Non-Additive Appropriateness Measures

Summary

In this chapter we have investigated non-additive appropriateness measures where the mass assignment values on labels sets are aggregated disjunctively using a t-conorm. Such measures are in fact generalisations of the additive measures studied throughout this volume since the latter can be obtained by selecting the t-conorm f_v (a, b) = min (1, a + b) and insisting that mass assignment values sum to one. A number of properties of generalised appropriateness measures have been studied, in particular for the special cases where f_v is an Archimedean or Strict Archimedean t-conorm or where f_v = max. In the latter case, referred to as possibilistic appropriateness measures, we identify a family of generalised mass selection functions for which the appropriateness measures of a conjunction of labels corresponds to a t-norm applied to the appropriateness measures of the conjuncts. Finally, we give an axiomatic characterization of generalised appropriateness measures and then discuss how best to interpret the failure of the law of excluded for these non-additive measures.