Discussion on Normalization Methods of Interval Weights

Yimeng Sui; Zhenyuan Wang

doi:doi:10.11648/j.sjams.20160405.19

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Discussion on Normalization Methods of Interval Weights

Yimeng Sui, Zhenyuan Wang

Received: 16 October 2016 Accepted: Published: 17 October 2016

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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.

DOI	10.11648/j.sjams.20160405.19
Published in	Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5, October 2016)
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), 2024. Published by Science Publishing Group

Keywords

Normalization Methods, Weighted Average, Interval Weights, Information Fusion

References

[1]	D. -Q. Li, J. -Y. Wang, and H. -X. Li, Note on “The normalization of interval and fuzzy weights”, Fuzzy Sets and Systems 160 (2009) 2722-2725.
[2]	O. Pavlacka, On various approaches to normalization of interval and fuzzy weights, Fuzzy Sets and Systems 243 (2014) 110-130.
[3]	P. Sevastjanov, L. Dymova, and P. Bartosiewicz, A new approach to normalization of interval and fuzzy weights, Fuzzy Sets and Systems 198 (2012) 34-45.
[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.
[5]	Z. Wang, R. Yang, and K. -S. Leung, Nonlinear integrals and their Applications in Data Mining, World Scientific, 2010.

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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

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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

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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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@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}
}

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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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Author Information

Yimeng Sui

Department of Mathematics, University of Nebraska at Omaha, Omaha, United Stated
Zhenyuan Wang

Department of Mathematics, University of Nebraska at Omaha, Omaha, United Stated

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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

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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

Copy | Download

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

Copy | 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}
}

Copy | Download

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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