T-norm and uninorm-based combination of belief functions

Abstract

The distinctness assumption is a limitation to the use of the unnormalized Dempster's rule. Denoeux recently proposed an alternative rule, called the cautious rule, which does not rely on this assumption. He further showed that the cautious rule and the unnormalized Dempster's rule belong to two families of combination rules having different algebraic properties. This paper revisits this latter point: the cautious and unnormalized Dempster's rules can be seen as member of families of combination rules based on triangular norms and uninorms, respectively. Furthermore, both rules have a special position in their respective family: they are the least committed elements. This paper also provides a means of obtaining an infinity of rules in the family of uninorm-based combination rules.