Combination in the theory of evidence via a new measurement of the conflict between evidences

•A new factor to measure the conflict between evidences is introduced.•That factor is used to define a new rule of combination in evidence theory.•A set of needed properties for combination rules in evidence theory is exposed.•A comparative study on some new and classic rules is carried out.•Several examples are presented to show the performance. The Belief Function theory (BFT) has been frequently used to combine or aggregate different sources of information. In the BFT, a lot of rules to combine the available pieces of evidence have been proposed. The first one of them was Dempster’s rule of combination (DRC). It presents several drawbacks principally motivated by the normalization process used via a measure of conflict-based-combination between two pieces of evidence. This measure must be differentiated from conflict as an uncertainty-based-information measure of a piece of evidence in BFT. Many combination rules have been developed to solve the drawbacks that DRC presents, but each of them also has non-desirable behaviors in certain situations. In this work, we propose a set of mathematical properties that must be satisfied by every combination rule in BFT; we analyze some of the most known combination rules proposed in the literature, taking into account properties and behaviors. On the other hand, in this research, we present a new hybrid rule that verifies the required mathematical properties and does not present undesirable behaviors that other rules suffer. Finally, we show that the results of our proposal when it is used in practical applications are coherent.