Before implementing a design of a large engineering system different design proposals are evaluated. The information used by experts to evaluate different options may be vague and/or incomplete. Although different probabilistic tools and techniques have been used to deal with these kinds of problems, it seems better to use the fuzzy linguistic approach to model vagueness and the Dempster-Shafter theory of evidence for modeling incompleteness and ignorance. In the evaluation of alternative designs, different criteria can be considered. In this article an evaluation process is developed in terms of Safety and Cost analysis. Both criteria involve uncertainty, vagueness, and ignorance due to their nature. Therefore, we propose an evaluation process defined in a linguistic framework where both criteria will be conducted in different utility spaces, i.e., in a multigranular linguistic domain. Once the evaluation framework has been defined, we present an evaluation process based on a Multi-Expert Multi-Criteria decision model that will be able to deal with multigranular linguistic information without loss of information in order to evaluate different design options for an engineering system in a precise manner. Accordingly, we propose the use of a multigranular linguistic model based on the Linguistic Hierarchies presented by Herrera and Martíez ("A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multi-expert decision-making." IEEE Trans Syst Man Cybern B 2001;31(2):227-234).