Criteria satisfaction under measure based uncertainty

A fundamental task in decision-making is the determination, in the face of uncertain information, of the satisfaction of some criteria in terms of a scalar value. Our objective here is to help support this task. We first discuss the process of selecting an uncertainty model for our knowledge, here we emphasize the tradeoff between functionality of the representation and its ability to model our knowledge, cointention. We next discuss the process of scalarization, determining a single value to represent some uncertain value. Some features required of operations used for scalarization are introduced. We look at the scalarization procedures used in probability theory, the expected value, and that used in possibility theory. We then turn to a more general framework for the representation of uncertain information based on a set measure.