Information volume of mass function based on extropy

The information volume of mass function based on extropy is proposed in this paper. Although the information volume of the probability distribution can be calculated by Shannon entropy, how to calculate the information of the mass function is still being explored. Recently, the concept of extropy was proposed by Lad et al. Based on extropy, the information volume of mass function is proposed in this paper. For a basic probability assignment function (BPA), if the focal elements of the frame of discernment (FOD) are all single elements, the information volume proposed in this paper is equal to the corresponding extropy. Otherwise, the information volume is greater than the corresponding extropy. Besides, when the cardinality of the FOD is identical, both the total uncertainty case and the mass function distribution of the maximum extropy have the same information volume. More precisely, the distribution of the latter can be regarded as the former obtained by decomposing the BPA once. Finally, the experiment proves that the maximum information volume increases with the increase in the cardinality of the FOD, and has the same limit value log $$_2e$$ as the maximum extropy. Some numerical examples are given to prove the nature of the information volume.