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...

В настоящей заметке, для удобства российских и русскоговорящих читателей, на русском языке кратко рассмотрено содержание книги "Введение в Суб-Интервальный...

The proof of the theorem of existence of the ruptures, namely the proof of maximality, is improved. The theorem may be used in economics and explain the well-known problems such as Allais’ paradox. Illustrated examples of ruptures are presented.

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 report, that has been presented on the Third International Conference on Mathematical Modelling of Social and Economical Dynamics MMSED-2010, is devoted to applications of the modern achievements of probability theory to economics. The "four-fold-pattern" paradox is used as an example of...

The definition of an arrangement infringement has been given. Several characteristics of hurricanes as large-scale events and the objectives for the first stages of an insurance data analysis have been sketched out. Scale hypotheses, insurance and investment problems have been formulated. The...