Combining Fuzzy and Probabilistic Knowledge Using Belief Functions

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Claude Langrand
Hung T. Nguyen

Publication Date

10-2001

Comments

UTEP-CS-01-27.

Published in: Proceedings of the Second Vietnam-Japan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'2001, Hanoi, December 7-8, 2001, pp. 191-198.

Abstract

Some knowledge comes in probabilistic terms, some in fuzzy terms. These formalisms are drastically different, so it is difficult to combine the corresponding knowledge. A natural way to combine fuzzy and probabilistic knowledge is to find a formalism which enables us to express both types of knowledge, and then to use a combination rule from this general formalism. In this paper, as such a formalism, we propose to use belief functions. For the case when the universe of discourse is the set of all real numbers, we derive new explicit easy-to-compute analytical formulas for the resulting combination.