A novel binary composite similarity measure with optimistic and pessimistic attitudes for evidence fusion

In Dempster-Shafer (DS) evidence theory, the basic probability assignment function (i.e., “evidence” provided by an information source) is used to model uncertain information, and Dempster's combination rule is employed to fuse multiple pieces of evidence to obtain a more reliable comprehensive result for decision-making. However, when there is a high degree of conflict between two pieces of evidence, the fused result may be counter-intuitive, thereby deteriorating decision accuracy. Hence, constructing appropriate similarity measures to quantify the degree of conflict between two pieces of evidence becomes crucial for resolving these counter-intuitive outcomes. Currently, traditional similarity measures (S) are predominantly obtained through a linear transformation of evidence distance (d). For instance, the similarity between two pieces of evidence is calculated as “S = 1-d”. Such simplistic “univariate” linear transformations suffer from limitations like insufficient precision and poor adaptability. Therefore, this paper proposes a novel binary composite evidence similarity measure. In the transformation process, two distinct mapping attitudes of “optimistic” and “pessimistic” are considered, and the corresponding parameters are given to adjust to the change trend of the two attitudes. In addition, we theoretically prove that the proposed binary composite measure satisfies the core properties of similarity measures (non-negativity, symmetry, boundedness, non-degeneracy, positive monotonicity, and extreme conflict). Finally, the proposed measure is compared and analyzed with mainstream similarity measures through multiple representative numerical cases and application cases in specialized fields such as fault diagnosis and target recognition. The experimental results validate the superiority of the proposed measure in terms of measurement accuracy.