Based on Klir’s framework of uncertainty, the total uncertainty (also called ambiguity) of belief function is linear addition of discord and nonspecificity. Though uncertainty measures of belief function have been discussed widely, there is no measure that can satisfy the monotonicity and range consistency properties at the same time. In this article, we discuss uncertainty measure of belief function from the perspective of information fractal dimension. An uncertainty quantity called evenness and its measure Eve are proposed, which can represent the belief propensity degree of belief function. We first propose the measures of diversity (normalized nonspecificity) and the element evenness (normalized discord), and then fuse them to calculate Eve. The proposed method can not only measure the subnormal mass function but also interpret the different views of Klir and Smets on “Uncertainty.” In addition, we extend Klir’s framework of uncertainty based on the proposed information quantities.

The theory of evidence (TE) has been largely used for many applications. This theory is a generalization of probability distribution and offers a mathematical representation for two types of uncertainty-based information: 1) discord and 2) nonspecificity. Several measures have already been developed to quantify these two types of uncertainty. They have been called total uncertainty (TU) measures since they quantify both types of uncertainty. The generalized Hartley measure and the maximum entropy have been the only measures so far that satisfy a list of properties very desirable for practical applications. Recently, two new measures of nonspecificity and TU based on belief intervals have been proposed. These two measures do not satisfy the properties of additivity, superadditivity, and subadditivity in the TE. The present critique is about these shortcomings and provides a more complete analysis of those uncertainty measures with respect to a list of desired properties. A potential consequence of an ill-characterized measure may yield selecting an inappropriate rule for decision-making in the processing chain from data to information to decisions.

Recently, a measure of “total uncertainty” (TU) in Dempster-Shafer theory, based on the pignistic distribution called ambiguity measure (AM), have been modified. The resulting new measure has been simply referred as modified AM (MAM). In the literature, it has been shown that AM, in addition to showing some undesirable behaviors, has important drawbacks related to two essential properties for such measures: 1) subadditivity and 2) monotonicity. The MAM measure has been developed to solve the AM subadditivity problem, but this paper demonstrates that MAM suffers the same drawback as AM with respect to monotonicity. A measure of uncertainty that cannot meet the monotonicity requirement has an important drawback for its exploitation in operational contexts such as in analytics, information fusion, and decision support. This paper aims at identifying and discussing drawbacks of this type of measures (AM, MAM). Our main motivation is to insist upon the important requirement of monotonicity that a TU measure should possess to improve its potential of being used and trusted in applications. This discussion is due time since the monotonicity problem needs first to be solved to avoid building too high expectations for usefulness and potential exploitation of such measures in operational communities.

This paper proposes an approach referred as: iterative refinement of possibility distributions by learning (IRPDL) for pixel-based image classification. The IRPDL approach is based on the use of possibilistic reasoning concepts exploiting expert knowledge sources as well as ground possibilistic seeds learning. The set of seeds is constructed by incrementally updating and refining the possibility distributions. Synthetic images as well as real images from the RIDER Breast MRI database are being used to evaluate the IRPDL performance. Its performance is compared with three relevant reference methods: region growing, semi-supervised fuzzy pattern matching, and Markov random fields. The IRDPL performance (in terms of recognition rate, 87.3%) is close to the Markovian method (88.8%) that is considered to be the reference in pixel-based image classification. IRPDL outperforms the other two methods, respectively, at the recognition rates of 83.9% and 84.7%. In addition, the proposed IRPDL requires fewer parameters for the mathematical representation and presents a reduced computational complexity.

Both image registration and fusion can be formulated as estimation problems. Instead of estimating the registration parameters and the true scene separately as in the conventional way, we propose a maximum likelihood approach for joint image registration and fusion in this paper. More precisely, the fusion performance is used as the criteria to evaluate the registration accuracy. Hence, the registration parameters can be automatically tuned so that both fusion and registration can be optimized simultaneously. The expectation maximization algorithm is employed to solve this joint optimization problem. The Cramer-Rao bound (CRB) is then derived. Our experiments use several types of sensory images for performance evaluation, such as visual images, IR thermal images, and hyperspectral images. It is shown that the mean square error of estimating the registration parameters using the proposed method is close to the CRBs. At the mean time, an improved fusion performance can be achieved in terms of the edge preservation measure Q(AB/F), compared to the Laplacian pyramid fusion approach.

Defence Research and Development Canada at Valcartier is pursuing the exploration of situation analysis concepts and the prototyping of computer-based decision support systems to maintain the state of situational awareness for the decision maker. The integration of the human element at the beginning of the analysis process is an important facet of our approach. The mathematical formalism and methodology proposed will be illustrated on concrete examples for visibility-based terrain analysis and reasoning for combat search and rescue (CSAR) operations. The work presented is based on the North Atlantis scenario GIS dataset, depicting a conflict taking place over an imaginary continent. The dataset is composed of topographic, hydrographical, transportation, and other typical land cover layers. Applications presented will include landing site determination as well as shortest path to crash site determination.

A crucial point in the decision-level identity fusion is to combine information in an appropriate way to generate an optimal decision, according to the individual information coming from a set of different sensors. An interesting approach was developed for the decision- level identity fusion, which use optimization techniques to minimize an objective function which measure the dissimilarities between the combination result and the set of initial sensor reports. Several objective functions were already proposed for the similar sensor fusion (SSF) and the dissimilar sensor fusion (DSF) models. In this paper, we present these fusion methods, we raise some questions and make some improvements, and finally we study the behaviour of these fusion rules on several examples.

MacDonald Dettwiler is leading a PRECARN partnership project to develop an advanced simulation testbed for the evaluation of the effectiveness of Network Enabled Operations in a coastal large volume surveillance situation. The main focus of this testbed is to study concepts like distributed information fusion, dynamic resources and networks configuration management, and self synchronising units and agents. This article presents the system architecture with an emphasis on our approach for distributed information fusion.

In the theory of evidence, two kinds of uncertainty coexist, nonspecificity and discord. An aggregate uncertainty (AU) measure has been defined to include these two kinds of uncertainty, in an aggregate fashion. Meyerowitz et al. proposed an algorithm for calculating AU and validated its practical usage. Although this algorithm was proven to be absolutely correct by Klir and Wierman, in some cases, it remains too complex. In fact, when the cardinality of the frame of discernment is very large, it can be impossible to calculate AU. Therefore, based on Klir's and Harmanec's seminal work, we give some justifications for restricting the computation of AU(Bel) to the core of the corresponding belief function, and we also propose an algorithm to calculate AU(Bel), the F-algorithm, which reduces the computational complexity of the original algorithm of Meyerowitz et al. We prove that this algorithm gives the same results as Meyerowitz's algorithm, and we outline conditions under which it reduces the computational complexity significantly. Moreover, we illustrate the use of the F-algorithm in computing AU in a practical scenario of target identification.

Characterisation of an information fusion system (IFS) is a very difficult challenge. There are many levels of information fusion and there are many decision fusion models. One can argue that each problem is very specific and thus developing a generalized framework is utopia. This paper presents a simplified, and sometimes naive representation of IFS. This representation is based on characterising the inputs and outputs of IFS. An IFS is thus seen as a function that transforms the input into an output given some conditions. These conditions might include controls, background knowledge, and goals queries. We present a set of properties that might be considered to characterise a fusion function. This paper also discusses some challenges of distributed information fusion as a pre-requisite of Net-enabled operations

In the framework of evidence theory, ambiguity is a general term proposed by Klir and Yuan in 1995 to gather the two types of uncertainty coexisting in this theory: discord and nonspecificity. Respecting the five requirements of total measures of uncertainty in the evidence theory, different ways have been proposed to quantify the total uncertainty, i.e., the ambiguity of a belief function. Among them is a measure of aggregate uncertainty, called AU, that captures in an aggregate fashion both types of uncertainty. But some shortcomings of AU have been identified, which are that: 1) it is complicated to compute; 2) it is highly insensitive to changes in evidence; and 3) it hides the distinction between the two types of uncertainty that coexist in every theory of imprecise probabilities. To overcome the shortcomings, Klir and Smith defined the TU1measure that is a linear combination of the AU measure and the nonspecificity measure N. But the TU1measure cannot solve the problem of computing complexity, and brings a new problem with the choice of the linear parameter delta. In this paper, an alternative measure to AU for quantifying ambiguity of belief functions is proposed. This measure, called Ambiguity Measure (AM), besides satisfying all the requirements for general measures also overcomes some of the shortcomings of the AU measure. Indeed, AM overcomes the limitations of AU by: 1) minimizing complexity for minimum number of focal points; 2) allowing for sensitivity changes in evidence; and 3) better distinguishing discord and nonspecificity. Moreover, AM is a special case of TU1that does not need the parameter delta

Two novel neural data fusion algorithms based on a linearly constrained least square (LCLS) method are proposed. While the LCLS method is used to minimize the energy of the linearly fused information, two neural-network algorithms are developed to overcome the ill-conditioned and singular problems of the sample covariance matrix arisen in the LCLS method. The proposed neural fusion algorithms are samples for implementation using both software and hardware. Compared with the existing fusion methods, the proposed neural data fusion method has an unbiased statistical property and does not require any a priori knowledge about the noise covariance. It is shown that the proposed neural fusion algorithms converge globally to the optimal fusion solution when the sample covariance matrix is singular, and converge globally with exponential rate when the sample covariance matrix is nonsingular. We apply the proposed neural fusion method to image and signal fusion, and it is shown that the quality of the solution can be greatly enhanced by the proposed technique.

We consider the problem of identity fusion for a multisensor target tracking system whereby the sensors generate reports on the target identities. Since sensor reports are typically fuzzy, incomplete, or inconsistent, the fusion of such sensor reports becomes a major challenge. In this paper, we introduce a new identity fusion method based on the minimization of inconsistencies among the sensor reports by using a convex quadratic programming formulation. In contrast to Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing complexity, our approach is highly efficient (polynomial time solvable). Moreover, our approach can fuse sensor reports of the form more general than that allowed by the evidential reasoning theory. Simulation results show that our method generates reasonable fusion results which are similar to that obtained via the evidential reasoning theory.