Theory of evidence

J. Dezert. Towards a New Concept of Autonomous Craft Navigation. A Link Between Probabilistic Data Association Filtering and the Theory of Evidence. PhD thesis, Universite d Orsay, Prance, 1990. 

G. Shafer. A mathematical theory of evidence. Princeton University Press, 1976. 

Dempster-Shafer Theory of Evidence is a generalization of the Bayesian theory based on degrees of belief rather than probabilities. 

Shafer, G.A., A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976. 

Gordon, J., and Shortliffe, E. H. (1984), The Dempster-Schafer Theory of Evidence, in Rw/e-Bosed Expert Systems The MYCIN Experiments of the Stanford Heuristic Programming Project, Addison-Wesley, Reading, MA. 

A Dempster-Shafer theory of evidence approach to model uncertainty analysis... 

From a general point of view, the theory of evidence makes basic probabihty assignments (bpa) m(A) on sets A (the focal sets) ofthe power set P (Z) of the event space Z. This allows the natural encoding of evidence in favor of the different events which may occur. 

Irrespective of the taxonomy used, epistemic and aleatory uncertainty, or uncertainty and variation, alternatives to probability have been suggested for the representation of the epistemic concept. These include interval or imprecise probabihty (Coolen 2004, Coolen Utkin 2007, Utkin Coolen 2007, Weichselberger 2000), fuzzy set theory and the associated theory of possibility (Zadeh 1965, Zadeh 1978, Unwin 1986), and the theory of behef functions (Shafer 1976), also known as evidence theory or the Dempster-Shafer theory of evidence. 

The functions of belief concern a quantification of credibility attached to the events. Shafer s theory of evidence considers a finite universe of reference, X, upon which are determined belief coefficients obtained by distributing a global mass of belief equal to 1 among all possible events (JO). A mass, m, can be defined as follows ... 

Park, N.W. 2010. Application of Dempster-Shafer theory of evidence to GIS-based landsUde susceptibility analysis. Environmental Earth Sciences 62(2) 367-376. 

In 1976, Shafer (Bhatnagar and Kanal, 1991) developed the theory of evidence. 

In the theory of evidence, a mass function is used. The mass function is induced by the available evidence, and it assigns parts of a finite amount of belief to a subset of S . Each assignment of a mass to a subset s of S represents that part of our belief that supports s without being able to allocate this belief among strict subsets of s. 

The theory of evidence was first generated by Dempster (1968) and further developed by Shafer (1976). It is often referred to as the Dempster-Shafer theory of evidence or D-S theory. The D-S theory was originally used for information aggregation in expert systems as an approximate reasoning tool (Mantaras, 1990). Subsequently, it has been used in decision making under uncertainty (Yager, 2004). 

Baraldi, P, Compare, M., Zio, E. 2013a. Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer Theory of evidence. Information Sciences 245 112-113. 

Kacprzyk, J. Fedrizzi, M., 1994. Advances in Demp-ster-Shafer theory of evidence. Wiley, New York, pp. 51-69. 

In the safety analysis of complex systems, the treatment of uncertainty must distinguish the aleatory uncertainties, which represent the intrinsic randomness of the phenomena, from the epistemic uncertainties resulting from a lack of knowledge. This separation has to be done through a two-level uncertainty propagation the internal level concerning the aleatory variables and the external level the epistemic variables. For the propagation of epistemic uncertainties, it appears more appropriate to use extra-probabilistic approaches such as interval analysis or Dempter-Shafer Theory of Evidence (DSTE). 

The theory of evidence assumes that it is possible to conduct a synthesis of information for particular elementary measures of probability. Information can be synthesised even if it is contradictory or comes from various sources (Dempster 1967, Shafer 1976). Such synthesis can be described by the following formula ... 

Shafer G. Mathematical Theory of Evidence. Princetown University Press (1976)... 

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