Discrete labels and rich foci in theory of evidence

Evidence theory allows to build a large family of combination operators, based mostly on intersections and unions between the focal elements expressed by the experts, and multiplications and additions on the masses affected to these focal elements. We explore algebraic structures where these operators behave differently, masses being linguistic labels, or focal elements being more, or less, than an union of singletons of a discernment space. In some cases, we have to forget this space and the notion of singleton to place ourselves in the space of possible focal elements. We propose three new structures for linguistic labels, replacing masses. We show how to adapt the theory of evidence to six constrained spaces for the focal elements expressed by the experts.