Abstract
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.
Highlights
The theory of belief functions, known as Dempster-Shafer Theory (DST) was developed by Shafer [1] in 1976 from Dempster’s works [2]
This paper presents a new combination method, called modified rigid coarsening (MRC), to get the final Bayesian basic belief assignments (BBAs) based on hierarchical decomposition of the frame of discernment, which can be seen as an intermediary approach between the two aforementioned methods
The results show that regarding the accuracy of recommendations, MRC is extremely close to classical proportional conflict redistribution rule #6 (PCR6); and the computational time of MRC can be obviously superior to that of PCR6
Summary
The theory of belief functions, known as Dempster-Shafer Theory (DST) was developed by Shafer [1] in 1976 from Dempster’s works [2]. The last step of this hierarchical process is to calculate the combined (Bayesian) BBA of all focal elements according to the connection weights of the bintree structure, where the number of layers l of the tree depends on the cardinality |Θ| of the original FoD Θ. At layer l = 3: We use again the proportional redistribution method which gives us the BBAs of the sub-frames O3 in Table 5: Step 3: The connection weights λi are computed from the assignments of coarsening elements. It is worth noting that when the given BBAs are not Bayesian, the first step is to use the existing Probabilistic Transformation (PT) to transform them to Bayesian BBAs. In order to use the propoLsed combination method in the RSs, modified rigid coarsening is mathematically denoted as . As shown in [33], DSmP makes a remarkable improvement compared with BetP and CuzzP, since a more judicious redistribution of the ignorance masses to the singletons has been adopted by DSmP
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