Linear-time computational techniques based on the structure of an evidence space have beendeveloped for combining multiple pieces of evidence using Dempster’s rule (orthogonal sum),which is available on a number of contending hypotheses. They offer a means of making thecomputation-intensive calculations involved more efficient in certain circumstances. Unfortunately,they restrict the orthogonal sum of evidential functions to the dichotomous structure thatapplies only to elements and their complements. In this paper, we present a novel evidence structurein terms of a triplet and a set of algorithms for evidential reasoning. The merit of this structureis that it divides a set of evidence into three subsets, distinguishing the trivial evidential elementsfrom the important ones—focusing particularly on some elements of an evidence space. It avoidsthe deficits of the dichotomous structure in representing the preference of evidence and estimatingthe basic probability assignment of evidence. We have established a formalism for this structureand the general formulae for combining pieces of evidence in the form of the triplet, which havebeen theoretically and empirically justified. C
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