Upper and Lower Probabilities Induced by a Multivalued Mapping

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src="https://media.springernature.com/w72/springer-static/cover-hires/book/978-3-540-44792-4?as=webp" srcset="https://media.springernature.com/w144/springer-static/cover-hires/book/978-3-540-44792-4?as=webp 2x" alt=""> </picture> <span class="app-article-masthead__journal-title ">Classic Works of the Dempster-Shafer Theory of Belief Functions</span> </a> <span class="app-article-masthead__conference-info"></span> </div> </div> </div> </section> </div> <div class="c-article-main u-container u-mt-24 u-mb-32 l-with-sidebar" id="main-content" data-component="article-container"> <main class="js-main-column u-serif c-chapter-body" data-track-component="chapter"> <article lang="en"> <div class="c-article-header"> <header> <div class="app-overview-section"> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Arthur_P_-Dempster" data-author-popup="auth-Arthur_P_-Dempster">Arthur P. Dempster</a><sup class="u-js-hide"></sup> </li></ul> <div class="app-overview-section__separator app-overview-section__book-series"> <div class="app-book-series-listing"> <div> <svg class="app-book-series-listing__icon" width="24" height="24" aria-hidden="true" focusable="false"><use href="#icon-eds-i-book-series-medium"></use></svg> </div> <div> <p data-test="series-link"> <span class="app-book-series-listing__description">Part of the book series:</span> <a href="https://www.springer.com/series/2941" data-track="click" data-track-action="open book series" data-track-label="link">Studies in Fuzziness and Soft Computing</a> ((STUDFUZZ,volume 219)) </p> </div> </div> </div> <div class="app-overview-section__separator" data-test="article-metrics"> <div id="altmetric-container"> <ul class="app-article-metrics-bar u-list-reset" data-test="article-metrics"> <li class="app-article-metrics-bar__item" data-test="access-count"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-accesses-medium"></use> </svg>4471 <span class="app-article-metrics-bar__label">Accesses</span></p> </li> <li class="app-article-metrics-bar__item" data-test="citation-count"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-citations-medium"></use> </svg>196 <span class="app-article-metrics-bar__label"> <a href="http://citations.springer.com/item?doi=10.1007/978-3-540-44792-4_3" target="_blank" rel="noopener" title="Visit Springer Citations for full citation details" data-track="click" data-track-action="Citation count" data-track-label="link">Citations</a> </span></p> </li> </ul> </div> </div> </div> </header> </div> <div data-article-body="true" data-track-component="chapter body" class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 id="Abs1" class="c-article-section__title js-section-title js-c-reading-companion-sections-item"><span class="c-article-section__title-number"> </span>Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>A multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over subsets of S. Some basic properties of such systems are explored in Sects. 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Sect. 3. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information, as discussed in Sects. 4 and 5. 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Yager (<span data-author-role-id="auth--">Dr.</span>) (<span data-author-role-id="auth--">Dr.</span>)</p></li><li id="Aff3"><p class="c-article-author-affiliation__address">Department of Management and Information Systems, University of Akron College of Business Administration, 351 Akron, OH 4325-4801, USA</p><p class="c-article-author-affiliation__authors-list">Liping Liu </p></li></ol></div></div></section><section data-title="Rights and permissions" lang="en"><div class="c-article-section" id="rightslink-section"><h2 id="rightslink" class="c-article-section__title js-section-title js-c-reading-companion-sections-item"><span class="c-article-section__title-number"> </span>Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"><p class="c-article-rights" data-test="rightslink-content"><a data-track="click" data-track-action="view rights and permissions" data-track-label="link" href="https://s100.copyright.com/AppDispatchServlet?publisherName=SpringerNature&orderBeanReset=true&orderSource=SpringerLink&title=Upper%20and%20Lower%20Probabilities%20Induced%20by%20a%20Multivalued%20Mapping&author=Arthur%20P.%20Dempster&contentID=10.1007%2F978-3-540-44792-4_3&copyright=Springer-Verlag%20Berlin%20Heidelberg&publication=eBook&publicationDate=2008&startPage=57&endPage=72&imprint=Springer-Verlag%20Berlin%20Heidelberg">Reprints and permissions</a></p></div></div></section><section data-title="Copyright information"><div class="c-article-section" id="copyright-information-section"><h2 id="copyright-information" class="c-article-section__title js-section-title js-c-reading-companion-sections-item"><span class="c-article-section__title-number"> </span>Copyright information</h2><div class="c-article-section__content" id="copyright-information-content"><p>© 2008 Springer-Verlag Berlin Heidelberg</p></div></div></section><section aria-labelledby="chapter-info" data-title="About this chapter" lang="en"><div class="c-article-section" id="chapter-info-section"><h2 id="chapter-info" class="c-article-section__title js-section-title js-c-reading-companion-sections-item"><span class="c-article-section__title-number"> </span>About this chapter</h2><div class="c-article-section__content" id="chapter-info-content"><div class="c-bibliographic-information"><div class="c-bibliographic-information__column"><h3 class="c-article__sub-heading" id="citeas">Cite this chapter</h3><p class="c-bibliographic-information__citation" data-test="bibliographic-information__cite_this_chapter">Dempster, A.P. (2008). Upper and Lower Probabilities Induced by a Multivalued Mapping. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. 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