User:Helgus/ Mathematical eventology

Mathematical eventology is a mathematical language of eventology; a new direction the probability theory; is based on the Kolmogorov axiomatics of probability theory added by two eventological principles: duality of notion of a set of random events and a random set of events and triad of notion (event, probability of event, value of event); studies eventological distributions — probability distributions of sets of events — and eventological structures of dependencies of sets of events.

Unlike probability theory, theory of random events focuses mainly on direct and regular studying of random events and their dependencies. — can be considered as the basic results of mathematical eventology.
 * Allocation of the theory of random events into an independent direction of probability theory;
 * Developing mathematical eventful language (eventological distribution, set of random events, random set of events, event-terrace, set-means and so on), based on eventological principles of duality and triad, including
 * crisp mathematical eventology (theory of random events) that studies random events and sets of random events, its probability distributions and structures of its dependencies;
 * fuzzy mathematical eventology (theory of fuzzy events) that studies fuzzy events and sets of fuzzy events, its probability distributions and structures of its dependencies and generalizes fuzzy set theory, possibility theory and Dempster-Shafer theory of evidence; and also
 * efficiency of theory of random events in many applied areas which is direct consequence of universality of mathematical event language

Major terms and fields of mathematical eventology

 * Eventological triad: (event, probability and value)
 * Probability of event
 * Value of event
 * Event, probability and value
 * Conditional event, conditional probability and conditional value
 * Value, information and entropy of event
 * Conditional value, conditional information and conditional entropy
 * Gibbsean eventological model "probability of event — value of event"
 * Eventological duality (between sets of events and random sets of events)
 * Random set of events (random event set)
 * Set of random events
 * Eventological distribution of a set of random events
 * Set-means of a random set of events
 * Set-means of a set of random events
 * Eventological theory of dependencies of events
 * Structures of dependencies of a set of events
 * Frechet's covariances and correlations of events
 * Eventological copula
 * Eventological Bayes's theorem
 * Eventological Mobius inversing
 * Set-formulae of Mobius inversing events-terraces
 * Formulae of Mobius inversing eventological distributions
 * Additive set-functions and measures

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

At bounds of eventology

 * Subjective events, subjective probability and subjective value
 * Gibbsean eventological model "probability of event — value of event"
 * The phantom eventological distributions