The theory of dual co∼event means (original) (raw)

2016, Proc. of the XV Intern. FAMEMS-2016 Conf. on Financial and Actuarial Math and Eventology of Multivariate Statistics, Krasnoyarsk, SFU (Oleg Vorobyev ed.), 44-93

This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famems1, Vorobyev2016famems2} about the new theory of experience and chance as the theory of co~events. Here I introduce the concepts of two co~event means, which serve as dual co~event characteristics of some co~event. The very idea of dual co~event means has become the development of two concepts: mean-measure set \cite{Vorobyev1984} and mean-probable event \cite{Vorobyev2012fames4, Vorobyev2013sfu}, which were first introduced as two independent characteristics of the set of events, so that then, within the framework of the theory of experience and chance, the idea can finally get the opportunity to appear as two dual faces of the same co~event. I must admit that, precisely, this idea, hopelessly long and lonely stood at the sources of an indecently long string of guesses and insights, did not tire of looming, beckoning to the new co~event description of the dual nature of uncertainty, which I called the theory of experience and chance or the certainty theory. The constructive final push to the idea of dual co~event means has become two surprisingly suitable examples, with which I was fortunate to get acquainted in 2015, each of which is based on the statistics of the experienced-random experiment in the form of a co~event. Eventology, theory of experience and chance, event, co~event, experience, chance, to happen, to experience, to occur, probability, believability, mean-believable (mean-experienced) terraced bra-event, mean-probable (mean-possible) ket-event, mean-believable-probability (mean-experienced-possible) co~event, experienced-random experiment, dual event means, dual co~event means, bra-means, ket-means, Bayesian analysis, approval voting, forest approval voting.