For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to more general ones, and some useful results for applications are derived by the extended ones.
| Published in |
Applied and Computational Mathematics (Volume 4, Issue 1-2)
This article belongs to the Special Issue New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications |
| DOI | 10.11648/j.acm.s.2015040102.13 |
| Page(s) | 10-14 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Zadeh’s Extension Principle, Fuzzy Inner Product, Fuzzy Distance
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APA Style
Masamichi Kon. (2014). A Note on Zadeh's Extension Principle. Applied and Computational Mathematics, 4(1-2), 10-14. https://doi.org/10.11648/j.acm.s.2015040102.13
ACS Style
Masamichi Kon. A Note on Zadeh's Extension Principle. Appl. Comput. Math. 2014, 4(1-2), 10-14. doi: 10.11648/j.acm.s.2015040102.13
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Download@article{10.11648/j.acm.s.2015040102.13,
author = {Masamichi Kon},
title = {A Note on Zadeh's Extension Principle},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {1-2},
pages = {10-14},
doi = {10.11648/j.acm.s.2015040102.13},
url = {https://doi.org/10.11648/j.acm.s.2015040102.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040102.13},
abstract = {For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to more general ones, and some useful results for applications are derived by the extended ones.},
year = {2014}
}
TY - JOUR T1 - A Note on Zadeh's Extension Principle AU - Masamichi Kon Y1 - 2014/12/27 PY - 2014 N1 - https://doi.org/10.11648/j.acm.s.2015040102.13 DO - 10.11648/j.acm.s.2015040102.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 10 EP - 14 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2015040102.13 AB - For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to more general ones, and some useful results for applications are derived by the extended ones. VL - 4 IS - 1-2 ER -
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