Abstract
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 [15,16,20] 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.
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Daniel, M. (2012). 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. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_55
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DOI: https://doi.org/10.1007/978-3-642-31718-7_55
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