Conjunctive combination of belief functions from dependent sources using positive and negative weight functions

This paper investigates the conjunctive combination of belief functions from dependent sources based on the cautious conjunctive rule (CCR). Weight functions in the canonical decomposition of a belief function are divided into two parts, namely, positive and negative weight functions, whose characteristics are described. Positive and negative weight functions of two belief functions are used to construct a new partial ordering between the belief functions. The partial ordering determines the committed relationship between two belief functions, which is different from that generated by the weight function based partial ordering in the CCR when one or two belief functions are not unnormalized separable. A new rule is developed using the constructed partial ordering to combine belief functions from dependent sources. The relevant properties are described and demonstrated by examples. A performance assessment problem is investigated to demonstrate the validity and applicability of the proposed rule and compare it with the CCR.