A distance of quantum mass function and its application in multi-source information fusion method based on discount coefficient

Distance measures provide a novel perspective for measuring the difference or consistency between bodies of evidence, which have been used in a wide range of fields. However, under the framework of quantum mass function, existing distances cannot measure the difference. Hence, this paper formulates a new distance measure, referred to as the distance of the quantum mass functions. The purpose of this distance measure is to quantify the difference between quantum mass functions. It can be demonstrated mathematically that it is a strict distance measure that satisfies the nonnegativity, symmetry, definiteness, triangle inequality. The proposed distance measure is a generalization of the classical evidence distance, and it introduces the concept of Minkowski distance as well. It is therefore not only able to reflects the difference of discord and non-specificity in the mass functions, but it also has the advantage of Minkowski distance, as well as high compatibility. Moreover, A number of numerical examples are also provided to illustrate its properties and advantages. Using the proposed distance measure, we design a new information fusion method based on the discount coefficient within a complex framework. As a further investigation, the proposed fusion method is applied to several data sets experiments and results indicate that compared to other methods, it has a certain potential in the field of multi-source information fusion under the framework of evidence theory.