Weaving K-fusion frames in hilbert spaces

\begin{document}$ K $\end{document} -fusion frames are generalizations of fusion frames in frame theory. In this paper, based on the weaving frames and \begin{document}$ K $\end{document} -fusion frames, we propose the notion of weaving \begin{document}$ K $\end{document} -fusion frames and conduct relevant research. First, we give some characterizations of weaving \begin{document}$ K $\end{document} -fusion frames. Then, by means of operator theory and frame theory, we present several novel construction approaches of weaving \begin{document}$ K $\end{document} -fusion frames. Finally, we discuss transitivity of weaving \begin{document}$ K $\end{document} -fusion frames.