A new belief interval-based total uncertainty measure for Dempster-Shafer theory

Dempster Shafer (DS) theory, an extension of probability theory, is widely used for modeling uncertainty in information. It is based on the concept of basic probability assignment. Each basic probability value has a corresponding belief interval. These intervals offer a practical and understandable way to quantify uncertainty. However, none of the belief-interval-based uncertainty measures currently in use satisfies all the necessary mathematical properties and behavioral requirements. Therefore this work proposes an uncertainty measure (������������) which satisfies most of the mathematical properties, and a generic set of four behavioral requirements. This work identifies a specific set of four behavioral requirements based on the four possible distinct cases of belief intervals. ������������ is verified over identified specific set of behavioral requirements, where it is found that the uncertainty value depends on both the length and the plausibility of the belief interval; uncertainty value increases with increase in the length of a belief interval, and if lengths of two belief intervals are equal, uncertainty value increases or decreases with increase or decrease in the Shannon's entropy over plausibility value.