Validating criteria with imprecise data in the case of trapezoidal representations

We are interested in the issue of determining an alternative’s satisfaction to a criterion when the alternative’s associated attribute value is imprecise. We introduce two approaches to the determination of criteria satisfaction in this uncertain environment, one based on the idea of containment and the other on the idea of possibility. We are particularly interested in the case in which the imprecise data is expressed in terms of a trapezoidal type distribution. We provide an algorithmic solution to this problem enabling it to be efficiently implemented in a digital environment. A number of examples are provided illustrating our algorithms.