Constructing Multiple Frames of Discernment for Multiple Subproblems

In this paper we extend a methodology for constructing a frame of discernment from belief functions for one problem, into a methodology for constructing multiple frames of discernment for several different subproblems. The most appropriate frames of discernment are those that let our evidence interact in an interesting way without exhibit too much internal conflict. A function measuring overall frame appropriateness is mapped onto a Potts spin neural network in order to find the partition of all belief functions that yields the most appropriate frames.

[1]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[2]  F. Y. Wu The Potts model , 1982 .

[3]  Carsten Peterson,et al.  A New Method for Mapping Optimization Problems Onto Neural Networks , 1989, Int. J. Neural Syst..

[4]  Zbigniew W. Ras,et al.  Methodologies for Intelligent Systems , 1991, Lecture Notes in Computer Science.

[5]  H. Ichihashi,et al.  AN UNCERTAINTY MEASURE WITH MONOTONICITY UNDER THE RANDOM SET INCLUSION , 1993 .

[6]  S. K. Michael Wong,et al.  Upper and Lower Entropies of Belief Functions Using Compatible Probability Functions , 1993, ISMIS.

[7]  Johan Schubert On nonspecific evidence , 1993, Int. J. Intell. Syst..

[8]  Fred Richman,et al.  Calculating Maximum-Entropy Probability densities for Belief Functions , 1994, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  G. Klir,et al.  MEASURING TOTAL UNCERTAINTY IN DEMPSTER-SHAFER THEORY: A NOVEL APPROACH , 1994 .

[10]  Johan Schubert Finding a posterior Domain Probability Distribution by Specifying Nonspecific Evidence , 1995, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  Specifying nonspecific evidence , 2003, Int. J. Intell. Syst..

[12]  G. Klir,et al.  ON THE COMPUTATION OF UNCERTAINTY MEASURE IN DEMPSTER-SHAFER THEORY , 1996 .

[13]  Johan Schubert,et al.  Managing inconsistent intelligence , 2000, Proceedings of the Third International Conference on Information Fusion.

[14]  Mats Bengtsson,et al.  Dempster–Shafer clustering using Potts spin mean field theory , 2001, Soft Comput..

[15]  Johan Schubert,et al.  Fast Dempster-Shafer clustering using a neural network structure , 2003, ArXiv.

[16]  Johan Schubert Clustering belief functions based on attracting and conflicting metalevel evidence , 2003, ArXiv.

[17]  Johan Schubert,et al.  Clustering belief functions based on attracting and conflicting metalevel evidence using Potts spin mean field theory , 2003, Inf. Fusion.

[18]  H. Sidenbladh,et al.  Sequential clustering with particle filters-estimating the number of clusters from data , 2005, 2005 7th International Conference on Information Fusion.

[19]  Hedvig Kjellström,et al.  An information fusion demonstrator for tactical intelligence processing in network-based defense , 2007, Inf. Fusion.

[20]  Johan Schubert Clustering decomposed belief functions using generalized weights of conflict , 2008, Int. J. Approx. Reason..

[21]  Arthur P. Dempster,et al.  A Generalization of Bayesian Inference , 1968, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[22]  J. Schubert Constructing and Reasoning about Alternative Frames of Discernment , 2010 .

[23]  L. Zadeh,et al.  Information, Uncertainty and Fusion , 2012 .