The Soft Consensus Model in the Multidistance Framework

  • Silvia Bortot
  • Mario Fedrizzi
  • Michele Fedrizzi
  • Ricardo Alberto Marques Pereira
  • Thuy Hong Nguyen
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 125)

Abstract

In the context of the soft consensus model due to (Fedrizzi et al. in Journal international journal of intelligent systems 14:63–77, 1999) [27], (Fedrizzi et al. in New mathematics and natural computation 3:219–237, 2007) [28], (Fedrizzi et al. in Preferences and Decisions: models and applications, studies in fuzziness and soft computing Springer, Heidelberg, pp. 159–182, 2010) [30], we investigate the reformulation of the soft dissensus measure in relation with the notion of multidistance, recently introduced by Martín and Mayor (Information processing and management of uncertainty in knowledge-based systems. Theory and methods, communications in computer and information science, springer, heidelberg, pp. 703–711 2010) [43], Martín and Mayor (Fuzzy sets and systems 167:92–100 2011) [44]. The concept of multidistance is as an extension of the classical concept of binary distance, obtained by means of a generalization of the triangular inequality. The new soft dissensus measure introduced in this paper is a particular form of sum-based multidistance. This multidistance is constructed on the basis of a binary distance defined by means of a subadditive scaling function, whose role is that of emphasizing small distances and attenuating large distances in preferences. We present a detailed study of the subadditive scaling function, which is analogous but not equivalent to the one used in the traditional form of the soft consensus model.

Keywords

Multidistances Dissensus measures Soft consensus model 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Silvia Bortot
    • 1
  • Mario Fedrizzi
    • 1
  • Michele Fedrizzi
    • 1
  • Ricardo Alberto Marques Pereira
    • 1
  • Thuy Hong Nguyen
    • 1
  1. 1.Department of Economics and ManagementUniversity of TrentoTrentoItaly

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