I don't have sufficient privileges on this site to create a tag, but I think that it would be useful to have a new tag imprecise-probability, which I would have applied, instead of four other somewhat misleading tags, to this question that I recently asked. [EDIT: There is at least one other question for which imprecise probability would be appropriate.]
Imprecise probability is a broad term for a class of concepts and methods that generalize ideas probability theory beyond real-valued probability measures. It's most readily viewed as a way of extending Bayesian probability to reflect uncertainty in degrees of confidence, but there are uses of the idea that don't necessarily reflect these Bayesian roots. The term covers, among other things, upper and lower previsions, upper and lower probability, interval-valued probability, credal sets, lower envelopes, and Choquet capacities (see e.g. Fabio Cozman's introductory page). There are at least three book-length mathematical treatments: Walley's classic Statistical Reasoning with Imprecise Probability, Augustin et al.'s Introduction to Imprecise Probability, and Troffaes and de Cooman's Lower Previsions (along with earlier works of mathematical philosophy such as Levi's The Enterprise of Knowledge). There is an academic society with regular conferences on the topic, the The Society for Imprecise Probability: Theories and Applications.
Imprecise probability is related to ideas for which we already have tags: probability-theory (obviously), fuzzy-logic and fuzzy-sets (the focus is usually on different axioms), and robust-statistics (since these make use of sets of probability measures). The expectation tag is also related, since upper and lower previsions generalize expectation. However, none of these tags seems correct for the topics mentioned at the beginning of the second paragraph above. I do think that "imprecise probability" is sometimes used in sense that allows it to overlap with the domains of the tags I just mentioned, but those tags nevertheless misleading for a question such as the one I asked.
Here's a possible tag description, copied from the SIPTA website:
Imprecise probability is understood in a very wide sense. It is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings, …) and quantitative modes (interval probabilities, belief functions, upper and lower previsions, …). Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete.
(Ellipses in the original.)