Towards a linguistic probability theory

The term "fuzzy probability" was first introduced in the 1970s but has since come to describe two distinct concepts which have been somewhat confused in the literature of the field. The first of these views fuzziness in probabilities as induced by fuzziness in the definition of events of interest, whereas the second uses fuzziness in probabilities as a way of modelling vagueness in subjective linguistic probability assignments. The difference between the two concepts of "fuzzy probability" examined is marked by relabelling the second "linguistic probability". An earlier attempt to provide a theory of such linguistic probabilities is then examined and found to place unreasonable restrictions on the choice of fuzzy probabilities. On the basis of this critique an improved theory is developed. Computational issues are then considered as a prelude to an example application: a Bayesian network with linguistically specified prior and conditional probabilities