Probabilistic Analysis of Belief Functions

Kramosil, Ivan

doi:10.1007/978-1-4615-0587-7

Cited by 29 publications

(14 citation statements)

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“…[Klir, 1998] Some researchers have found it useful to interpret the basic probability assignment as a classical probability, such as [Chokr and Kreinovich, 1994], and the framework of Dempster-Shafer theory can support this interpretation. The theoretical implications of this interpretation are well developed in [Kramosil, 2001]. This is a very important and useful interpretation of Dempster-Shafer theory but it does not demonstrate the full scope of the representational power of the basic probability assignment.…”

Section: 1: Dempster-shafer Theorymentioning

confidence: 97%

Combination of Evidence in Dempster-Shafer Theory

Sentz¹,

Ferson²

2002

777

564

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Dempster-Shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. DempsterShafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval. This is a potentially valuable tool for the evaluation of risk and reliability in engineering applications when it is not possible to obtain a precise measurement from experiments, or when knowledge is obtained from expert elicitation. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. This report surveys a number of possible combination rules for Dempster-Shafer structures and provides examples of the implementation of these rules for discrete and interval-valued data. 4 ACKNOWLEDGEMENTS

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Section: 1: Dempster-shafer Theorymentioning

confidence: 97%

Combination of Evidence in Dempster-Shafer Theory

Sentz¹,

Ferson²

2002

777

564

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“…After this fuzzy set theory was further developed and a series of research were done by several mathematicians. In the sequel the concept of fuzzy metric space was introduced by Kramosil and Michalek [ 13 ] in 1975. M .…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Theorems For Weakly Compatible Maps Under E.a. Property In Fuzzy 2-metric Spaces

Shojaei¹,

Banaei²,

Shojaei³

2013

J. Math. Computer Sci.

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“…Examples of the newer theories include fuzzy set theory [17,[42][43][44][45][46], interval analysis [47,48], evidence (Dempster-Shafer) theory [49][50][51][52][53][54][55], possibility theory [56,57], and theory of upper and lower previsions [58]. Some of these theories only deal with epistemic uncertainty; most deal with both epistemic and aleatory uncertainty; and some deal with other varieties of uncertainty (e.g., nonclassical logics appropriate for artificial intelligence and data fusion systems [59]).…”

Section: Improved Models For Epistemic Uncertaintymentioning

confidence: 99%

“…However, in evidence theory and in possibility theory, the mechanics of operations applied to bodies of evidence are completely different [54,57]. The mathematical foundations of evidence theory are well established and explained in several texts and key journal articles [49][50][51][52][53][54][55][61][62][63][64]. However, essentially all of the published applications of the theory are for simple model problems -not actual engineering problems [41,[65][66][67][68][69][70][71][72][73][74].…”

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confidence: 99%

Evidence Theory for Engineering Applications

Oberkampf¹,

Helton²

2004

Engineering Design Reliability Handbook

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Computational analysis of the performance, reliability, and safety of engineered systems is spreading rapidly in industry and government. To many managers, decision makers, and politicians not trained in computational simulation, computer simulations can appear most convincing. Terminology such as "virtual prototyping," "virtual testing," "full physics simulation," and "modeling and simulation-based acquisition" are extremely appealing when budgets are highly constrained; competitors are taking market share; or when political constraints do not allow testing of certain systems. To assess the accuracy and usefulness of computational simulations, three key aspects are needed in the analysis and experimental process: computer code and solution verification; experimental validation of most, if not all, of the mathematical models of the engineered system being simulated; and estimation of the uncertainty associated with analysis inputs, physics models, possible scenarios experienced by the system, and the outputs of interest in the simulation. The topics of verification and validation are not addressed here, but these are covered at length in the literature (see, for example, [1-6]). A number of fields have contributed to the development of uncertainty estimation techniques and procedures, such as nuclear reactor safety, underground storage of radioactive and toxic wastes, and structural dynamics (see, for example, [7][8][9][10][11][12][13][14][15][16][17][18]). only thought to be within specified intervals; for example, the parameters are estimated from expert opinion, not measurements. Assume each of these parameters is treated as a random variable and assigned the least informative distribution (i.e., a uniform distribution). If extreme system responses correspond to extreme values of these parameters (i.e., values near the ends of the uniform distribution), then their probabilistic combination could predict a very low probability for such extreme system responses. Given that the parameters are only known to occur within intervals, however, this conclusion is grossly inappropriate. Improved Models for Epistemic UncertaintyDuring the past two decades, the information theory and expert systems communities have made significant progress in developing a number of new theories that can be pursued for modeling epistemic uncertainty. Examples of the newer theories include fuzzy set theory [17,[42][43][44][45][46], interval analysis [47,48], evidence (Dempster-Shafer) theory [49][50][51][52][53][54][55], possibility theory [56,57], and theory of upper and lower previsions [58]. Some of these theories only deal with epistemic uncertainty; most deal with both epistemic and aleatory uncertainty; and some deal with other varieties of uncertainty (e.g., nonclassical logics appropriate for artificial intelligence and data fusion systems [59]).A recent article summarizes how these theories of uncertainty are related to one another from a hierarchical viewpoint [60]. The article shows that evidence theory is a generalization of cl...

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Probabilistic Analysis of Belief Functions

Cited by 29 publications

References 0 publications

Combination of Evidence in Dempster-Shafer Theory

Combination of Evidence in Dempster-Shafer Theory

Fixed Point Theorems For Weakly Compatible Maps Under E.a. Property In Fuzzy 2-metric Spaces

Evidence Theory for Engineering Applications

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