Mathematical Modelling and Applications

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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.

DOI 10.11648/j.mma.20160102.12
Published in Mathematical Modelling and Applications (Volume 1, Issue 2, December 2016)
Page(s) 36-45
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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

Weighted Hesitant Fuzzy Set, Correlation Measure, Medical Diagnosis Problem

References
[1] Zhang Zh., Wu Ch., Weighted hesitant fuzzy sets and their application to multi-criteria decision making, British Journal of Mathematics and Computer Science 4(2014) 1091-1123.
[2] Murthy C.A., Pal S.K., Majumder, D.D., Correlation between two fuzzy membership functions, Fuzzy Sets and Systems17(1985) 23-38.
[3] Chiang D.A., Lin N.P., Partial correlation of fuzzy sets, Fuzzy Sets and Systems 110(2000) 209-215.
[4] Gerstenkorn T., Manko J., Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems 44(1991) 39-43.
[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.
[14] B. Farhadinia, An efficient similarity measure for intuitionistic fuzzy sets, J. Soft Computing 18 (2014) 85-94.
[15] B. Farhadinia, Fuzzy multicriteria decision-making method based on a family of novel measured functions under vague environment, J. Intelligent and Fuzzy Systems 27 (2014) 2797-2808.
[16] B. Farhadinia, A.I. Ban, Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers, J. Mathematical and Computer Modelling 57 (2013) 812-825.
[17] Chen N., Xu Z., Xia M., Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Applied Mathematical Modelling 37(2013) 2197-2211.
[18] Xu Z., Xia M., On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems 26(2011) 410-425.
[19] Xia M., Xu Z., Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning 52(2011) 395-407.
[20] Jaccard P., Distribution de la flore alpine dans le Bassin des Drouces et dans quelques regions voisines, Bulletin de la Socit Vaudoise des Sciences Naturelles 37(1901) 241-272.
[21] Dice L.R., Measures of the amount of ecologic association between species, Ecology 26(1945) 297-302.
Author Information
  • Department Mathematics, Quchan University of Advanced Technology, Iran

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    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://download.sciencepg.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.
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