×

A Boolean generalization of the Dempster-Shafer construction of belief and plausibility functions. (English) Zbl 0949.03048

Boolean-valued set theory is known to be a model of all axioms of Zermelo-Fraenkel Set Theory, where the language of set theory has a well-defined and natural meaning in Boolean models. This implies that every notion of classical set theory (and of any mathematical theory formalized within classical set theory) can be directly translated to set theory.
In the paper under review this translation is done for the construction of plausibility and belief measures given basic probability assignment. This is a part of Dempster-Shafer evidence theory.
The author shows that this translation has good categorical properties and that in the case of power set algebra it coincides with the construction in Dempster’s original work.
There is no link to real world applications motivating this construction in a similar way as the original Dempster-Shafer theory was motivated by problems of, e.g., updating knowledge. The author concludes that the task of formulating a general Boolean evidence theory following the steps of Dempster and Shafer is left for future work. We can conclude that a substantial part of mathematical work is done in this paper.

MSC:

03E72 Theory of fuzzy sets, etc.
03E40 Other aspects of forcing and Boolean-valued models
28E10 Fuzzy measure theory
03B52 Fuzzy logic; logic of vagueness
PDFBibTeX XMLCite