We provide a continuous representation of quasi-concave mappings by their upper level sets. A possible motivation is the extension to quasi-concave mappings of a result by Ulam and Hyers, which states that every approximately convex mapping can be approximated by a convex mapping.

We have observed when applying Value Efficiency Analysis [21] that decision makers wish to provide preference information related to existing rather than virtual (efficient) units. This observation motivated us to develop an approach based on the preference comparisons of existing units. The...