Measures of uncertainty

In spite of the fact the engineers are familiar with the idea that physical systems can be modelled in various ways, it is often stated that probability theory is the only way of modelling uncertainties and degrees of belief about those uncertainties. The thesis advanced here is that within certain bounds (which are specified) there are many ways of representing uncertainty. In particular the ideas of probability and fuzzy sets are shown to be entirely compatible. A voting model is used to illustrate the argument before the basis of the formal treatment is outlined. Finally a set of conjectures are advanced about the types of problem that might best be tackled by probabilistic and fuzzy inference.