NDLI: Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas

Content Provider	Springer Nature Link
Author	Yager, Ronald R.
Copyright Year	2013
Abstract	We first introduce the Dempster–Shafer belief structure and highlight its role in the representation of information about a random variable for which our knowledge of the probabilities is interval-valued. We investigate the formation of the cumulative distribution function (CDF) for these types of variables. It is noted that this is also interval-valued and is expressible in terms of plausibility and belief measures. The class of aggregation operators known as copulas are introduced and a number of their properties are provided. We discuss Sklar’s theorem, which provides for the use of copulas in the formulation of joint CDFs from the marginal CDFs of classic random variables. We then look to extend these ideas to the case of joining the marginal CDFs associated with Dempster–Shafer belief structures. Finally we look at the formulation CDFs obtained from functions of multiple D–S belief structures.
Starting Page	393
Ending Page	414
Page Count	22
File Format	PDF
ISSN	15684539
Journal	Fuzzy Optimization and Decision Making
Volume Number	12
Issue Number	4
e-ISSN	15732908
Language	English
Publisher	Springer US
Publisher Date	2013-05-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Uncertainty modeling Copula Belief-structure Cumulative distribution function Imprecise random variable Mathematical Logic and Foundations Probability Theory and Stochastic Processes Optimization Calculus of Variations and Optimal Control; Optimization Artificial Intelligence (incl. Robotics) Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Logic Software

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