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 [1], Alcantud, de Andres Calle and Cascon [2] and Bosch [3], among others and from Decision Making Theory: Gonzalez-Arteaga, Alcantud and de Andres Calle [4] and Gonzalez-Pachon [5], Herrera, Herrera-Viedma and Chiclana [7], Herrera-Viedma et al. [6] and Wu et al. [8], 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 [1] J. Alcalde-Unzu and M. Vorsatz. Measuring the cohesiveness of preferences: An axiomatic analysis. Social Choicer and Welfare, 41:965–988, 2013. [2] 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. [3] R. Bosch. Characterizations of Voting Rules and Consensus Measures. PhD thesis, Tilburg University, 2005. [4] 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. [5] J. Gonzalez-Pachon and C. Romero. Distance-based consensus methods: a goal programming approach. Omega, 27(3):341–347, 1999. [6] 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. [7] 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. [8] 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

A comparative analysis between two statistical deviation–based consensus measures in group decision making problems

The mean absolute deviation and the standard deviation, two statistical measures commonly used in quantifying variability, may become an interesting tool when defining consensus measures. Two consensus indexes which obtain the level of consensus in some problems of Group Decision Making are introduced in this paper by expanding the aforementioned statistical concepts. A comparative analysis reveals that the levels of consensus derived from these indexes are close to those obtained employing distance functions when a fuzzy preference relations frame is considered, so they turn out to be a useful tool in this context. In addition, these indexes are different from each other and with the distance functions considered. Thus, they are applicable tools in the calculation of consensus in our context and are different from those commonly used

The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences.

In this paper we present an overview of the soft consensus model in group decision making and we investigate the dynamical patterns generated by the fundamental pairwise preference interactions on which the model is based. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus measure plays a key role in the model and induces a network of pairwise interactions between the individual preferences. The structure of fuzzy relations is present at both the individual and the collective levels of description of the soft consensus model: pairwise preference intensities between alternatives at the individual level, and pairwise interaction coefficients between decision makers at the collective level. The collective measure of dissensus is based on non linear scaling functions of the linguistic quantifier type and expresses the degree to which most of the decision makers disagree with respect to their preferences regarding the most relevant alternatives. The graded notion of consensus underlying the dissensus measure is central to the dynamical unfolding of the model. The original formulation of the soft consensus model in terms of standard numerical preferences has been recently extended in order to allow decision makers to express their preferences by means of triangular fuzzy numbers. An appropriate notion of distance between triangular fuzzy numbers has been chosen for the construction of the collective dissensus measure. In the extended formulation of the soft consensus model the extra degrees of freedom associated with the triangular fuzzy preferences, combined with non linear nature of the pairwise preference interactions, generate various interesting and suggestive dynamical patterns. In the present paper we investigate these dynamical patterns which are illustrated by means of a number of computer simulations.

Validation of Soft Classification Models using Partial Class Memberships: An Extended Concept of Sensitivity & Co. applied to the Grading of Astrocytoma Tissues

We use partial class memberships in soft classification to model uncertain labelling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data. Classifier performance is usually expressed as fractions of the confusion matrix, such as sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE. All calculations apply to classical crisp classification as well as to soft classification (partial class memberships and/or one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance. We implement the proposed performance measures in the R package "softclassval", which is available from CRAN and at http://softclassval.r-forge.r-project.org. Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.Comment: The manuscript is accepted for publication in Chemometrics and Intelligent Laboratory Systems. Supplementary figures and tables are at the end of the pd

Evaluation of e-learning web sites using fuzzy axiomatic design based approach

High quality web site has been generally recognized as a critical enabler to conduct online business. Numerous studies exist in the literature to measure the business performance in relation to web site quality. In this paper, an axiomatic design based approach for fuzzy group decision making is adopted to evaluate the quality of e-learning web sites. Another multi-criteria decision making technique, namely fuzzy TOPSIS, is applied in order to validate the outcome. The methodology proposed in this paper has the advantage of incorporating requirements and enabling reductions in the problem size, as compared to fuzzy TOPSIS. A case study focusing on Turkish e-learning websites is presented, and based on the empirical findings, managerial implications and recommendations for future research are offered

Agent-Based Product Configuration: towards Generalized Consensus Seeking

This paper will present an evolution of a fuzzy agent based platform which performed products configuration. As a first step, we used the notion of consensus to establish robust results at the end of the configuration process. We implemented the concept of generalized consensus which implied the consideration of consensuses from the beginning, in this way robust data are treated during the entire process and the final result enables the designer to distinguish the robust components and flexible ones in a set of configurations.Comment: 8 pages, 8 figures, 5 table

From governance to meta-governance in tourism?: Re-incorporating politics,interests and values in the analysis of tourism governance

Despite its theorization in the political and policy sciences in the early 1990s, the concept of metagovernance has gained relatively little recognition in tourism studies. Nevertheless, its significance in the political sciences and policy literature, especially as a result of the perceived failure of governance systems following the recent global financial crisis, has only served to reinforce its relevance. Metagovernance addresses some of the perceived failures of traditional governance approaches and associated interventions, and has enabled the understanding of central-state led regimes of shadowed hierarchical authorities and local-level micro-practices of social innovation and self-government. In contrast, tourism studies have tended to restrict study of the political dimension of tourism governance and the role of the state under the traditional parallelism between government and governance. Examination of how governance is itself governed enables a better understanding of the practices of planning and policy making affecting tourism and destinations. In particular, the applications of concepts of governance are inextricably linked to a given set of value assumptions which predetermine the range of its application. A short example of the application of the metagovernance paradigm is provided from the New Zealand context. It is concluded that governance mechanisms are not value-neutral and instead serve to highlight the allocation of power in a destination and the dominance of particular values and interests