An ordinal metrical scale built on a fuzzy nominal scale

Abstract

The Measurement theory defines a measurement as a mapping from a set of empirical property manifestations to a set of abstract property values called symbols. The ordinal metrical scales were introduced within the context of Psychophysics as a way to solve the problem of multidimensional scaling. Usually the distances used to define such scales are based on the hypothesis that symbols are vectors of numbers and that each component is expressed on an interval scale or a ratio scale. In a recent paper was introduced a distance-based scale that represents manifestations from an empirical world with fuzzy subsets of lexical terms. This approach supposes only the existence of a fuzzy nominal scale and allows a choice into a wider set of distances to build the ordinal metrical scales. This paper focuses on the knowledge source used to choose a scale definition and takes metrical scales built on fuzzy nominal scale as example. Then it opens a discussion on the reality of some distances in the empirical world.