A theorem of existence of ruptures in the probability scale has been proven. The theorem can be used, e.g., in economics and forecasting. It can assist to solve paradoxes such as Allais paradox and the “four-fold-pattern” paradox and to create the correcting formula of forecasting.

The theorem of existence of the ruptures in the probability scale has been proved for a discrete case. The theorem can be used, e.g., in economics and forecasting. It can assist to solve paradoxes such as Allais paradox and the “four-fold-pattern” paradox and to create the correcting formula...

The theorem of existence of ruptures in the probability scale has been proved. The theorem can be used, e.g., in economics and forecasting. It can assist to solve paradoxes such as Allais paradox and the “four-fold-pattern” paradox and to create the correcting formula of forecasting.

The theorem of existence of the ruptures in the probability scale is used to solve some problems of modelling of the economic behavior of a man. The “four-fold-pattern” paradox is considered as an example of such solution.

The principle of uncertain future: the probability of a future event contains an (hidden) uncertainty. The first consequence of the principle: the real values of high probabilities are lower than the preliminarily determined ones; conversely, the real values of low probabilities can be higher...

This paper is a brief review and development of a part of the plenary report in the Moscow Institute of Physics and Technology. Two existing tools of sub-interval analysis (the sub-interval arithmetic, including incomplete data analysis, and sub-interval images) are reviewed and elements of two...

A forbidden zones theorem, mathematical approach and model are proposed in the present article. In particular, the approach supposes that people decide as if there were some biases of the expectations of measurement data. The article is motivated by the need of a theoretical support for the...

In this post the contents of the book "Introduction to Sub-Interval Analysis and its Applications" are briefly reviewed in the Russian language, for the convenience of Russian and Russian-speaking readers.

This short paper is devoted to two items: 1) An analysis of Prelec’s weighting function at the probability p = 1 is highlighted (this analysis was performed by R. Duncan Luce in two articles with Ragnar Steingrimsson and János Aczél and here is referred to as the “Luce problem”). 2) The...

The article represents a brief review and development of the plenary report in the Moscow Institute of Physics and Technology. Three existing tools of sub-interval analysis (sub-interval arithmetic, incomplete data analysis and images) are reviewed and elements of two new tools (sub-interval...