The Dichotomous Approach to Soft Consensus Measurement

Abstract

Generally in soft consensus models a preference relation defined on a set of options is associated with each individual concerned. In this paper it is supposed that each individual may assume a position of adversion or propension with respect to every option. With respect to some option the individuals may also assume no position. We define this model of fuzzy consensus dichotomous while we call the usual model relational. The fuzzy-logic-based calculus used in the relational model can be also applied to the dichotomous model. Furthermore, we propose a soft consensus measure based on the Choquet integral considered as a fuzzy integral to capture some specific situations. The dichotomous model of soft consensus performs very well with some real life problems, e. g. to describe the possible coalitions between parties in a parliament or stockholders in a company. In order to point out its features, the dichotomous model is applied to a description of some apects of the the Italian political debate.