The tness value of a knowledge base (KB) can be unknown and only some imprecise information about it can be obtained. In some cases this information is given by means of an interval where we know the tness is contained. Thus, the comparison of two randomly distributed intervals is necessary in this context in order to be able to determine the preferences among individuals. This contribution is a rst approach to the use of statistical preference as a tool to compare this kind of intervals. We consider the probabilistic relation associated to the stochastic comparison of every pair of intervals and we study the cycle-transitivity of this relation. The defuzzication of this probabilitic relation, that is, the statistical preference relation, is studied and some properties are obtained. Our studies are particulary detailed for the case of the uniform distribution.
In some cases the fitness value of a knowledge base is not completely determined, but just bounded in an interval. In this case the fitness value is modelled by a random variable. Thus the comparison of random variables allows to compare the fitness values when they are not completely determined. In this contribution we consider a quite new proposal in stochastic comparison: statistical preference. We recall the advantages of this method with respect to (the classical) stochastic dominance. We also order by statistical preference two fitness values modelled by beta distributions with some special parameters.
Distillation at an infinite reflux ratio in combination with an infinite number of trays has been investigated.