Abstract: Concept cognition in a network is an important direction in the field of network data analysis. Starting from the necessity operator and possibility operator in formal concept analysis, this paper puts forward variable precision possibility operator, and illustrates that the classical possibility operators are special cases of the variable precision possibility operators. Furthermore, some properties of the possibility operators are studied, and their significances in the study of infectious disease networks are explained. Then, based on the variable precision possibility operators, two generalized network concepts and their upper approximations, lower approximations and boundary regions are proposed, and the upper and lower approximations and their boundary regions under variable precision possibility operators are illustrated to have much richer semantics through an example. After that, combined with the network eigenvalue method in complex network analysis, the network weak concepts are defined, and a network weak concept acquisition method based on variable precision possibility operator is presented. Finally, our algorithm is used to conduct some experiments on the UCI database, and the obtained results show that variable-precision possibility operators have advantages in network concept cognition.

Key words: concept cognition, formal context, network weak concept, necessity operator, variable precision possibility operator