The BBAs of elements of the sub-frames Ω₂₂ for Example 1.

<p>The BBAs of elements of the sub-frames Ω₂₂ for Example 1.</p

Overall computational time between three combination methods.

<p>(Movielens).</p

DSmT modeling function.

<p>DSmT modeling function.</p

Three Bayesian BBAs for Example 1.

<p>Three Bayesian BBAs for Example 1.</p

Contextual information.

<p>Contextual information.</p

The BBAs of elements of the sub-frames Ω₂₁ for Example 1.

<p>The BBAs of elements of the sub-frames Ω₂₁ for Example 1.</p

A fast combination method in DSmT and its application to recommender system

<div><p>In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users’ soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time.</p></div

General process of recommendations.

<p>General process of recommendations.</p

The BBAs of elements of the sub-frames Ω₃ Using MRC for Example 1.

<p>The BBAs of elements of the sub-frames Ω₃ Using MRC for Example 1.</p

Arrest de la cour des aides, qui, en réformant une sentence de l'élection de Soissons, du 3 juin 1752, pour n'avoir prononcé qu'une amende de mille livres contre trois fraudeurs, sur lesquels il a été saisi du tabac de contrebande, condamne chacun desdits fraudeurs en l'amende de mille livres, conformément au règlemens ; & en tous les dépens . Du 10 mars 1753

[Acte. 1753-03-10. Paris]Avec mode text