Abstract
We describe two functions on possibility distributions which allow one to compute binary operations with dependence either specified by a copula or partially defined by an imprecise copula. We use the fact that possibility distributions are consonant belief functions to aggregate two possibility distributions into a bivariate belief function using a version of Sklar's theorem for minitive belief functions, i.e. necessity measures. The results generalise previously published independent and Fréchet methods, allowing for any stochastic dependence to be specified in the form of a (imprecise) copula. This new method produces tighter extensions than previous methods when a precise copula is used. These latest additions to possibilistic arithmetic give it the same capabilities as p-box arithmetic, and provides a basis for a p-box/possibility hybrid arithmetic. This combined arithmetic provides tighter bounds on the exact upper and lower probabilities than either method alone for the propagation of general belief functions.
Original language | English |
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Title of host publication | The 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021) |
Place of Publication | Piscataway, N.J. |
Publisher | IEEE |
Pages | 169-179 |
Number of pages | 11 |
ISBN (Print) | 9780738126463 |
Publication status | Published - 3 Oct 2021 |
Event | The 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021) - New York, United States Duration: 30 Sept 2021 → 3 Oct 2021 |
Conference
Conference | The 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021) |
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Abbreviated title | ISPTA 2021 |
Country/Territory | United States |
City | New York |
Period | 30/09/21 → 3/10/21 |
Keywords
- possibility theory
- P-box
- copulas
- probabilistic arithmetic
- probability bounds analysis
- imprecise probabilities