T-norm and uninorm-based combination of belief functions

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.