Introduction to an Algebra of Belief Functions on Three-Element Frame of Discernment - A Quasi Bayesian Case

Autoři: Milan Daniel
Rok vydání: 2012
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Advances in Computational Intelligence
Projekty: Matematická fuzzy logika v informatice
Bibliografická citace: DANIEL, Milan. Introduction to an Algebra of Belief Functions on Three-Element Frame of Discernment - A Quasi Bayesian Case. In: GRECO, S., BOUCHON-MEUNIER, B., COLETTI, G., FEDRIZZI, M., MATARAZZO, B., YAGER, R. R., eds. Advances in Computational Intelligence. Heidelberg: Springer, 2012, S. 532-542. Communications in Computer and Information Science, 299. ISBN 978-3-642-31717-0. ISSN 1865-0929
Dostupné z: doi:10.1007/978-3-642-31718-7_55
DOI: 10.1007/978-3-642-31718-7_55
ID: 379837

Abstrakt

The study presents an introduction to algebraic structures related to belief functions (BFs) on 3-element frame of discernment. 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 the case of quasi Bayesian BFs. Dempster’s semigroup of BFs on 2-element frame of discernment by Hájek-Valdés is recalled. A new definition of Dempster’s semigroup (an algebraic structure) of BFs on 3-element frame is introduced; and its subalgebras in general, subalgebras of Bayesian BFs and of quasi Bayesian BFs are described and analysed. Ideas and open problems for future research are presented.