On cardinalities of different degrees of Belief functions conjunctive conflictness

Authors: Milan Daniel, Václav Kratochvíl
Publication year: 2024
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of the 24th Czech-Japan Seminar on Data Analysis and Decision Making
Bibliographic citation: DANIEL, Milan, KRATOCHVÍL, Václav. On cardinalities of different degrees of Belief functions conjunctive conflictness. In: Proceedings of the 24th Czech-Japan Seminar on Data Analysis and Decision Making. Praha: ÚTIA AV ČR, 2024, S. 14-25. ISBN 978-80-905688-0-8. Dostupné z: https://cjs.utia.cas.cz/2024/proceedings.pdf#section.0.2https://library.utia.cas.cz/separaty/2024/MTR/kratochvil-0600834.pdf
ID: 600834
Online record: View online record

Abstract

This paper examines mutual conflict behavior between belief function structures across different discernment frame sizes (\(\Omega\)). Through experiments on \(\Omega_2\) to \(\Omega_6\), we observe that as frame size increases, non-conflicting pairs and higher-order hidden conflicts become exceedingly relatively rare despite the exponential growth of cardinalities of their classes. The super-exponential growth of possible belief structures complicates exhaustive analysis, leading us to employ random sampling. Our findings reveal that the cardinality of a class of first-degree hidden conflicts (HC\(_1\)) grows faster than non-conflicts as frame size increases, highlighting the challenges and implications of applying belief function theory in complex decision-making scenarios.