Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems

B. Farhadinia

doi:doi:10.11648/j.mma.20160102.12

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Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems

B. Farhadinia

Published in Mathematical Modelling and Applications (Volume 1, Issue 2)

Received: 22 December 2015 Accepted: 15 February 2016 Published: 28 October 2016

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Abstract

Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element is defined in terms of several possible values together with their importance weight. But, Zhang and Wu’s definition of WHFS gives rise to a number of disadvantages which violate the well-known axioms for mathematical operations. To circumvent this issue, we refine the definition of WHFS and then we put forward some correlation measures for WHFSs. Finally, we give a practical example to illustrate the application of proposed correlation measures for WHFSs in medical diagnosis.

Published in	Mathematical Modelling and Applications (Volume 1, Issue 2)
DOI	10.11648/j.mma.20160102.12
Page(s)	36-45
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

Keywords

Weighted Hesitant Fuzzy Set, Correlation Measure, Medical Diagnosis Problem

References

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[8]	Qian G., Wang H., Feng X., Generalized hesitant fuzzy sets and their application in decision support system, Knowledge Based Systems 37(2013) 357-365.
[9]	Rodriguez R. M., Martinez L., Herrera F., Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Systems 20(2012) 109-119.
[10]	Farhadinia B., Distance and similarity measures for higher order hesitant fuzzy sets, Knowledge-Based Systems 55(2014) 43-48.
[11]	Farhadinia B., A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems, International Journal of Intelligent Systems 28(2013) 752-767.
[12]	Farhadinia B., Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets, Information Sciences 240(2013) 129-144.
[13]	B. Farhadinia, A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure, J. Knowledge-Based Systems 39 (2013) 79-84.
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APA Style

B. Farhadinia. (2016). Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Mathematical Modelling and Applications, 1(2), 36-45. https://doi.org/10.11648/j.mma.20160102.12

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ACS Style

B. Farhadinia. Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Math. Model. Appl. 2016, 1(2), 36-45. doi: 10.11648/j.mma.20160102.12

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AMA Style

B. Farhadinia. Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Math Model Appl. 2016;1(2):36-45. doi: 10.11648/j.mma.20160102.12

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@article{10.11648/j.mma.20160102.12,
  author = {B. Farhadinia},
  title = {Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems},
  journal = {Mathematical Modelling and Applications},
  volume = {1},
  number = {2},
  pages = {36-45},
  doi = {10.11648/j.mma.20160102.12},
  url = {https://doi.org/10.11648/j.mma.20160102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20160102.12},
  abstract = {Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element is defined in terms of several possible values together with their importance weight. But, Zhang and Wu’s definition of WHFS gives rise to a number of disadvantages which violate the well-known axioms for mathematical operations. To circumvent this issue, we refine the definition of WHFS and then we put forward some correlation measures for WHFSs. Finally, we give a practical example to illustrate the application of proposed correlation measures for WHFSs in medical diagnosis.},
 year = {2016}
}

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TY  - JOUR
T1  - Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems
AU  - B. Farhadinia
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.mma.20160102.12
DO  - 10.11648/j.mma.20160102.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 36
EP  - 45
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20160102.12
AB  - Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element is defined in terms of several possible values together with their importance weight. But, Zhang and Wu’s definition of WHFS gives rise to a number of disadvantages which violate the well-known axioms for mathematical operations. To circumvent this issue, we refine the definition of WHFS and then we put forward some correlation measures for WHFSs. Finally, we give a practical example to illustrate the application of proposed correlation measures for WHFSs in medical diagnosis.
VL  - 1
IS  - 2
ER  -

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Author Information

B. Farhadinia

Department Mathematics, Quchan University of Advanced Technology, Iran

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APA Style

B. Farhadinia. (2016). Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Mathematical Modelling and Applications, 1(2), 36-45. https://doi.org/10.11648/j.mma.20160102.12

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ACS Style

B. Farhadinia. Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Math. Model. Appl. 2016, 1(2), 36-45. doi: 10.11648/j.mma.20160102.12

Copy | Download

AMA Style

B. Farhadinia. Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems. Math Model Appl. 2016;1(2):36-45. doi: 10.11648/j.mma.20160102.12

Copy | Download

@article{10.11648/j.mma.20160102.12,
  author = {B. Farhadinia},
  title = {Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems},
  journal = {Mathematical Modelling and Applications},
  volume = {1},
  number = {2},
  pages = {36-45},
  doi = {10.11648/j.mma.20160102.12},
  url = {https://doi.org/10.11648/j.mma.20160102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20160102.12},
  abstract = {Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element is defined in terms of several possible values together with their importance weight. But, Zhang and Wu’s definition of WHFS gives rise to a number of disadvantages which violate the well-known axioms for mathematical operations. To circumvent this issue, we refine the definition of WHFS and then we put forward some correlation measures for WHFSs. Finally, we give a practical example to illustrate the application of proposed correlation measures for WHFSs in medical diagnosis.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Utility of Correlation Measures for Weighted Hesitant Fuzzy Sets in Medical Diagnosis Problems
AU  - B. Farhadinia
Y1  - 2016/10/28
PY  - 2016
N1  - https://doi.org/10.11648/j.mma.20160102.12
DO  - 10.11648/j.mma.20160102.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 36
EP  - 45
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20160102.12
AB  - Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element is defined in terms of several possible values together with their importance weight. But, Zhang and Wu’s definition of WHFS gives rise to a number of disadvantages which violate the well-known axioms for mathematical operations. To circumvent this issue, we refine the definition of WHFS and then we put forward some correlation measures for WHFSs. Finally, we give a practical example to illustrate the application of proposed correlation measures for WHFSs in medical diagnosis.
VL  - 1
IS  - 2
ER  -

Copy | Download