Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence
This work addresses foundational issues in uncertainty representation for researchers in fuzzy logic and evidence theory, offering a unified framework that is incremental but broadens existing theories.
The paper tackles the problem of representing and combining uncertain and fuzzy evidence by developing a general theory of epistemic random fuzzy sets, which unifies Dempster-Shafer theory and possibility theory, and demonstrates its application to statistical inference to reconcile possibilistic likelihood with Bayesian inference.
We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.