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Denoeux proposed an operator called the cautious conjunctive rule (CCR) to combine non-dogmatic belief functions (i.e., the frame is considered a focal element) from reliable dependent sources, which can occur in practice. However, in cases such as uncertain multiple attribute and group decision analyses, belief functions may denote data that vary in importance. This paper extends CCR as a weighted CCR (WCCR) to combine belief functions in consideration of their relative weights in such situations. Properties of WCCR are analyzed, proven, and demonstrated using numerical examples. In particular, the consideration of relative weights enables WCCR to combine dogmatic belief functions. The normalized WCCR is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in Anhui Province, China. [ABSTRACT FROM AUTHOR]