Influence maximization is a fundamental problem in social network analysis. This problem refers to the identification of a set of influential users as initial spreaders to maximize the spread of a message in a network. When such a message is spread, some users may be influenced by it. A common assumption of existing work is that the impact of a message is essentially binary: A user is either influenced (activated) or not influenced (non-activated). However, how strongly a user is influenced by a message may play an important role in this user’s attempt to influence subsequent users and spread the message further; existing methods may fail to model accurately the spreading process and identify influential users. In this article, we propose a novel approach to model a social network as a fuzzy graph where a fuzzy variable is used to represent the extent to which a user is influenced by a message (user’s activation level). By extending a diffusion model to simulate the spreading process in such a fuzzy graph, we conceptually formulate the fuzzy influence maximization problem for which three methods are proposed to identify influential users. Experimental results demonstrate the accuracy of the proposed methods in determining influential users in social networks.

影响力最大化是社交网络分析中的一个基本问题。该问题指的是识别一组有影响力的用户作为初始传播者，以最大化网络中消息的传播。当这样的消息被传播出去时，一些用户可能会受到影响。现有工作的一个常见假设是，消息的影响本质上是二元的：用户要么受到影响（激活），要么不受影响（未激活）。然而，用户受消息影响的程度可能会在该用户试图影响后续用户并进一步传播消息的过程中发挥重要作用；现有的方法可能无法准确地模拟传播过程并识别有影响力的用户。在本文中，我们提出了一种将社交网络建模为模糊图的新颖方法，其中模糊变量用于表示用户受消息影响的程度（用户的激活级别）。通过扩展扩散模型来模拟这种模糊图中的传播过程，我们从概念上阐述了模糊影响力最大化问题，为此提出了三种方法来识别有影响力的用户。实验结果证明了所提出的方法在确定社交网络中有影响力的用户方面的准确性。