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...

A general forecasting correcting formula, as a framework for long-use and standardized forecasts, is created. The formula provides new forecasting resources and new possibilities for expansion of forecasting including economic forecasting into the areas of municipal needs, middle-size and...

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.

An introduction to interval analysis of distributions, as a new direction of interval analysis, is presented, including illustrated examples. New formulas and additional restrictions for intervals of moments, including mean value, are obtained. Among them are Novoselov formulas for moments and...

The theorem of existence of the ruptures in the probability scale was proved in 2010. The theorem is used to analyze and to partially answer to the basic questions of insurance. The question is “To insure or not”. The goal of this paper is to reveal pure mathematical aspects of insurance...

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 principle of uncertain future: the probability of a future event contains a degree of (hidden) uncertainty. As a result, this uncertainty (in a sense, similar to vibrations, fluctuations) pushes the probability value back from the bounds to the middle of its range (from ~100% and ~0% to the...