Consensual Dynamics in Group Decision Making with Triangular Fuzzy Numbers

In this paper we study the modelling of consensus reaching in a 'soft' environment, i.e. when the individual testimonies are expressed as fuzzy preference relations. Here consensus is meant as the degree to which most of the experts agree on the preferences associated to the most relevant alternatives. First of all we derive a degree of dissensus based on linguistic quantifiers and then we introduce a form of network dynamics in which the quantifiers are represented by scaling functions. Next, assuming that the decision makers can express their preferences in a more flexible way, i.e. by means of triangular fuzzy numbers, we describe the iterative process of opinion changing towards consensus via the gradient dynamics of a cost function expressed as a linear combination of a dissensus cost function and an inertial cost function. Finally, some computer simulations are carried out together with a short description of a case study in progress.

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