A total uncertainty measure for D numbers based on belief intervals

TL;DR

This paper introduces a new total uncertainty measure for D numbers, a generalization of Dempster-Shafer theory, capturing discord, non-specificity, and non-exclusiveness in uncertainty reasoning.

Contribution

It proposes a novel total uncertainty measure for D numbers based on belief intervals, addressing an unresolved issue in the theory.

Findings

The measure captures discord, non-specificity, and non-exclusiveness.

Properties like range, monotonicity, and set consistency are established.

The measure enhances uncertainty quantification in D numbers.

Abstract

As a generalization of Dempster-Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that theory. In this paper, inspired by distance based uncertainty measures for Dempster-Shafer theory, a total uncertainty measure for a D number is proposed based on its belief intervals. The proposed total uncertainty measure can simultaneously capture the discord, and non-specificity, and non-exclusiveness involved in D numbers. And some basic properties of this total uncertainty measure, including range, monotonicity, generalized set consistency, are also presented.