A principled discussion of information combination rules in different representation settings

Depending on the representation setting, different combination rules have been proposed for fusing information from distinct sources. Moreover in each setting, different sets of axioms that combination rules should satisfy have been advocated, thus justifying the existence of alternative rules (usually motivated by situations where the behavior of other rules was found unsatisfactory). These sets of axioms are usually purely considered in their own settings, without in-depth analysis of common properties essential for all the settings. This paper introduces core properties that, once properly instantiated, are meaningful in different representation settings ranging from logic to imprecise probabilities. The following representation settings are especially considered: classical set representation, possibility theory, and evidence theory which is rich enough to include as particular cases i) sets (when there is one focal element), ii) probabilities (when focal elements are singletons), and iii) possibilities (when focal elements are nested). This unified discussion of combination rules across different settings is expected to provide some fresh look on some old but basic issues in information fusion.