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.
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Acknowledgments
This work has been supported by a Multidisciplinary University Research Initiative (MURI) grant (Number W911NF-09-1-0392) for “Unified Research on Network-based Hard/Soft Information Fusion”, issued by the US Army Research Office (ARO). This work has also been supported by an ONR grant for “Human Behavior Modeling Using Fuzzy and Soft Technologies”, award number N000141010121. We gratefully appreciate this support
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Yager, R.R. Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas. Fuzzy Optim Decis Making 12, 393–414 (2013). https://doi.org/10.1007/s10700-013-9163-z
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DOI: https://doi.org/10.1007/s10700-013-9163-z