Ed Wright, (IET, Inc.), email@example.com, and
Masami Takikawa, (IET, Inc.), firstname.lastname@example.org
In traditional data fusion applications, fusion is performed using data from sensors that are reasonably well understood and provide error models with known parameters. In today's operational asymmetric warfare environment, however, it is required to fuse information from a much broader set of sources (e.g, HUMINT, COMINT intercepts, and open source). Fusing information from such diverse sources necessitates handling of additional uncertainties about the meaning or semantics of data and characterization of sources. Such semantic fusion poses various challenges, including interpreting information (e.g., texts in various natural languages or outputs from sensors not well understood), mapping and aligning different ontologies, inferring credibility of sources, and integrating information in various forms of uncertainties such as probabilities, Dempster Shaffer (D-S) belief functions, and fuzzy logic.
We use Bayesian Networks as the common representation for alternative representations of uncertainty, including D-S and fuzzy-logic, in order to fuse information from multiple sources. We have developed probabilistic representations for use in hierarchical Bayesian inference, and the methodology for converting alternate uncertainty representations to probabilities. The development includes the methodology for learning probabilistic models of legacy systems when the existing representation is unknown. Our approach requires that we be able to incorporate D-S, fuzzy systems, and other ad hoc or unknown uncertainty representations.
For D-S we use the plausibility transformation from D-S to BN to obtain probabilities by using the plausibility function computed from the D-S belief function. Unlike other transformations (e.g., the pignistic one), this is compatible with Dempster's rule, and exactly the same results can be obtained by using efficient Bayesian inference.
For systems that use fuzzy membership to represent uncertainty, we represent the fuzzy report as evidence from a source with an unknown credibility model. If details of the fuzzy membership functions are available, that information is used to instantiate the credibility model. When no details are available, we recognize that there are many transformation methods available among fuzzy-logic membership functions, possibilities, D-S belief functions, Random-sets, and probabilities. We include second order uncertainty in the credibility model to represent the range of possible transformations. When multiple observations are available from a consistent fuzzy source, the BN model allows us to learn the parameters of an appropriate credibility model.
Systems with ad hoc or otherwise unknown uncertainty representations are also modeled using a generic credibility model with second order uncertainty. When multiple observations are available from a consistent fuzzy source, the BN model allows us to learn the parameters of an appropriate credibility model.
In addition to the theoretical and modeling work, we have created a simple model of fuzzy sensors and shown how a second-order uncertainty model can be used to interpret fuzzy sensor reports. We have also shown how these models allow us to change the interpretation of existing reports upon receiving new information about sensors or multiple reports from the same sensor.
Bayesian networks are also used to implement a computational model that characterizes the semantics of information. Such a computational model can be used to (1) incorporate semantic information in the fusion process; (2) deal with missing or uncertain semantic information; and (3) update results of previous inference to make use of new semantic information when it becomes available.
Benefits of using Bayesian networks as a semantic fusion framework include the ability of making coherent and optimal decisions using well-established Bayesian decision theory, a compact representation which makes knowledge elicitation and inference more tractable, the availability of advanced BN representation and inference mechanisms such as Multi-Entity Bayesian Networks (MEBNs) which combine Bayesian networks with first-order expressibility, enabling the creation of modular and reusable probability models.
In this paper, we describe MEBN models for semantic fusion with various uncertainty representations (e.g., fuzzy systems), and demonstrate their ability to fuse information in various uncertainty representations, make inference about the characteristics of unknown sources, and update fusion results with new semantic information.