Morphisms of Dempster's Semigroup: A Revision and Interpretation

Authors: Milan Daniel
Publication year: 2011
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of 14th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty CJS 2011
Projects: Mathematical Fuzzy Logic in Computer Science
Bibliographic citation: DANIEL, Milan. Morphisms of Dempster's Semigroup: A Revision and Interpretation. In: BARTÁK, Roman, ed. Proceedings of 14th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty CJS 2011. Praha: Matfyzpress, 2011, S. 26-34. ISBN 978-80-7378-179-8.
ID: 367898

Abstract

Analyzing three new approaches to interpretation, definition, and measurement of conflicts of belief Functions (BFs), we previously observed a possibility of expression of a BF Bel as Dempster's sum of non-conflicting BF Bel0 with the same plausibility decisional support as the original BF Bel has and of indecisive BF BelS which does not prefer any of the elements of frame of discernment. Based on this observation, the theory of homomorphisms of Dempster's semigroup (the algebra of non-extremal BFs on 2-element frame of discernment with Dempster's rule as its binary operation) is updated in the present contribution. New homomorphisms are introduced; their interpretation and relation to the original ones are presented.