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Original title:
Introduction to Algebra of Belief Functions on Three-element Frame of Discernment - A General Case
Authors: Daniel, Milan
Document type: Papers
Conference/Event: WUPES 2012, Mariánské Lázně (CZ), 2012-09-12 / 2012-09-15
Year: 2012
Language: eng
Abstract: This contribution presents the second part of the introductive study of algebraic structure of belief functions (BFs) on 3-element frame of discernment. Algebraic method by Hájek & Valdés for BFs on 2-element frames is generalized to larger frame of discernment. Due to complexity of the algebraic structure, the study is divided into 2 parts, the present one is devoted to a case of general BFs. The definition of Dempster's semigroup (an algebraic structure) of BFs on 3-element frame is recalled from the first part of the study. Results related to Bayesian and quasi Bayesian BFs from the first part are also briefly recalled. Further substructures related to another subsets of general BFs are described and analyzed (including idempotents, simple complementary BFs, generalizations of subsemigroups of simple BFs) and subalgebras isomorphic to Dempster's semigroup on 2-element frame of discernment. Ideas and open problems for future research are presented.
Keywords: belief function; conflict between belief functions; Dempster's semigroup; Dempster-Shafer theory; homomorphisms; uncertainty
Project no.: GAP202/10/1826 (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of 9th Workshop on Uncertainty Processing, ISBN 978-80-245-1885-5
Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0211882
Permalink: http://www.nusl.cz/ntk/nusl-126346
The record appears in these collections:
Research > Institutes ASCR > Institute of Computer Science
Conference materials > Papers
Authors: Daniel, Milan
Document type: Papers
Conference/Event: WUPES 2012, Mariánské Lázně (CZ), 2012-09-12 / 2012-09-15
Year: 2012
Language: eng
Abstract: This contribution presents the second part of the introductive study of algebraic structure of belief functions (BFs) on 3-element frame of discernment. Algebraic method by Hájek & Valdés for BFs on 2-element frames is generalized to larger frame of discernment. Due to complexity of the algebraic structure, the study is divided into 2 parts, the present one is devoted to a case of general BFs. The definition of Dempster's semigroup (an algebraic structure) of BFs on 3-element frame is recalled from the first part of the study. Results related to Bayesian and quasi Bayesian BFs from the first part are also briefly recalled. Further substructures related to another subsets of general BFs are described and analyzed (including idempotents, simple complementary BFs, generalizations of subsemigroups of simple BFs) and subalgebras isomorphic to Dempster's semigroup on 2-element frame of discernment. Ideas and open problems for future research are presented.
Keywords: belief function; conflict between belief functions; Dempster's semigroup; Dempster-Shafer theory; homomorphisms; uncertainty
Project no.: GAP202/10/1826 (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of 9th Workshop on Uncertainty Processing, ISBN 978-80-245-1885-5
Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0211882
Permalink: http://www.nusl.cz/ntk/nusl-126346
The record appears in these collections:
Research > Institutes ASCR > Institute of Computer Science
Conference materials > Papers
Record created 2012-10-16, last modified 2023-12-06