From Interval-Valued Probabilities to Interval-Valued Possibilities: Case Studies of Interval Computation under Constraints
Luis C. Gutiérrez, Martine C. Ceberio, Владик Крейнович, Rebekah L. Gruver, Mariana Peña, Mathew J. Rister, Abraham Saldaña, John A. Vasquez, Janelle Ybarra, Salem Benferhat · scholarworks - UTEP (The University of Texas at El Paso) · 2014
Abstract. In many engineering situations, we need to make decisions under uncertainty. In some cases, we know the probabilities pi of different situations i; these probabilities should add up to 1. In other cases, we only have expert estimates of the degree of possibility i of different situations; in accordance with the possibility theories, the largest of these degrees should be equal to 1. In practice, we often only know these degrees pi and i with uncertainty. Usually, we know the upper bound and the lower bound on each of these values. In other words, instead of the exact value of each degree, we only know the interval of its possible values, so we need to process such interval-valued degrees. Before we start processing, it is important to find out which values from these intervals are actually possible. For example, if only have two alternatives, and the probability of the first one is 0.5, then – even if the original interval for the second probability is wide – the only possible value of the second probability is 0.5. Once the intervals are narrowed down to possible values, we need to compute the range of possible values of the corresponding characteristics (mean, variance, conditional probabilities and possibilities, etc.). For each such characteristic, first, we need to come up with an algorithm for