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Nonlinear preferences in group decision‐making. Extreme values amplifications and extreme values reductions
Author(s) -
GarcíaZamora Diego,
Labella Álvaro,
Rodríguez Rosa M.,
Martínez Luis
Publication year - 2021
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22561
Subject(s) - preference , nonlinear system , scale (ratio) , computer science , group decision making , extreme value theory , fuzzy logic , group (periodic table) , operations research , mathematics , econometrics , psychology , artificial intelligence , social psychology , statistics , physics , quantum mechanics
Consensus Reaching Processes (CRPs) deal with those group decision‐making situations in which conflicts among experts' opinions make difficult the reaching of an agreed solution. This situation, worsens in large‐scale group decision situations, in which opinions tend to be more polarized, because in problems with extreme opinions it is harder to reach an agreement. Several studies have shown that experts' preferences may not always follow a linear scale, as it has commonly been assumed in previous CRP. Therefore, the main aim of this paper is to study the effect of modeling this nonlinear behavior of experts' preferences (expressed by fuzzy preference relations) in CRPs. To do that, the experts' preferences will be remapped by using nonlinear deformations which amplify or reduce the distance between the extreme values. We introduce such automorphisms to remap the preferences as Extreme Values Amplifications (EVAs) and Extreme Values Reductions (EVRs), study their main properties and propose several families of these EVA and EVR functions. An analysis about the behavior of EVAs and EVRs when are implemented in a generic consensus model is then developed. Finally, an illustrative experiment to study the performance of different families of EVAs in CRPs is provided.