Comparison on fuzzy sets: A new semantic distance

The main features of complex impact systems are imprecision (different levels of measurement of the available information) and uncertainty (stochastic and/or fuzzy). This paper deals with the problem of the presence of such qualitative information. In particular, first the use of concepts of fuzzy set theory in order to represent qualitative information will be defended in the light of their mathematical and pscyhological properties. Then a new semantic distance and a generalization of the Minkowski p-metric, which is particularly useful for mixed information (crisp, fuzzy and stochastic), are presented. In the appendices, the proof of the fulfillment of the triangle inequality property (a necessary condition for a distance metric) and a numerical algorithm for the semantic distance are given.