A multidistance approach to consensus modeling

We investigate the relationship between the soft measure of collective dissensus introduced in (Fedrizzi et al. Int J Intell Syst 14:63–77, 1999; Fedrizzi et al. New Math Nat Comput 3:219–237, 2007; Preferences and Decisions: Models and Applications, Springer, Heidelberg, 2010) and the multidistance approach to consensus evaluation described in (Brunelli et al. IPMU2012, Part I, CCIS, Springer, Berlin, 2012). The novelty of the contribution consists in the introduction of a particular type of sum-based multidistance used as a measure of dissensus, closely related with the one introduced in (Fedrizzi et al. New Math Nat Comput 3:219–237, 2007). This multidistance is characterized by the application of a subadditive filtering function whose effect is that of emphasizing small distances and attenuating large ones. An illustrative example is then developed in order to compare the new dissensus measure with the OWA-based multidistance obtained assuming that the weights are linearly decreasing with respect to increasing distance values.