This special issue contains a selection of articles from the First International Symposium on Imprecise Probabilities (ISIPTA). The symposium took place in Ghent, Belgium, during the month of June of 1999, under the organization of Gert de Cooman, Peter Walley, Sera®n Moral and Fabio Cozman. The success of the symposium led to the decision to hold a second one, to happen in Cornell, USA, in 2001. It is a pleasure to bring some of the research topics discussed at the symposium to an in¯uential journal; we hope readers will enjoy the articles with the same excitement we experienced during our stay in Ghent.
What was the scope of the symposium, and, consequently, what is the scope of this special issue? The term imprecise probability refers to any mathematical model that measures uncertainty without sharp, precise numerical probabilities. A variety of models have been developed with these characteristics; to name a few, probability intervals, sets of probabilities, capacities, belief functions, fuzzy measures, ordinal preferences. All these models, and several others, appear in the pages of this special issue. Such models have spread in a large number of ®elds, ranging from experimental psychology to controls engineering ± with an extraordinary amount of work being produced by arti®cial intelligence researchers. Some of the models, as the case of belief functions, are interpretable not only from the point of view of imprecision in probability, but this issue will concentrate mainly in this aspect. Some of this work has been unfortunately duplicated in dierent ®elds, due to the lack of a common venue for discussion about imprecise probabilities and the variety of meanings of the same mathematical models has been very often a source of confusion. The objective of the symposium was to start such a discussion and clarify this approach to ignorance and uncertainty.
We feel this goal was achieved: the symposium displayed a healthy mix of computer scientists, statisticians, economists, engineers, philosophers, mathematicians, psychologists, all engaged in lively debate.
Dealing with imprecision, incompleteness and ambiguity in probability values is an essential aspect of realistic decision-making; perhaps this is the reason why arti®cial intelligence researchers have investigated so many models