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

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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[5] Mitchell H.B., A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems 19(2004) 483-490.
[6] Torra V., Hesitant fuzzy sets, International Journal of Intelligent Systems 25(2010) 529-539.
[7] Farhadinia B., Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets, International Journal of Intelligent Systems 29(2014) 184-205.
[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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    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
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Author Information
  • Department Mathematics, Quchan University of Advanced Technology, Iran

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