Mihai Cristian Florea

Robust combination rules for evidence theory

Dempsters rule of combination in evidence theory is a powerful tool for reasoning under uncertainty. Since Zadeh highlighted the counter-intuitive behaviour of Dempsters rule, a plethora of alternative combination rules have been proposed. In this paper, we propose a general formulation for combination rules in evidence theory as a weighted sum of the conjunctive and disjunctive rules. Moreover, with the aim of automatically accounting for the reliability of sources of information, we propose a class of robust combination rules (RCR) in which the weights are a function of the conflict between two pieces of information. The interpretation given to the weight of conflict between two BPAs is an indicator of the relative reliability of the sources: if the conflict is low, then both sources are reliable, and if the conflict is high, then at least one source is unreliable. We show some interesting properties satisfied by the RCRs, such as positive belief reinforcement or the neutral impact of vacuous belief, and establish links with other classes of rules. The behaviour of the RCRs over non-exhaustive frames of discernment is also studied, as the RCRs implicitly perform a kind of automatic deconditioning through the simple use of the disjunctive operator. We focus our study on two special cases: (1) RCR-S, a rule with symmetric coefficients that is proved to be unique and (2) RCR-L, a rule with asymmetric coefficients based on a logarithmic function. Their behaviours are then compared to some classical combination rules proposed thus far in the literature, on a few examples, and on Monte Carlo simulations.

Approximation techniques for the transformation of fuzzy sets into random sets

With the recent rising of numerous theories for dealing with uncertain pieces of information, the problem of connection between different frames has become an issue. In particular, questions such as how to combine fuzzy sets with belief functions or probability measures often emerge. The alternative is either to define transformations between theories, or to use a general or unified framework in which all these theories can be framed. Random set theory has been proposed as such a unified framework in which at least probability theory, evidence theory, possibility theory and fuzzy set theory can be represented. Whereas the transformations of belief functions or probability distributions into random sets are trivial, the transformations of fuzzy sets or possibility distributions into random sets lead to some issues. This paper is concerned with the transformation of fuzzy membership functions into random sets. In practice, this transformation involves the creation of a large number of focal elements (subsets with non-null probability) based on the @a-cuts of the fuzzy membership functions. In order to keep a computationally tractable fusion process, the large number of focal elements needs to be reduced by approximation techniques. In this paper, we propose three approximation techniques and compare them to classical approximations techniques used in evidence theory. The quality of the approximations is quantified using a distance between two random sets.

Combining belief functions and fuzzy membership functions

In several practical applications of data fusion and more precisely in object identification problems, we need to combine imperfect information coming from different sources (sensors, humans, etc.), the resulting uncertainty being naturally of different kinds. In particular, one information could naturally been expressed by a membership function while the other could best be represented by a belief function. Usually, information modeled in the fuzzy sets formalism (by a membership function) concerns attributes like speed, length, or Radar Cross Section whose domains of definition are continuous. However, the object identification problem refers to a discrete and finite framework (the number of objects in the data base is finite and known). This implies thus a natural but unavoidable change of domain. To be able to respect the intrinsic characteristic of uncertainty arising from the different sources and fuse it in order to identify an object among a list of possible ones in the data base, we need (1) to use a unified framework where both fuzzy sets and belief functions can be expressed, (2) to respect the natural discretization of the membership function through the change of domain (from attribute domain to frame of discernment). In this paper, we propose to represent both fuzzy sets and belief function by random sets. While the link between belief functions and random sets is direct, transforming fuzzy sets into random sets involves the use of α-cuts for the construction of the focal elements. This transformation usually generates a large number of focal elements often unmanageable in a fusion process. We propose a way to reduce the number of focal elements based on some parameters like the desired number of focal elements, the acceptable distance from the approximated random set to the original discrete one, or the acceptable loss of information.

A conceptual definition of a holonic processing framework to support the design of information fusion systems

This paper proposes a conceptual definition of an information fusion (IF) processing framework. Several concepts borrowed from complex systems theory, informational philosophy and computer sciences have been integrated to conceptualize that framework. The concepts of holon and informon developed by Koestler, Sulis, Alonso, Paggi et al. are exploited here to develop an information fusion processing framework. The proposed functional holonic structure is suitable for processing any level of information abstraction of the Joint Directors of Laboratory (JDL) data fusion model. The framework comprises the characterization of a basic element of information and the definition of an IF cell as a basic IF system unit to achieve fusion of information. The framework advocates a goal-driven approach with notions coming from business sciences to take into account quality of information for managing the fusion process. The framework is illustrated through several examples namely with an elaborated case in remote sensing.

Dynamic estimation of evidence discounting rates based on information credibility

Information quality is crucial to any information fusion system as combining unreliable or partially credible pieces of information may lead to erroneous results. In this paper, Dempster-Shafer theory of evidence is being used as a framework for representing and combining uncertain pieces of information. We propose a method of dynamic estimation of evidence discounting rates based on the credibility of pieces of information. The credibility of a piece of information Cre ( I n ) is evaluated through a measure of consensus (corroboration degree) between a set of belief functions, and this measure serves as a basis for quantifying the credibility of the source (sensor or fusion node) itself, Cre ( S k ), used then as a discounting factor for all further belief functions provided by S k . The process is dynamic in the sense that the credibility of the source is revisited in the light of new incoming piece of information. The method proposed relies on a hybrid fusion topology in which the sensors are grouped according to the feature they measure (similar and dissimilar sensors), allowing to select different kinds of measure for estimating the corroboration degrees. Through simulations, we compare (a) the hybrid-combination using the source credibility and the robust combination rule (RCR-L) accounting automatically for sensorss credibility; (b) the hybrid-combination, with different membership degrees and corroboration degrees used to estimate the sources credibility. We show that the new hybrid topology together with the credibility-based evidence discounting estimation algorithm provide a faster identification of the observed object.

Unified approach to the fusion of imperfect data

For several years, researchers have explored the unification of the theories enabling the fusion of imperfect data and have finally considered two frameworks: the theory random sets and the conditional events algebra. Traditionally, the information is modeled and fused in one of the known theories: bayesian, fuzzy sets, possibilistic, evidential, or rough sets... Previous work has shown what kind of imperfect data these theories can best deal with. So, depending on the quality of the available information (uncertain, vague, imprecise, ...), one particular theory seems to be the preferred choice for fusion. However, in a typical application, the variety of sources provide different kinds of imperfect data. The classical approach is then to model and fuse the incoming data in a single theory being previously chosen. In this paper, we first introduce the various kinds of imperfect data and then the theories that can be used to cope with the imperfection. We also present the existing relationships between them and detail the most important properties for each theory. We finally propose the random sets theory as a possible framework for unification, and thus show how the individual theories can fit in this framework.

A Web–Service Approach for Multi–Sensor Data Fusion and Geographic Information Systems

Different concepts from the higher-levels data fusion, such as situation awareness, impact assessment, dynamic resource management, threat evaluation, and weapon assignment, as described in [Valin P, Technical Memorandum DRDC Valcartier TM 2008-090, 2008], can be addressed as a mix between the Geographic Information Systems (GIS) and the Multisensor Data Fusion (MSDF) systems. In compliance with the Department of National Defence and Canadian Forces Architecture Framework (DNDAF) and the Service Oriented Architecture (SOA), we develop a new web services implementation of MSDF System. The migration and the decomposition into web services of the Concept Analysis and Simulation Environment for Automatic Target Tracking and Identification (CASE ATTI) test bed, developed at DRDC Valcartier, is realized using a spiral approach. A validation process of the web services is proposed by comparison with the results generated by the CASE ATTI test bed.

Critiques on some combination rules for probability theory based on optimization techniques

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.