5 research outputs found
Exploring the Combination Rules of D Numbers From a Perspective of Conflict Redistribution
Dempster-Shafer theory of evidence is widely applied to uncertainty modelling
and knowledge reasoning because of its advantages in dealing with uncertain
information. But some conditions or requirements, such as exclusiveness
hypothesis and completeness constraint, limit the development and application
of that theory to a large extend. To overcome the shortcomings and enhance its
capability of representing the uncertainty, a novel model, called D numbers,
has been proposed recently. However, many key issues, for example how to
implement the combination of D numbers, remain unsolved. In the paper, we have
explored the combination of D Numbers from a perspective of conflict
redistribution, and proposed two combination rules being suitable for different
situations for the fusion of two D numbers. The proposed combination rules can
reduce to the classical Dempster's rule in Dempster-Shafer theory under a
certain conditions. Numerical examples and discussion about the proposed rules
are also given in the paper.Comment: 6 pages, 4 figure
Belief and plausibility measures for D numbers
As a generalization of Dempster-Shafer theory, D number theory provides a
framework to deal with uncertain information with non-exclusiveness and
incompleteness. However, some basic concepts in D number theory are not well
defined. In this note, the belief and plausibility measures for D numbers have
been proposed, and basic properties of these measures have been revealed as
well.Comment: 9 page
A total uncertainty measure for D numbers based on belief intervals
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.Comment: 14 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1711.0918
D numbers theory based game-theoretic framework in adversarial decision making under fuzzy environment
Adversarial decision making is a particular type of decision making problem
where the gain a decision maker obtains as a result of his decisions is
affected by the actions taken by others. Representation of alternatives'
evaluations and methods to find the optimal alternative are two important
aspects in the adversarial decision making. The aim of this study is to develop
a general framework for solving the adversarial decision making issue under
uncertain environment. By combining fuzzy set theory, game theory and D numbers
theory (DNT), a DNT based game-theoretic framework for adversarial decision
making under fuzzy environment is presented. Within the proposed framework or
model, fuzzy set theory is used to model the uncertain evaluations of decision
makers to alternatives, the non-exclusiveness among fuzzy evaluations are taken
into consideration by using DNT, and the conflict of interests among decision
makers is considered in a two-person non-constant sum game theory perspective.
An illustrative application is given to demonstrate the effectiveness of the
proposed model. This work, on one hand, has developed an effective framework
for adversarial decision making under fuzzy environment; One the other hand, it
has further improved the basis of DNT as a generalization of Dempster-Shafer
theory for uncertainty reasoning.Comment: 59 pages, 5 figure
Basic concepts, definitions, and methods in D number theory
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.Comment: 28 pages, 2 figure