A Similarity Measure between Basic Belief Assignments

Díaz, Javier; Rifqi, Maria; Bouchon‐Meunier, Bernadette

doi:10.1109/icif.2006.301730

Cited by 25 publications

(24 citation statements)

References 13 publications

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“…Generally speaking, this yields a slower speed of convergence to θ 1 . For example, for one source S 3 in the Table 1, if S 3 is combined with itself once according to (6), the combinational result is is .Therefore, ESMS filter might also result in losing some useful information, while it filter some bad information. 2) On the Figure 4, one sees the role played by the ESMS filter.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In 2006 also, Diaz et al [6] proposed a new measure of similarity between bba's based on Tversky's similarity measure [37]. Note that in belief function theories, the direct use of classical measures used in Probability theory (say like Kullback Leibler (KL) distance [3]) cannot be applied directly because bba's are not probability measures in general.…”

Section: Introductionmentioning

confidence: 99%

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Evidence supporting measure of similarity for reducing the complexity in information fusion☆

Dezert

Smarandache

et al. 2011

Information Sciences

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This paper proposes a new solution for reducing the number of sources of evidence to be combined in order to diminish the complexity of the fusion process required in some applications where the real-time constraint and strong computing resource limitation are of prime importance. The basic idea consists in selecting, among the whole set of sources of evidence, only the biggest subset of sources which are not too contradicting based on a criterion of Evidence Supporting Measure of Similarity (ESMS) in order to process solely the coherent information received. The ESMS criterion serves actually as a generic tool for outlier source identification and rejection. Since the ESMS between several belief functions can be defined using several distance measures, we browse the most common ones in this paper and we describe in detail the principle of our Generalized Fusion Machine (GFM). The last part of the paper shows the improvement of the performances of this new approach with respect to the classical one in a real-data based and real-time experiment for robot perception using sonar sensors.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evidence supporting measure of similarity for reducing the complexity in information fusion☆

Dezert

Smarandache

et al. 2011

Information Sciences

View full text Add to dashboard Cite

show abstract

“…Jousselme et al [2] defined a distance between two evidence bodies. J.Diaz et al [3] presented an evidence distance considering the proximity of reference frame to the frame of discernment. Cuzzolin [4] and Ristic [5] respectively extended the Euclidean distance and Bhattacharyya distance from probability theory to DST.…”

Section: Introductionmentioning

confidence: 99%

A New Method to Determine Evidence Distance

Shi

Chen

2010

2010 International Conference on Computational Intelligence and Software Engineering

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DS evidence theory is a hot topic in multi-sensor data fusion because of its advantages in multi-source information presentation and processing. Considering the difficulties of sensor reliability priority information acquisition, how to compute reliability of sensor via the evidence distance in multisensor data fusion system and how to select consistent evidence for combination via the evidence distance when many homogeneous sensors exist are the open issues. In this paper, a new evidence distance is presented in order to avoid the disadvantage of Diaz's distance measure in the logical selection of tuning parameter and Jousselme's distance measure in not considering the proximity of reference frame to the frame of discernment. This method firstly defines a fuzzy linguistic term set to express the proximity of reference frame to the frame of discernment, in which the semantics of the terms is given by a triangular membership function and a rewarding or penalizing function. Then similarity measurement matrix is achieved by weighting the rewarding or penalizing function using membership degree. Finally Jousselme's distance framework is used to compute the evidence distance. Two numerical examples illustrate the efficiency of the method proposed.

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“…As to what distances are the most appropriate, Jousselme et al [29] have recently conducted a nice survey of the distance or similarity measures so far introduced in belief calculus, come out with an interesting classification, and proposed a number of generalizations of known measures. Other similarity measures between belief functions have been proposed by Shi et al [30], Jiang et al [31], and others [32], [33]. Many of these measures can be in principle employed to define conditional belief functions, or to approximate belief functions by necessity or probability measures.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, generalizations to belief functions of the classical Kullback-Leibler divergence between probability distributions or other measures based on information theory such as fidelity and entropy-based norms [41] can be studied. Many other similarity measures have indeed been proposed [30], [31], [32], [33]. The application to the approximation problem of similarity measures more specific to belief functions or inspired by classical probability is a huge task, of which this paper is just a first step.…”

Section: Introductionmentioning

confidence: 99%

$L_{p}$ Consonant Approximations of Belief Functions

Cuzzolin

2014

IEEE Trans. Fuzzy Syst.

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In this paper we solve the problem of approximating a belief measure with a necessity measure or "consonant belief function" in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among them. As a first step in this line of study, we seek here approximations which minimize L p norms. Approximations in the mass space can be interpreted in terms of mass redistribution, while approximations in the belief space generalize the maximal outer consonant approximation. We compare them with each other and with other classical approximations, and illustrate them with the help of a running example. Index TermsTheory of evidence, possibility theory, consonant belief functions, geometric approach, simplicial complex, (outer) consonant approximation, isopignistic function, L p norms.

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A Similarity Measure between Basic Belief Assignments

Cited by 25 publications

References 13 publications

Evidence supporting measure of similarity for reducing the complexity in information fusion☆

Evidence supporting measure of similarity for reducing the complexity in information fusion☆

A New Method to Determine Evidence Distance

$L_{p}$ Consonant Approximations of Belief Functions

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