Details
| Original language | English |
|---|---|
| Pages (from-to) | 1415-1423 |
| Number of pages | 9 |
| Journal | Soft Computing |
| Volume | 17 |
| Issue number | 8 |
| Early online date | 26 Feb 2013 |
| Publication status | Published - Aug 2013 |
| Externally published | Yes |
Abstract
Markov chains provide quite attractive features for simulating a system's behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.
Keywords
- DSI, Imprecise probability, Interval arithmetic, Markov set-chains
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Geometry and Topology
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In: Soft Computing, Vol. 17, No. 8, 08.2013, p. 1415-1423.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Verified stochastic methods
T2 - Markov set-chains and dependency modeling of mean and standard deviation
AU - Rebner, Gabor
AU - Beer, Michael
AU - Auer, Ekaterina
AU - Stein, Matthias
PY - 2013/8
Y1 - 2013/8
N2 - Markov chains provide quite attractive features for simulating a system's behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.
AB - Markov chains provide quite attractive features for simulating a system's behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.
KW - DSI
KW - Imprecise probability
KW - Interval arithmetic
KW - Markov set-chains
UR - http://www.scopus.com/inward/record.url?scp=84880807695&partnerID=8YFLogxK
U2 - 10.1007/s00500-013-1009-7
DO - 10.1007/s00500-013-1009-7
M3 - Article
AN - SCOPUS:84880807695
VL - 17
SP - 1415
EP - 1423
JO - Soft Computing
JF - Soft Computing
SN - 1432-7643
IS - 8
ER -