To Properly Reflect Physicists' Reasoning about Randomness, We Also Need a Maxitive (Possibility) Measure

Authors

Andrei M. Finkelstein
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Scott A. Starks, The University of Texas at El PasoFollow
Hung T. Nguyen

Publication Date

2-2005

Comments

UTEP-CS-04-42a.

Published in Proceedings of the 2005 IEEE International Conference on Fuzzy Systems FUZZ-IEEE'2005, Reno, Nevada, May 22-25, 2005, pp. 1044-1049

Abstract

According to the traditional probability theory, events with a positive but very small probability can occur (although very rarely). For example, from the purely mathematical viewpoint, it is possible that the thermal motion of all the molecules in a coffee cup goes in the same direction, so this cup will start lifting up.

In contrast, physicists believe that events with extremely small probability cannot occur. In this paper, we show that to get a consistent formalization of this belief, we need, in addition to the original probability measure, to also consider a maxitive (possibility) measure.