Decision-making under uncertainty processed by lattice-valued possibilistic measures

Ivan Kramosil

Kybernetika (2006)

  • Volume: 42, Issue: 6, page 629-646
  • ISSN: 0023-5954

Abstract

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The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.

How to cite

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Kramosil, Ivan. "Decision-making under uncertainty processed by lattice-valued possibilistic measures." Kybernetika 42.6 (2006): 629-646. <http://eudml.org/doc/33829>.

@article{Kramosil2006,
abstract = {The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.},
author = {Kramosil, Ivan},
journal = {Kybernetika},
keywords = {decision making under uncertainty; complete lattice; lattice- valued possibilistic measures; possibilistic decision function; minimax and Bayesian optimization; decision making under uncertainty; complete lattice; lattice-valued possibilistic measures; possibilistic decision function; minimax and Bayesian optimization},
language = {eng},
number = {6},
pages = {629-646},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Decision-making under uncertainty processed by lattice-valued possibilistic measures},
url = {http://eudml.org/doc/33829},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Kramosil, Ivan
TI - Decision-making under uncertainty processed by lattice-valued possibilistic measures
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 6
SP - 629
EP - 646
AB - The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed.
LA - eng
KW - decision making under uncertainty; complete lattice; lattice- valued possibilistic measures; possibilistic decision function; minimax and Bayesian optimization; decision making under uncertainty; complete lattice; lattice-valued possibilistic measures; possibilistic decision function; minimax and Bayesian optimization
UR - http://eudml.org/doc/33829
ER -

References

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  5. Dubois D., Nguyen, H., Prade H., Possibility theory, probability theory and fuzzy sets: misunderstandings, bridges and gaps, In: The Handbook of Fuzzy Sets Series (D. Dubois and H. Prade, eds.), Kluwer Academic Publishers, Boston, 2000, pp. 343–438 
  6. Faure R., Heurgon E., Structures Ordonnées et Algèbres de Boole, Gauthier-Villars, Paris 1971 Zbl0219.06001MR0277440
  7. Hájek P., Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Boston 1998 Zbl1007.03022MR1900263
  8. Halmos P. R., Measure Theory, D. van Nostrand, New York – Toronto – London 1950 Zbl0283.28001MR0033869
  9. Kramosil I., Extensions of partial lattice-valued possibility measures, Neural Network World 13 (2003), 4, 361–384 
  10. Loève M., Probability Theory, D. van Nostrand, New York – Toronto – London 1960 Zbl0385.60001MR0123342
  11. Sikorski R., Boolean Algebras, Second edition. Springer-Verlag, Berlin – Göttingen – Heidelberg – New York 1964 Zbl0191.31505MR0242724
  12. Wald A., Statistical Decision Functions, Wiley, New York 1950 Zbl0229.62001MR0036976

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