An element-set-labelling a Cartesian product by measurable binary relations which leads to postulates of the theory of experience and chance as a theory of co$\sim$events”, Proc. of the XV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics $\$ the Workshop on Hilbert's Sixth Problem, SFU, Krasnoyarsk, 2016, 9–24

[9] O. Yu. Vorobyev, “Postulating the theory of experience and chance as a theory of co$\sim$events (co$\sim$beings)”, Proc. of the XV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics the Workshop on Hilbert's Sixth Problem, SFU, Krasnoyarsk, 2016, 25–43, arXiv: 1801.07147

[10] O. Yu. Vorobyev, “Theory of dual co$\sim$event-based means”, Proc. of the XV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics $\$ the Workshop on Hilbert's Sixth Problem, SFU, Krasnoyarsk, 2016, 44–93

[11] L.A. Zadeh, “Fuzzy sets”, Information and Control, 8:3 (1965), 338–353 | DOI | MR | Zbl

[12] L.A. Zadeh, A note on similarity-based definitions of possibility and probability, Information Sciences, 267 (2014), 334–336 | DOI | MR | Zbl

[13] H.-J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic Publishers, Dordrecht, Netherlands, 2001 | MR