Set-models of information-gap uncertainty: axioms and an inference scheme

The sparsity and complexity of information in many technological situations has led to the development of new methods for quantifying uncertain evidence, and new schemes of inference from uncertain data. This paper deals with set-models of information-gap uncertainty which employ geometrical rather than measure-theoretic tools, and which are radically different from both probability and fuzzy-logic possibility models. The first goal of this paper is the construction of an axiomatic basis for info-gap models of uncertainty. The result is completely different from Kolmogorovʹs axiomatization of probability. Once we establish an axiomatically distinct framework for uncertainty, we arrive at a new possibility for inference and decision from uncertain evidence. The development of an inference scheme from info-gap models of uncertainty is the second goal of this paper. This inference scheme is illustrated with two examples: a logical riddle and a mechanical engineering design decision.