Partial Ordering Of Hyper Powersets And Matrix Representation Of Belief Functions Within Dsmt
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Partial ordering of hyper-powersets and matrix representation of belief functions within DSmT
In this paper, we examine several issues for ordering or partially ordering elements of hyperpowertsets involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT) developed by the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation of belief functions.
Partial ordering on hyper-power sets
In this chapter, we examine several issues for ordering or partially or dering elements of hyper-power sets involved in the DSmT. We will show the benefit of some of these issues to obtain a nice and interesting structure of matrix represen tation of belief functions.
Advances and Applications of DSmT for Information Fusion (Collected works), second volume
Author: Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2006-01-01
This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by 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.