What is the new element that introduced algebra?
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Respuesta:
The study presents an introduction to algebraic structures related to belief functions (BF) in a 3-element discernment framework. The Hájek & Valdés method for BFs in 2-element frames [15,16,20] generalizes to a broader framework of discernment. Due to the complexity of the algebraic structure, the study is divided into 2 parts, the present one is dedicated to the case of quasi-Bayesian BF. The Dempster BF semi-group is remembered in the 2-element discernment framework of Hájek-Valdés. A new definition of the Dempster semigroup (an algebraic structure) of BF is introduced in a 3-element framework; and its subalgebras in general, subalgebras of Bayesian BF and quasi-Bayesian BF are described and analyzed. Ideas and open problems are presented for future research.
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