Abstract
The Dempster-Shafer Theory (DST) or Evidence Theory has been commonly used to deal with uncertainty. It is based on the basic probability assignment concept (BPA). The upper entropy on the credal set associated with a BPA is the only uncertainty measure in DST that verifies all the necessary mathematical properties and behaviors. Nonetheless, its computation is notably complex. For this reason, many alternatives to this measure have been recently proposed, but they do not satisfy most of the mathematical requirements and present some undesirable behaviors. Belief intervals have been frequently employed to quantify uncertainty in DST in the last years, and they can represent the uncertainty-based-information better than a BPA. In this research, we develop a new uncertainty measure that consists of the maximum of entropy on the credal set corresponding to belief intervals for singletons. It verifies all the crucial mathematical requirements and presents good behavior, solving most of the shortcomings found in uncertainty measures proposed recently. Moreover, its calculation is notably easier than the upper entropy on the credal set associated with the BPA. Therefore, our proposed uncertainty measure is more suitable to be used in practical applications.
Highlights
The Dempster-Shafer Theory (DST), known as Evidence Theory [1], [2], has been commonly employed to deal with uncertainty in practical applications such as statistical classification [3], target identification [4], medical diagnosis [5], or face recognition [6]
We have proposed a new uncertainty measure that consists of the maximum of entropy on the credal set corresponding to belief intervals for singletons
It has been presented as an alternative to the maximum of entropy on the credal set associated with a basic probability assignment (BPA), which is the only uncertainty measure proposed so far that verifies all the mathematical properties and requirements of behavior for uncertainty measures in DST
Summary
The Dempster-Shafer Theory (DST), known as Evidence Theory [1], [2], has been commonly employed to deal with uncertainty in practical applications such as statistical classification [3], target identification [4], medical diagnosis [5], or face recognition [6]. The upper entropy on the credal set associated with a BPA, proposed in [9], is the only uncertainty measure in DST that satisfies all the essential mathematical properties and behaviors [10]. That measure, developed by Harmanec and Klir in [12], consists of the upper entropy on the credal set associated with a BPA m, denoted by S∗ (Pm) This measure, in [9], was established as appropriated to quantify the total uncertainty in DST since it satisfied the required properties. The only uncertainty measure in DST that verifies the six required mathematical properties is the upper entropy on the credal set associated with a BPA m, S∗ (Pm) [10]. The generalization of the Deng entropy and Hinter is still an open question
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