Fuzzy Measures with Different Levels of Granularity

In this paper we will represent the uncertainty about a particular event, A, by means of an interval [l(A), u(A)]. The extremes of such interval are linguistic values from a particular scale or level of granularity. The problem is how to transform an uncertainty value or interval with arbitrary extremes into an interval expressed on a specific scale. Two conditions are requested to do this transformation: i) Improper information, not contained in the original, must not be obtained, ii) The loss of information must not be too great. Several approaches are considered, and their properties and behaviour are studied. Most of them are based on different methods of ranking fuzzy numbers. Finally, several examples of particular transformations are considered.