Basic concepts, definitions, and methods in D number theory
This work addresses foundational issues in DNT for handling uncertain information, but it is incremental as it builds on existing theory without broad empirical validation.
The paper tackles the lack of a systematic framework in D number theory (DNT) by formally defining non-exclusiveness, proposing a method to combine multiple D numbers, and defining new belief and plausibility measures, but it does not provide concrete results or numbers as applications are deferred to future work.
As a generalization of Dempster-Shafer theory, D number theory (DNT) aims to provide a framework to deal with uncertain information with non-exclusiveness and incompleteness. Although there are some advances on DNT in previous studies, however, they lack of systematicness, and many important issues have not yet been solved. In this paper, several crucial aspects in constructing a perfect and systematic framework of DNT are considered. At first the non-exclusiveness in DNT is formally defined and discussed. Secondly, a method to combine multiple D numbers is proposed by extending previous exclusive conflict redistribution (ECR) rule. Thirdly, a new pair of belief and plausibility measures for D numbers are defined and many desirable properties are satisfied by the proposed measures. Fourthly, the combination of information-incomplete D numbers is studied specially to show how to deal with the incompleteness of information in DNT. In this paper, we mainly give relative math definitions, properties, and theorems, concrete examples and applications will be considered in the future study.