Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow p(k) ∼ ck −α . We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free network robustness to random failures with average connectivity constant is equivalent to maximize the entropy of the degree distribution. By examining the relationship of the entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free network to random failures. We conclude that the entropy of the degree distribution is an effective measure of network's resilience to random failures.

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.

Linguistic large-scale group decision making (LGDM) problems are more and more common nowadays. In such problems a large group of decision makers are involved in the decision process and elicit linguistic information that are usually assessed in different linguistic scales with diverse granularity because of decision makers' distinct knowledge and background. To keep maximum information in initial stages of the linguistic LGDM problems, the use of multigranular linguistic distribution assessments seems a suitable choice, however, to manage such multigranular linguistic distribution assessments, it is necessary the development of a new linguistic computational approach. In this paper, it is proposed a novel computational model based on the use of extended linguistic hierarchies, which not only can be used to operate with multigranular linguistic distribution assessments but also can provide interpretable linguistic results to decision makers. Based on this new linguistic computational model, an approach to linguistic large-scale multiattribute group decision making is proposed and applied to a talent selection process in universities.Index Terms-Group decision making (GDM), large-scale GDM (LGDM), linguistic distribution assessment, multigranular linguistic information.

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