Merging Interval-Based Possibilistic Belief Bases

In the last decade, several approaches were introduced in literature to merge multiple and potentially conflicting pieces of information. Within the growing field of application favourable to distributed information, data fusion strategies aim at providing a global and consistent point of view over a set of sources which can contradict each other. Moreover, in many situations, the pieces of information provided by these sources are uncertain. Possibilistic logic is a well-known powerful framework to handle such kind of uncertainty where formulas are associated with real degrees of certainty belonging to [0, 1]. Recently, a more flexible representation of uncertain information was proposed, where the weights associated with formulas are in the form of intervals. This interval-based possibilistic logic extends classical possibilistic logic when all intervals are singletons, and this flexibility in representing uncertain information is handled without extra computational costs. In this paper, we propose to extend a well known approach of possibilistic merging to the notion of interval-based possibilistic knowledge bases. We provide a general semantic approach and study its syntactical counterpart. In particular, we show that convenient and intuitive properties of the interval-based possibilistic framework hold when considering the belief merging issue.