Characterization of fuzzy order relation by fuzzy cone

Masamichi Kon

Kybernetika (2022)

  • Volume: 58, Issue: 5, page 779-789
  • ISSN: 0023-5954

Abstract

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In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones.

How to cite

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Kon, Masamichi. "Characterization of fuzzy order relation by fuzzy cone." Kybernetika 58.5 (2022): 779-789. <http://eudml.org/doc/299352>.

@article{Kon2022,
abstract = {In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones.},
author = {Kon, Masamichi},
journal = {Kybernetika},
keywords = {fuzzy order relation; fuzzy cone},
language = {eng},
number = {5},
pages = {779-789},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Characterization of fuzzy order relation by fuzzy cone},
url = {http://eudml.org/doc/299352},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Kon, Masamichi
TI - Characterization of fuzzy order relation by fuzzy cone
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 5
SP - 779
EP - 789
AB - In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones.
LA - eng
KW - fuzzy order relation; fuzzy cone
UR - http://eudml.org/doc/299352
ER -

References

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  2. Khan, A. A., Tammer, C., Zălinescu, C., Set-valued Optimization: An Introduction with Applications., Springer-Verlag, Berlin 2015. 
  3. Kon, M., Fuzzy Set Optimization (in Japanese)., Hirosaki University Press, Japan 2019. 
  4. Kon, M., Kuwano, H., , Fixed Point Theory Appl. 2013 (2013), 327. DOI
  5. Kuroiwa, D., Tanaka, T., Ha, T. X. D., , Nonlinear Analysis, Theory, Methods Appl. 30 (1997), 1487-1496. DOI
  6. Peressini, A. L., Ordered Topological Vector Spaces., Harper and Row, New York 1967. 
  7. Young, R. C., , Math. Ann. 104 (1931), 260-290. DOI
  8. Zadeh, L. A., , Inform. Control 8 (1965), 338-353. Zbl0942.00007DOI
  9. Zadeh, L. A., , Inform. Sci. 3 (1971), 177-200. DOI
  10. Zhang, H.-P., Pérez-Fernández, R., Beats, B. De, , Fuzzy Sets Systems 384 (2020), 1-22. DOI

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