Calculations of graded ill-known sets

Masahiro Inuiguchi

Kybernetika (2014)

  • Volume: 50, Issue: 2, page 216-233
  • ISSN: 0023-5954

Abstract

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To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the expense of precision. We give a necessary and sufficient condition that lower and upper approximations of function values of graded ill-known sets are obtained as function values of lower and upper approximations of graded ill-known sets.

How to cite

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Inuiguchi, Masahiro. "Calculations of graded ill-known sets." Kybernetika 50.2 (2014): 216-233. <http://eudml.org/doc/261849>.

@article{Inuiguchi2014,
abstract = {To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the expense of precision. We give a necessary and sufficient condition that lower and upper approximations of function values of graded ill-known sets are obtained as function values of lower and upper approximations of graded ill-known sets.},
author = {Inuiguchi, Masahiro},
journal = {Kybernetika},
keywords = {ill-known set; lower approximation; upper approximation; ill-known set; lower approximation; upper approximation},
language = {eng},
number = {2},
pages = {216-233},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Calculations of graded ill-known sets},
url = {http://eudml.org/doc/261849},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Inuiguchi, Masahiro
TI - Calculations of graded ill-known sets
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 2
SP - 216
EP - 233
AB - To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the expense of precision. We give a necessary and sufficient condition that lower and upper approximations of function values of graded ill-known sets are obtained as function values of lower and upper approximations of graded ill-known sets.
LA - eng
KW - ill-known set; lower approximation; upper approximation; ill-known set; lower approximation; upper approximation
UR - http://eudml.org/doc/261849
ER -

References

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  8. Tijms, H., Understanding Probability: Chance Rules in Everyday Life., Cambridge Univ. Press., Cambridge 2004. Zbl1073.60001MR2421977
  9. Yager, R. R., 10.1108/eb005681, Kybernetes 13 (1984), 103-110. Zbl0544.03008MR0740495DOI10.1108/eb005681
  10. Zadeh, L. A., 10.1016/S0019-9958(65)90241-X, Inform. and Control 8 (1965), 3, 338-353. Zbl0942.00007MR0219427DOI10.1016/S0019-9958(65)90241-X
  11. Zadeh, L. A., 10.1016/0020-0255(75)90036-5, Inform. Sci. 8 (1975), 199-246. MR0386369DOI10.1016/0020-0255(75)90036-5
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