A Boolean generalization of the Dempster-Shafer construction of belief and plausibility functions

Rok, strany: 1999, 117 - 125

The present paper focuses on the relation of boolean fuzzy sets with the Dempster-Shafer theory of evidence. It is shown that a $B$-fuzzy set is actually a boolean basic probability assignment in $X$. This defines $B$-possibility and $B$-necessity measures which play the role of $B$-upper and $B$-lower probabilities. If $( B, p)$ is a probability algebra then we have a way to quantity these functions and these are shown to be the general plausibility and belief measures used as the basis of the theory of evidence. In the particular case where $ B$ is a power set algebra, we also show that the above construction coincides with the one presented in Dempster's original work.

ISO 690:

Markakis, G. 1999. A Boolean generalization of the Dempster-Shafer construction of belief and plausibility functions. In Tatra Mountains Mathematical Publications, vol. 16, no.1, pp. 117-125. 1210-3195.

APA:

Markakis, G. (1999). A Boolean generalization of the Dempster-Shafer construction of belief and plausibility functions. Tatra Mountains Mathematical Publications, 16(1), 117-125. 1210-3195.