D numbers theory: a generalization of Dempster-Shafer evidence theory

TL;DR

This paper introduces D numbers theory (DNT), a generalization of Dempster-Shafer theory that relaxes the exclusivity assumption among hypotheses, enabling better modeling of uncertain and linguistic information in real-world applications.

Contribution

The paper develops D numbers theory (DNT), including a new combination rule and a measure of exclusiveness, extending Dempster-Shafer theory to handle non-exclusive hypotheses.

Findings

DNT effectively models uncertain information with non-exclusive hypotheses.

The combination rule reduces to classical Dempster rule when hypotheses are exclusive.

Numerical example demonstrates DNT's efficiency in linguistic decision making.

Abstract

Efficient modeling of uncertain information in real world is still an open issue. Dempster-Shafer evidence theory is one of the most commonly used methods. However, the Dempster-Shafer evidence theory has the assumption that the hypothesis in the framework of discernment is exclusive of each other. This condition can be violated in real applications, especially in linguistic decision making since the linguistic variables are not exclusive of each others essentially. In this paper, a new theory, called as D numbers theory (DNT), is systematically developed to address this issue. The combination rule of two D numbers is presented. An coefficient is defined to measure the exclusive degree among the hypotheses in the framework of discernment. The combination rule of two D numbers is presented. If the exclusive coefficient is one which means that the hypothesis in the framework of discernment is exclusive of each other totally, the D combination is degenerated as the classical Dempster combination rule. Finally, a linguistic variables transformation of D numbers is presented to make a decision. A numerical example on linguistic evidential decision making is used to illustrate the efficiency of the proposed D numbers theory.