Assigning Numerical Scores to Linguistic Expressions

Abstract

In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed.

Open Questions in Utility Theory

“…In other quite different and multidisciplinary contexts, this is sometimes called an isotony, an entropy function, a measurement, a score or an order-preserving map. (See e.g [8,10,17,18,30,31,43,49,77]…”