A new consensus measure based on Pearson correlation coefficient
Obtaining consensual solutions is an important issue in decision making processes. It depends on several factors such as experts’ opinions, principles, knowledge, experience, etc. In the literature we can find a considerable amount of consensus measurement from different research areas (from a Social Choice perspective: Alcalde-Unzu and Vorsatz , Alcantud, de Andres Calle and Cascon  and Bosch , among others and from Decision Making Theory: Gonzalez-Arteaga, Alcantud and de Andres Calle  and Gonzalez-Pachon , Herrera, Herrera-Viedma and Chiclana , Herrera-Viedma et al.  and Wu et al. , among others ). Most of them have a common point, they are based on distances or similarity functions. In the present contribution we propose a new approach based on the use of the Pearson correlation coefficient to measure consensus. Moreover, we suppose a general framework considering experts’ opinions modelled by fuzzy preference relation. The new correlation consensus measurement takes into account concordance between preferences intensities for pairs of alternatives and it verifies important properties. In addition, we prove that our proposal is a different approach to traditional consensus measures based on distances or similarities. References  J. Alcalde-Unzu and M. Vorsatz. Measuring the cohesiveness of preferences: An axiomatic analysis. Social Choicer and Welfare, 41:965–988, 2013.  J. C. R. Alcantud, R. de Andes Calle, and J. M. Cascon. Consensus and the act of voting. Studies in Microeconomics, 1(1):1–22, 2013.  R. Bosch. Characterizations of Voting Rules and Consensus Measures. PhD thesis, Tilburg University, 2005.  T. Gonzalez-Arteaga, J.C.R. Alcantud, and R. de Andres Calle. A cardinal dissensus measure based on the Mahalanobis distance. European Journal of Operational Research, In press.  J. Gonzalez-Pachon and C. Romero. Distance-based consensus methods: a goal programming approach. Omega, 27(3):341–347, 1999.  E. Herrera-Viedma, F. J. Cabrerizo, J. Kacprzyk, and W. Pedrycz. A review of soft consensus models in a fuzzy environment. Information Fusion, 17:4–13, 2014.  E. Herrera-Viedma, F. Herrera, and F. Chiclana. A consensus model for multiperson decision making with different preference structures. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 32(3):394–402, 2002.  J. Wu, F. Chiclana, and E. Herrera-Viedma. Trust based consensus model for social network in an incomplete linguistic information context. Applied Soft Computing, 35:827– 839, 2015.
Citation : Gonzalez-Arteaga, T., de Andres Calle, R. and Chiclana, F. (2016) A new consensus measure based on Pearson correlation coefficient. Accepted for presentation at ESTYLF 2016.
Research Group : Centre for Computational Intelligence
Research Institute : Institute of Artificial Intelligence (IAI)
Peer Reviewed : Yes