In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.

Consensus Reaching in Social Network Group Decision Making: Research Paradigms and Challenges

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.

A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

A theoretical visual interaction framework to model consensus in social network group decision making (SN-GDM) is put forward with following three main components: (1) construction of trust relationship; (2) trust based recommendation mechanism; and (3) visual adoption mechanism. To do that, dual trust propagation is investigated to connect incomplete trust relationship by trusted third partners, in a way that it can fit our intuition in these cases: trust values decrease while distrust values increase. Trust relationship is proposed to be used in determining the trust degree of experts and in aggregating individual opinions into a collective one. Three levels of consensus degree are defined and used to identify the inconsistent experts. A trust based recommendation mechanism is developed to generate advices according to individual trust relationship, making recommendations more likeable to be implemented by the inconsistent experts to achieve higher levels of consensus. Therefore, it has an advantage with respect to existing interaction models because it does not force the inconsistent experts to accept advices irrespective of their trust on them. Finally, a visual adoption mechanism, which provides visual information representations on experts individual consensus positions before and after adopting the recommendation advices, is presented and analysed theoretically. Experts can select their appropriate feedback parameters to achieve a balance between group consensus and individual independence. Consequently, the proposed visual interaction model adds real and needed flexibility in guiding the consensus reaching process in SN-GDM.

A visual interaction consensus model for social network group decision making with trust propagation

Nowadays, societal and technological trends demand the management of large scale of decision makers in group decision-making (GDM) contexts. In a large-scale GDM, decision makers often have individual concerns and satisfactions, and also they will use heterogeneous preference representation structures to express their preferences. Meanwhile, it is difficult to set the numerical consensus threshold to judge whether a consensus degree can be acceptable or not in the consensus reaching process in a large-scale GDM. This study proposes a novel consensus reaching model for the heterogeneous large-scale GDM with the individual concerns and satisfactions. In this consensus reaching model, a selection process is proposed to obtain the individual preference vectors, to divide decision makers into different clusters, and to yield the preference vector of the large group. Following this, a consensus measure method that considers the individual concerns on alternatives is defined for measuring the consensus degree, and a linguistic approach is developed to measure the individual and collective satisfactions regarding the consensus degree. Finally, a feedback adjustment process is proposed and utilized to help decision makers adjust their preferences. A practical example and a simulation analysis are presented to demonstrate the validity of the proposed consensus reaching model.

Consensus Building for the Heterogeneous Large-Scale GDM With the Individual Concerns and Satisfactions

A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust

Innovative methodology for measuring consensus based on the Pearson correlation coefficient is proposed.Experts express their opinions on alternatives or issues by means of reciprocal preference relations.We provide interesting properties for the new consensus measure proposed.An illustrative example with discussion is presented. The achievement of a 'consensual' solution in a group decision making problem depends on experts' ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts' opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.

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A new measure of consensus with reciprocal preference relations

We provide a methodology to perform an extensive and systematized analysis of problems where experts voice their opinions on the attributes of projects through a hesitant fuzzy decision matrix. This provides the decision-maker with ample information on which he or she can rely in order to make the final decision, in the form of segments instead of numbers. These segments derive from weighted average of new parametric expressions for two tenable indices of satisfaction, the distance to an ideal or the similarity to an anti-ideal, and permit to give a profuse unified picture of the relative performance of the projects. When the parameter grows, these indices tend to replicate the evaluation by respective simplistic expressions that only depend on the least, resp., the largest, evaluation and the number of evaluations in each cell.

/pdf/a-segment-based-approach-to-the-analysis-of-project-1vps6x8d2i.pdf

A segment-based approach to the analysis of project evaluation problems by hesitant fuzzy sets

The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture the strength of the correlations. We present a new approach based on the classical Pearson correlation coefficient for crisp values. In this way we can express not only the strength of the relationship between two hesitant fuzzy sets, but also whether they are positively or negatively associated.

/pdf/new-correlation-coefficients-for-hesitant-fuzzy-sets-1t9xdaa7z8.pdf

New correlation coefficients for hesitant fuzzy sets

The need for organizations to evaluate their environmental practices has been recently increasing. This fact has led to the development of many approaches to appraise such practices. In this paper, a novel decision model to evaluate company’s environmental practices is proposed to improve traditional evaluation process in different facets. Firstly, different reviewers’ collectives related to the company’s activity are taken into account in the process to increase company internal efficiency and external legitimacy. Secondly, following the standard ISO 14031, two general categories of environmental performance indicators, management and operational, are considered. Thirdly, since the assumption of independence among environmental indicators is rarely verified in environmental context, an aggregation operator to bear in mind the relationship among such indicators in the evaluation results is proposed. Finally, this new model integrates quantitative and qualitative information with different scales using a multi-granular linguistic model that allows to adapt diverse evaluation scales according to appraisers’ knowledge.

Managing Interacting Criteria: Application to Environmental Evaluation Practices

We introduce the use of the Mahalanobis distance for the analysis of the cohesiveness of a group of linear orders or complete preorders.
We prove that arbitrary codifications of the preferences are incompatible with this formulation,
while affine transformations permit to compare profiles on the basis of such a proposal.
This measure seems especially fit for the cases where the alternatives are correlated,
e.g.,
committee selection when the candidates are affiliated to political parties.

Rocío de Andrés Calle

Papers

A new measure of consensus with reciprocal preference relations

A segment-based approach to the analysis of project evaluation problems by hesitant fuzzy sets

New correlation coefficients for hesitant fuzzy sets

Managing Interacting Criteria: Application to Environmental Evaluation Practices

Codifications of complete preorders that are compatible with Mahalanobis disconsensus measures