Bayes-invariant transformations of uncertainty representations

Ronald Mahler

doi:10.1117/12.667108

17 May 2006 Bayes-invariant transformations of uncertainty representations

Ronald Mahler

Proceedings Volume 6235, Signal Processing, Sensor Fusion, and Target Recognition XV; 62350O (2006) https://doi.org/10.1117/12.667108
Event: Defense and Security Symposium, 2006, Orlando (Kissimmee), Florida, United States

Abstract

Much effort has been expended on devising "conversions" of one uncertainty representation scheme to another- fuzzy to probabilistic, Dempster-Shafer to probabilistic, to fuzzy, etc. Such efforts have been hindered by the fact that uncertainty representation formalisms vary considerably in the degree of complexity of information which they encode. For example, 2^M - 1 numbers are required to specify a Dempster-Shafer basic mass assignment (b.m.a.) on a space with M elements; whereas only M - 1 numbers are required to specify a probability distribution on the same space. Consequently, any conversion of b.m.a.'s to probability distributions will result in a huge loss of information. In addition, conversion from one uncertainty representation formalism to another should be consistent with the data fusion methodologies intrinsic to these formalisms. For b.m.a.'s to be consistently converted to fuzzy membership functions, for example, Dempster's combination should be transformed into fuzzy conjunction in some sense. In this paper we show that a path out of such quandaries is to realize that in many applications all information must ultimately be reduced to state estimates and covariances. Adopting a Bayesian approach, we identify Bayes-invariant conversions between various uncertainty representation formalisms.

Citation Download Citation

Ronald Mahler "Bayes-invariant transformations of uncertainty representations", Proc. SPIE 6235, Signal Processing, Sensor Fusion, and Target Recognition XV, 62350O (17 May 2006); https://doi.org/10.1117/12.667108

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KEYWORDS

Fuzzy logic

Data conversion

Data fusion

Curium

Data compression

Image compression

Logic

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