Qualitative and interval algebras for robust decision making under uncertainty

Decision support systems intended for operation under real world conditions require reasoning mechanisms that are robust in the face of degraded data. We present two algebras for reasoning with incomplete and imprecise data that are suitable for such systems. The first is an extended qualitative algebra which includes operations over real numbers. This is appropriate for reasoning with largely symbolic data. The other is an interval algebra, built around the paradigm of interval analysis, which is designed to deal with largely numerical data. We demonstrate how the algebras may be used for robust reasoning, and show how they might be applied to a decision problem in a medical domain.