a b s t r a c tMulti-Criteria Decision Analysis (MCDA) methods are widely used in various fields and disciplines. While most of the research has been focused on the development and improvement of new MCDA methods, relatively limited attention has been paid to their appropriate selection for the given decision problem. Their improper application decreases the quality of recommendations, as different MCDA methods deliver inconsistent results. The current paper presents a methodological and practical framework for selecting suitable MCDA methods for a particular decision situation. A set of 56 available MCDA methods was analysed and, based on that, a hierarchical set of methods' characteristics and the rule base were obtained. This analysis, rules and modelling of the uncertainty in the decision problem description allowed to build a framework supporting the selection of a MCDA method for a given decision-making situation. The practical studies indicate consistency between the methods recommended with the proposed approach and those used by the experts in reference cases. The results of the research also showed that the proposed approach can be used as a general framework for selecting an appropriate MCDA method for a given area of decision support, even in cases of data gaps in the decision-making problem description. The proposed framework was implemented within a web platform available for public use at www.mcda.it.Please cite this article as: J. W ątróbski et al., Generalised framework for multi-criteria method selection, Omega (2018), https://doi.

The world of network science is fascinating and filled with complex phenomena that we aspire to understand. One of them is the dynamics of spreading processes over complex networked structures. Building the knowledge-base in the field where we can face more than one spreading process propagating over a network that has more than one layer is a challenging task, as the complexity comes both from the environment in which the spread happens and from characteristics and interplay of spreads' propagation. As this cross-disciplinary field bringing together computer science, network science, biology and physics has rapidly grown over the last decade, there is a need to comprehensively review the current state-of-the-art and offer to the research community a roadmap that helps to organise the future research in this area. Thus, this survey is a first attempt to present the current landscape of the multi-processes spread over multilayer networks and to suggest the potential ways forward.INDEX TERMS complex networks, information diffusion, multilayer networks, spreading processes

Information spreading in complex networks is often modeled as diffusing information with certain probability from nodes that possess it to their neighbors that do not. Information cascades are triggered when the activation of a set of initial nodes -seeds -results in diffusion to large number of nodes. Here, several novel approaches for seed initiation that replace the commonly used activation of all seeds at once with a sequence of initiation stages are introduced. Sequential strategies at later stages avoid seeding highly ranked nodes that are already activated by diffusion active between stages. The gain arises when a saved seed is allocated to a node difficult to reach via diffusion. Sequential seeding and a single stage approach are compared using various seed ranking methods and diffusion parameters on real complex networks. The experimental results indicate that, regardless of the seed ranking method used, sequential seeding strategies deliver better coverage than single stage seeding in about 90% of cases. Longer seeding sequences tend to activate more nodes but they also extend the duration of diffusion. Various variants of sequential seeding resolve the trade-off between the coverage and speed of diffusion differently.The process of making the complex decisions is difficult, so it is often worth making partial decisions and to track their consequences before proceeding further. Such strategy was proven useful in areas such as: general theory of decision making 1, 2 , financial markets 3, 4 , epidemiology 5 and marketing 6 . Here, we show that sequential, consecutive approach is also highly efficient in choosing the individuals, called seeds, that when activated will widely spread information or opinion in a social network. The current research on influence maximization and information spread in complex networks focuses mainly on single stage seed initiation. An exception is new product adaptation with early diffusion of product samples 7,8 to benefit from consumer responses and product spread. The main challenge is finding a method for selection of seeds to maximize the final spread of information within the network. If the total number of seeds to be used is limited, e.g. due to restricted budget, a typical approach is to rank all nodes in the network according to some criteria, select top n nodes as seeds and activate them at once to initiate the diffusion.Influence maximization problem in complex networks was defined by Kempe 9 . Analyses of various factors affecting the diffusion and social influence in complex networks include the efficiency of using different centrality measures for ranking influencers for selection 10 , impact of homophily for successful seeding 11 , and heterogeneous thresholds on congestion 12 , finding the critical initiator fraction beyond which the cascade becomes global 13 or importance of different network features in predicting spread 14 . Selection of initial seeds was also analyzed, including incentives for innovators to start diffusion 15 and the multi-market entry pe...

Poland. his main research interests in social networks and information diffusion are backed with a practical background in the field of Web system development.abStract: While profitable business models elude many virtual worlds, sales of virtual products are a potentially lucrative source of revenue. One new addition to this strategy is virtual gifting, whereby users purchase virtual products to give to other users. The monetary value of such virtual good transactions is economically significant but no prior study has examined this phenomenon in a strictly virtual context. We apply theory from the economics literature to examine gifting behavior in a virtual world in which users' social status is reflected in observable social connections (friendships) and interactions (personal messages). We find strong evidence that gifting is associated with future enhancements of the gift giver's social status, consistent with a social status-seeking motivation, thus confirming a theorized behavior that is difficult to study in the real world. Our study has implications for system proprietors and managers because we show that gift giving increases system use continuance. We identify various antecedents of gift giving, which may assist a manager in identifying users who are most inclined to give gifts and enable the manager to signal the social exchange benefits to users as a way of improving their social connections.key WordS and phraSeS: gift economy, MMOg, status in virtual worlds, virtual gifts, virtual worlds.