Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities

被引：384

作者：

Dubois, Didier ^{[1
]}

Foulloy, Laurent ^{[2
]}

Mauris, Gilles ^{[2
]}

Prade, Henri ^{[1
]}

机构：

[1] Inst. de Rech. en Info. de Toulouse, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

[2] Lab. Info., Syst., Traitement I./C., Universite de Savoie, BP 806, 74016 Annecy, France

来源：

Reliable Computing | 2004年 / 10卷 / 04期

关键词：

Computational methods - Functions - Mathematical models - Mathematical transformations - Monte Carlo methods - Probability - Problem solving;

D O I：

10.1023/B:REOM.0000032115.22510.b5

中图分类号：

学科分类号：

摘要：

Apossibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the confidence intervals of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

引用

页码：273 / 297