We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
International audienceWe prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set Ξ, the function mapping any random set distribution to the distribution of its intersection (under independence assumption) with Ξ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the L k norm distance between inclusion func-tionals also known as commonalities. Moreover, the function mapping any random set distribution to the distribution of its union (under independence assumption) with Ξ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the L k norm distance between hitting func-tionals also known as plausibilities. Using the epistemic random set interpretation of belief functions, we also discuss the ability of these distances to yield conflict measures. All the proofs in this paper are derived in the framework of Dempster-Shafer belief functions. Let alone the discussion on conflict measures, it is straightforward to transcribe the proofs into the general (non necessarily epistemic) random set terminology
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.