This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights keep the same proportion as those of original interval weights. It is found that, in some newly normalization methods, they violate these goodness criteria. In current work, for interval weights, we propose a new normalization method that reserves both proportions of the distances from interval centers to the origin and of interval lengths, and also eliminates the redundancy from the original given interval weights. This new method can be widely applied in information fusion and decision making in environments with uncertainty.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5) |
| DOI | 10.11648/j.sjams.20160405.19 |
| Page(s) | 249-252 |
| 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), 2016. Published by Science Publishing Group |
Normalization Methods, Weighted Average, Interval Weights, Information Fusion
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| [4] | Y. -M. Wang, and T. M. S. Elhag, On the normalization of interval and fuzzy weights, Fuzzy Sets and Systems 157 (2006) 2456-2471. |
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APA Style
Yimeng Sui, Zhenyuan Wang. (2016). Discussion on Normalization Methods of Interval Weights. Science Journal of Applied Mathematics and Statistics, 4(5), 249-252. https://doi.org/10.11648/j.sjams.20160405.19
ACS Style
Yimeng Sui; Zhenyuan Wang. Discussion on Normalization Methods of Interval Weights. Sci. J. Appl. Math. Stat. 2016, 4(5), 249-252. doi: 10.11648/j.sjams.20160405.19
AMA Style
Yimeng Sui, Zhenyuan Wang. Discussion on Normalization Methods of Interval Weights. Sci J Appl Math Stat. 2016;4(5):249-252. doi: 10.11648/j.sjams.20160405.19
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Download@article{10.11648/j.sjams.20160405.19,
author = {Yimeng Sui and Zhenyuan Wang},
title = {Discussion on Normalization Methods of Interval Weights},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {4},
number = {5},
pages = {249-252},
doi = {10.11648/j.sjams.20160405.19},
url = {https://doi.org/10.11648/j.sjams.20160405.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.19},
abstract = {This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights keep the same proportion as those of original interval weights. It is found that, in some newly normalization methods, they violate these goodness criteria. In current work, for interval weights, we propose a new normalization method that reserves both proportions of the distances from interval centers to the origin and of interval lengths, and also eliminates the redundancy from the original given interval weights. This new method can be widely applied in information fusion and decision making in environments with uncertainty.},
year = {2016}
}
TY - JOUR T1 - Discussion on Normalization Methods of Interval Weights AU - Yimeng Sui AU - Zhenyuan Wang Y1 - 2016/10/17 PY - 2016 N1 - https://doi.org/10.11648/j.sjams.20160405.19 DO - 10.11648/j.sjams.20160405.19 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 249 EP - 252 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20160405.19 AB - This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights keep the same proportion as those of original interval weights. It is found that, in some newly normalization methods, they violate these goodness criteria. In current work, for interval weights, we propose a new normalization method that reserves both proportions of the distances from interval centers to the origin and of interval lengths, and also eliminates the redundancy from the original given interval weights. This new method can be widely applied in information fusion and decision making in environments with uncertainty. VL - 4 IS - 5 ER -
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