Fuzzy m-ary adjacency relations in social network analysis: Optimization and consensus evaluation

The main contribution of this paper consists in extending the ‘soft’ consensus paradigm of fuzzy group decision making developed under the framework of numerical fuzzy preferences. We address the problem of consensus evaluation by endogenously computing the importance of the decision makers in terms of their influence strength in the network. To this aim, we start from centrality measure and combine it with the fuzzy m-ary adjacency relation approach. In this way, we introduce a flexible consensus measure that takes into account the influence strength of the decision makers according to their eigenvector centrality. Moreover, we propose an optimization problem which determines the maximum number of the most important decision makers that share a fixed desirable consensus level.