By editors Florentin Smarandache, Jean Dezert
This moment quantity devoted to Dezert-Smarandache idea (DSmT) in info Fusion brings in new fusion quantitative principles (such because the PCR1-6, the place PCR5 for 2 assets does the main mathematically distinctive redistribution of conï¬icting plenty to the non-empty units within the fusion literature), qualitative fusion ideas, and the idea Conditioning Rule (BCR) that is diversified from the classical conditioning rule utilized by the fusion group operating with the Mathematical concept of facts. different fusion principles are built in line with T-norm and T-conorm (hence utilizing fuzzy good judgment and fuzzy set in info fusion), or extra basic fusion ideas in line with N-norm and N-conorm (hence utilizing neutrosophic common sense and neutrosophic set in details fusion), and an try and unify the fusion ideas and fusion theories. The recognized fusion ideas are prolonged from the facility set to the hyper-power set and comparability among principles are made on many examples. One deï¬nes the measure of intersection of 2 units, measure of union of 2 units, and measure of inclusion of 2 units which all assist in enhancing the all current fusion ideas in addition to the credibility, plausibility, and communality services. The ebook chapters are written through Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang.
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Additional resources for Advances and Applications of DSmT for Information Fusion (Collected works), second volume
11. 06. 06. 036. 290 One clearly sees that mDS (A ∪ B) gets some mass from the conflicting mass although A ∪ B does not deserve any part of the conflicting mass since A ∪ B is not involved in the conflict (only A and B are involved in the conflicting mass). Dempster’s rule appears to authors opinions less exact than PCR5 and Inagaki’s rules  because it redistribute less exactly the conflicting mass than PCR5, even than PCR4 and minC, since Dempter’s rule takes the total conflicting mass and redistributes it to all non-empty sets, even those not involved in the conflict.
E. s (X) = m1 (X) + m2 (X) + . . s = s, but in some degenerate cases it can be less). In the degenerate case when all column sums of all non-empty sets involved in the conflict are zero, then the conflicting mass is transferred to the non-empty disjunctive form of all sets together which were involved in the conflict together. But if this disjunctive form happens to be empty, then the problem reduces to a degenerate void problem and thus all conflicting mass is transferred to the empty set or we can assume (if one has enough reason to justify such assumption) that the frame of discernment might contain new unknown hypotheses all summarized by θ0 and under this assumption all conflicting mass is transferred onto the unknown possible θ0 .
M1 ⊕ . . ). This severe drawback of WAO and PCR1 forces us to develop the next PCR rules satisfying the neutrality property of VBA with better redistributions of the conflicting information. 2 Example for PCR1 (degenerate case) For non degenerate cases with Shafer’s model, PCR1 and WAO provide the same results. So it is interesting to focus the reader’s attention on the difference between PCR1 and WAO in a simple degenerate case corresponding to a dynamic fusion problem. Let’s take the following example showing the restriction of applicability of static-WAO9 .