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...

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 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 theorems of existence of the ruptures have been proved. The ruptures can exist near the borders of finite intervals and of the probability scale. The theorems can be used, e.g., in economics and forecasting.

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 article raises the question of possible existence of ruptures, gaps in the probability scale which are caused by noises, uncertainties. A hypothesis of existence of such ruptures may be used to solve a number of problems of, e.g., utility theory in economics. The calculations give the...

A possibility of the existence of a discontinuity of Prelec’s (probability weighting) function W(p) at the probability p = 1 is discussed. This possibility is supported by the Aczél–Luce question whether Prelec’s weighting function W(p) is equal to 1 at p = 1, by the purely mathematical...

A need for experiments on the certainty effect near the certainty (near the probability p = 1) is stated in this paper. The need supported by the Aczél–Luce question whether Prelec’s weighting function W(p) is equal to 1 at p = 1, by the purely mathematical restrictions and the...