A Statistical Comparative Study of Different Similarity Measures of Consensus in Group Decision Making




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Peer reviewed



An essential aim in group decision making (GDM) problems is to achieve a high level of consensus among experts. Consensus is defined as general or widespread agreement, and it is usually modelled mathematically via a similarity function measuring how close experts’ opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts’ opinions or preferences. In the literature, different metrics or distance functions have been proposed to implement in consensus models, but no study has been carried out to analyse the influence the use of different distance functions can have in the GDM process. This paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in GDM. By using the nonparametric Wilcoxon matched-pairs signed-ranks test, it is concluded that different distance functions can produce significantly different results. Moreover, it is also shown that their application also has a significant effect on the speed of achieving consensus. Finally, these results are analysed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions.


Research conducted in collaboration between DMU and University of Granada (Spain). DIGITS, Department of Informatics, Faculty of Technology, De Montfort University, Leicester LE1 9BH, UK; Department of Quantitative Methods in Economic and Business, University of Granada, 18071 Granada, Spain; Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain; Department of Computer Science and A.I., University of Granada, 18071 Granada, Spain
NOTICE: this is the author’s version of a work that was accepted for publication in <Journal title>. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences. http://dx.doi.org/10.1016/j.ins.2012.09.014


Group decision making, Fuzzy preferences, Similarity, Consensus, Decision support rules, Wilcoxon test


Chiclana, F., Tapia-Garcia, J.M., del Moral, M.J. and Herrera-Viedma, E. (2013) A Statistical Comparative Study of Different Similarity Measures of Consensus in Group Decision Making. Information Sciences, 221, pp. 110-123


Research Institute

Institute of Artificial Intelligence (IAI)