A model in partial orders for comparing objects by dualistic measures

Abstract Measuring resemblance between objects is a fundamental problem in numerical taxonomy that arises when constructing dissimilarity coefficients from multivariate descriptions of objects and when comparing classifications of objects. Although traditional analyses use measures of either similarity or dissimilarity, both Tversky and Faith have developed dualistic measures of resemblance that are linear combinations of similarity and dissimilarity measures. Being neither fish nor fowl, such measures may through cancellation lose distinctive features normally associated with similarity or dissimilarity. We employ a very general model, involving valuations on partially ordered sets, to describe a parametric family of dualistic resemblance measures, to derive its basic properties, and to relate it to recent proposals made by Faith. Measures in the family retain various features of dissimilarity; although usually nonmetric, they are characterizable nevertheless in terms of valuation metrics on partially ordered sets.

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