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Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application

Year 2022, Volume: 5 Issue: 1, 16 - 23, 30.04.2022
https://doi.org/10.33187/jmsm.1039613

Abstract

The FFS is an influential extension of the available IFS and PFS, whose benefit is to better exhaustively characterize ambiguous information. For FFSs, the correlation between them is usually evaluated by the correlation coefficient. To reflect the perspective of professionals, in this paper, a new correlation coefficient of FFSs is proposed and investigated. The correlation coefficient is very important and frequently used in every field from engineering to economics, from technology to science. In this paper, we propose a new correlation coefficient and weighted correlation coefficient formularization to evaluate the affair between two FFSs. A numerical example of diagnosis has been gotten to represent the efficiency of the presented approximation. Outcomes calculated by the presented approximation are compared with the available indices.

References

  • [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1) (1986), 87-96.
  • [2] D. A. Chiang, N. P. Lin, Correlation of fuzzy sets, Fuzzy Sets Syst., 102(2) (1999), 221-226.
  • [3] S. T. Liu, C. Kao, Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets Syst., 128(2) (2002), 267-275.
  • [4] Z. Liang, P. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognit. Lett., 24(15) (2003), 2687-2693.
  • [5] W. D. Vander, M. Nachtegael, E. E. Kerre, A new similarity measure for image processing, J. Comput. Methods Sci. Eng., 3(2) (2003), 209-222.
  • [6] W. D. Vander, M. Nachtegael, E. E. Kerre, Using similarity measures and homogeneity for the comparison of images, Image Vis. Comput., 22(9) (2004), 695-702.
  • [7] G. W. Wei, H. J. Wang, R. Lin, Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information, Know. Inf. Syst., 26(2) (2011), 337-349.
  • [8] Z. S. Xu, J. Chen, J. J. Wu, Cluster algorithm for intuitionistic fuzzy sets, Inf. Sci., 178(19) (2008), 3775-3790.
  • [9] M. Kiris¸ci, A case study for medical decision making with the fuzzy soft sets, Afrika Matematika, 31(3) (2020) 557-564, doi:10.1007/s13370-019-00741-9.
  • [10] M. Kiris¸ci, N. S¸ims¸ek, Decision making method related to Pythagorean fuzzy soft sets with infectious diseases application, J. King. Saud. Univ. - Comput. Inf. Sci., (2021), doi:10.1016/j.jksuci.2021.08.010.
  • [11] X. Peng, Y. Yang, J. Song, Y. Jiang, Pythagorean fuzzy soft set and its application, Computer Engineering, 41(7) (2015), 224-229.
  • [12] X. Peng, G. Selvachandran, Pythagorean fuzzy set: state of the art and future directions, Artif. Intell. Rev., 52(3) (2019), 1873-1927, doi:10.1007/s10462- 017-9596-9.
  • [13] R. R. Yager, Pythagorean fuzzy subsets, Proc. Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013).
  • [14] R. R. Yager, Pythagorean membership grade in multicriteria decision makng, IEEE Fuzzy Syst., 22 (2014), 958-965.
  • [15] R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers and decision making, Int. J. Intell. Syst., 28 (2013), 436-452.
  • [16] X. L. Zhang, Z. S. Xu, Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061-1078.
  • [17] F. Smarandache, A unifying field in logics: Neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics, Phoenix, Xiquan, (2003).
  • [18] P. A. Ejegwa, Distance and similarity measures for Pythagorean fuzzy sets, Granul. Comput., 5 (2018), 225-238, doi:10.1007/s41066-018-00149-z.
  • [19] P. A. Ejegwa, B. O. Onasanya, Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process, Notes on Intuitionistic Fuzzy Sets, 25(1) (2018), 43-58, doi:10.7546/nifs.2019.25.1.43-58.
  • [20] A. Guleria, R. K. Bajaj, On Pythagorean fuzzy matrices, operations and their applications in decision making and medical diagnosis, Soft Computing., 23(17) (2018), 7889, doi:10.1007/s00500-018-3419-z.
  • [21] R. M. Hashim, M. Gulistan, I. Rehman, N. Hassan, A. M. Nasruddin, Neutrosophic bipolar fuzzy set and its application in medicines preparations, Neutrosophic Sets and Systems, 31 (2020), 86-100, doi:10.5281/zenodo.3639217.
  • [22] M. Kiris¸ci, H. Yilmaz, M. U. Saka, An ANFIS perspective for the diagnosis of type II diabetes, Annals of Fuzzy Mathematics and Informatics, 17 (2019), 101-113.
  • [23] M. Kiris¸ci, Comparison the medical decision-making with intuitionistic fuzzy parameterized fuzzy soft set and Riesz summability, New Math. Nat. Comput., 15 (2019), 351-359. doi:10.1142/S1793005719500194.
  • [24] M. Kiris¸ci, Medical decision making with respect to the fuzzy soft sets, J. Interdiscip. Math., 23(4) (2020), 767-776, doi:10.1080/09720502.2020.1715577.
  • [25] M. Kiris¸ci, W􀀀 soft sets and medical decision-making application, Int. J. Comput. Math., 98(4) (2021), 690-704, doi:10.1080/00207160.2020.1777404.
  • [26] M. Saeed, M. Saqlain, A. Mehmood, K. Naseer, S. Yaqoob, Multi-polar neutrosophic soft sets with application in medical diagnosis and decision-making, Neutrosophic Set Syst., 33 (2020), 183-207.
  • [27] G. Shahzadi, M. Akram, Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information, Journal of Intelligent & Fuzzy Systems, 40(1) (2021), 1401-1416.
  • [28] N. X. Thao, A new correlation coefficient of the intuitionistic fuzzy sets and its application, J. Intell. Fuzzy. Syst., 35(2) (2018), 1959-1968.
  • [29] Q. Zhou, H. Mo, Y. Deng, A new divergence measure of Pythagorean fuzzy sets based on belief function and its application in medical diagnosis, Mathematics, 8 (2020), 2227-7390, doi:10.3390/math8010142
  • [30] R. Arora, H. Garg, A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making, Eng. Appl. Artif. Intell., 72(C) (2018), 80-92.
  • [31] H. Bustince, P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 74(2) (1995), 237-244.
  • [32] Y. Chen, X. Peng, G. Guan, H. Jiang, Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information, J. Intell. Fuzzy Syst., 6(5) (2014), 2547-2556.
  • [33] P. A. Ejegwa, Novel correlation coefficient for intuitionistic fuzzy sts and its application to multi-criteria decision-making problems, Int. J. Fuzzy Syst. Appl., 10(2) (2021), 39-58.
  • [34] P. A. Ejegwa, C. Jana, Some new weighted correlation coefficients between Pythagorean fuzzy sets and their applications, In: Garg, H., (Eds.), Pythagorean fuzzy sets, Springer, (2021), 39-64.
  • [35] B. Farhadinia, Correlation for dual hesistant fuzzy sets and dual interval-valued hesitant fuzzy set, Int. J. Intell. Syst., 29(2) (2014), 184-205.
  • [36] H. Garg, Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process, J. Ind. Manag. Optim., 14(4) (2018), 1501-1519.
  • [37] H. Garg, A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making, Int. J. Intell. Sys., 31(12) (2016), 1234-1252, doi:10.1002/int.21827.
  • [38] H. Garg, K. Kumar, A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application, Sci. Iran. E., 25(4) (2018), 2373-2388.
  • [39] H. Garg, D. Rani, A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making, Appl. Intell., 49(2) (2019), 496-512.
  • [40] H. Garg, G. Shahzadi, M. Akram, Decision-making analysis based on Fermatean fuzzy Yager aggregation operators with application in COVID-19 testing facility, Mathematical Problems in Engineering, 2020 (2020) Article ID 7279027, doi:10.1155/2020/7279027.
  • [41] H. Liao, Z. Xu, X. J. Zeng, Novel correlation coefficients between hesitant fuzzy sets and their application in decision making, Knowl. Based Syst., 82 (2015), 115-127.
  • [42] S. Singh, A. H. Ganie, On some correlation coefficients in Pythagorean fuzzy environment with applications, Int. J. Intell. Syst., 35 (2020), 682-717.
  • [43] T. Senapati, R. R. Yager, Fermatean fuzzy sets, Journal of Ambient Intelligence and Humanized Computing, 11(2) (2020), 663-674.
  • [44] T. Senapati, R. R. Yager, Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making, Informatica 30(2) (2019), 391-412.
  • [45] T. Senapati, R. R. Yager, Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods, Eng. Appl. Artif. Intell., 85 (2019) 112-121, doi:10.1016/j.engappai.2019.05.012.
  • [46] D. Liu, Y. Liu, X. Chen, Fermatean fuzzy linguistic set and its application in multicriteria decision making,Int. J. Intell. Syst., 34(5) (2019), 878-894, doi: 10.1002/int.22079.
  • [47] D. Liu, Y. Liu, L. Wang, Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods, J. Intell. Syst. 34(11) (2019), 2807-2834, doi:10.1002/int.22162.
  • [48] M. Kiris¸ci, Fermatean fuzzy soft set with enttropy measure, Journal of Ambient Intelligence & Humanized Computing, (2021).
  • [49] M. Kiris¸ci, Fermatean hesitant fuzzy sets with medical decision making application, Computers and Structures, (2021).
  • [50] M. Kiris¸ci, I. Demir, N. S¸ims¸ek, Fermatean fuzzy ELECTRE multi-criteria group decision-making and most suitable biomedical material selection, Artificial Intelligence in Medicine, (2021).
  • [51] N. S¸ims¸ek, M. Kiris¸ci, Incomplete fermatean fuzzy preference relations and group decision making, Applied Mathematical Modelling, (2021).
Year 2022, Volume: 5 Issue: 1, 16 - 23, 30.04.2022
https://doi.org/10.33187/jmsm.1039613

Abstract

References

  • [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1) (1986), 87-96.
  • [2] D. A. Chiang, N. P. Lin, Correlation of fuzzy sets, Fuzzy Sets Syst., 102(2) (1999), 221-226.
  • [3] S. T. Liu, C. Kao, Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets Syst., 128(2) (2002), 267-275.
  • [4] Z. Liang, P. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognit. Lett., 24(15) (2003), 2687-2693.
  • [5] W. D. Vander, M. Nachtegael, E. E. Kerre, A new similarity measure for image processing, J. Comput. Methods Sci. Eng., 3(2) (2003), 209-222.
  • [6] W. D. Vander, M. Nachtegael, E. E. Kerre, Using similarity measures and homogeneity for the comparison of images, Image Vis. Comput., 22(9) (2004), 695-702.
  • [7] G. W. Wei, H. J. Wang, R. Lin, Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information, Know. Inf. Syst., 26(2) (2011), 337-349.
  • [8] Z. S. Xu, J. Chen, J. J. Wu, Cluster algorithm for intuitionistic fuzzy sets, Inf. Sci., 178(19) (2008), 3775-3790.
  • [9] M. Kiris¸ci, A case study for medical decision making with the fuzzy soft sets, Afrika Matematika, 31(3) (2020) 557-564, doi:10.1007/s13370-019-00741-9.
  • [10] M. Kiris¸ci, N. S¸ims¸ek, Decision making method related to Pythagorean fuzzy soft sets with infectious diseases application, J. King. Saud. Univ. - Comput. Inf. Sci., (2021), doi:10.1016/j.jksuci.2021.08.010.
  • [11] X. Peng, Y. Yang, J. Song, Y. Jiang, Pythagorean fuzzy soft set and its application, Computer Engineering, 41(7) (2015), 224-229.
  • [12] X. Peng, G. Selvachandran, Pythagorean fuzzy set: state of the art and future directions, Artif. Intell. Rev., 52(3) (2019), 1873-1927, doi:10.1007/s10462- 017-9596-9.
  • [13] R. R. Yager, Pythagorean fuzzy subsets, Proc. Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013).
  • [14] R. R. Yager, Pythagorean membership grade in multicriteria decision makng, IEEE Fuzzy Syst., 22 (2014), 958-965.
  • [15] R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers and decision making, Int. J. Intell. Syst., 28 (2013), 436-452.
  • [16] X. L. Zhang, Z. S. Xu, Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061-1078.
  • [17] F. Smarandache, A unifying field in logics: Neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics, Phoenix, Xiquan, (2003).
  • [18] P. A. Ejegwa, Distance and similarity measures for Pythagorean fuzzy sets, Granul. Comput., 5 (2018), 225-238, doi:10.1007/s41066-018-00149-z.
  • [19] P. A. Ejegwa, B. O. Onasanya, Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process, Notes on Intuitionistic Fuzzy Sets, 25(1) (2018), 43-58, doi:10.7546/nifs.2019.25.1.43-58.
  • [20] A. Guleria, R. K. Bajaj, On Pythagorean fuzzy matrices, operations and their applications in decision making and medical diagnosis, Soft Computing., 23(17) (2018), 7889, doi:10.1007/s00500-018-3419-z.
  • [21] R. M. Hashim, M. Gulistan, I. Rehman, N. Hassan, A. M. Nasruddin, Neutrosophic bipolar fuzzy set and its application in medicines preparations, Neutrosophic Sets and Systems, 31 (2020), 86-100, doi:10.5281/zenodo.3639217.
  • [22] M. Kiris¸ci, H. Yilmaz, M. U. Saka, An ANFIS perspective for the diagnosis of type II diabetes, Annals of Fuzzy Mathematics and Informatics, 17 (2019), 101-113.
  • [23] M. Kiris¸ci, Comparison the medical decision-making with intuitionistic fuzzy parameterized fuzzy soft set and Riesz summability, New Math. Nat. Comput., 15 (2019), 351-359. doi:10.1142/S1793005719500194.
  • [24] M. Kiris¸ci, Medical decision making with respect to the fuzzy soft sets, J. Interdiscip. Math., 23(4) (2020), 767-776, doi:10.1080/09720502.2020.1715577.
  • [25] M. Kiris¸ci, W􀀀 soft sets and medical decision-making application, Int. J. Comput. Math., 98(4) (2021), 690-704, doi:10.1080/00207160.2020.1777404.
  • [26] M. Saeed, M. Saqlain, A. Mehmood, K. Naseer, S. Yaqoob, Multi-polar neutrosophic soft sets with application in medical diagnosis and decision-making, Neutrosophic Set Syst., 33 (2020), 183-207.
  • [27] G. Shahzadi, M. Akram, Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information, Journal of Intelligent & Fuzzy Systems, 40(1) (2021), 1401-1416.
  • [28] N. X. Thao, A new correlation coefficient of the intuitionistic fuzzy sets and its application, J. Intell. Fuzzy. Syst., 35(2) (2018), 1959-1968.
  • [29] Q. Zhou, H. Mo, Y. Deng, A new divergence measure of Pythagorean fuzzy sets based on belief function and its application in medical diagnosis, Mathematics, 8 (2020), 2227-7390, doi:10.3390/math8010142
  • [30] R. Arora, H. Garg, A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making, Eng. Appl. Artif. Intell., 72(C) (2018), 80-92.
  • [31] H. Bustince, P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 74(2) (1995), 237-244.
  • [32] Y. Chen, X. Peng, G. Guan, H. Jiang, Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information, J. Intell. Fuzzy Syst., 6(5) (2014), 2547-2556.
  • [33] P. A. Ejegwa, Novel correlation coefficient for intuitionistic fuzzy sts and its application to multi-criteria decision-making problems, Int. J. Fuzzy Syst. Appl., 10(2) (2021), 39-58.
  • [34] P. A. Ejegwa, C. Jana, Some new weighted correlation coefficients between Pythagorean fuzzy sets and their applications, In: Garg, H., (Eds.), Pythagorean fuzzy sets, Springer, (2021), 39-64.
  • [35] B. Farhadinia, Correlation for dual hesistant fuzzy sets and dual interval-valued hesitant fuzzy set, Int. J. Intell. Syst., 29(2) (2014), 184-205.
  • [36] H. Garg, Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process, J. Ind. Manag. Optim., 14(4) (2018), 1501-1519.
  • [37] H. Garg, A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making, Int. J. Intell. Sys., 31(12) (2016), 1234-1252, doi:10.1002/int.21827.
  • [38] H. Garg, K. Kumar, A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application, Sci. Iran. E., 25(4) (2018), 2373-2388.
  • [39] H. Garg, D. Rani, A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making, Appl. Intell., 49(2) (2019), 496-512.
  • [40] H. Garg, G. Shahzadi, M. Akram, Decision-making analysis based on Fermatean fuzzy Yager aggregation operators with application in COVID-19 testing facility, Mathematical Problems in Engineering, 2020 (2020) Article ID 7279027, doi:10.1155/2020/7279027.
  • [41] H. Liao, Z. Xu, X. J. Zeng, Novel correlation coefficients between hesitant fuzzy sets and their application in decision making, Knowl. Based Syst., 82 (2015), 115-127.
  • [42] S. Singh, A. H. Ganie, On some correlation coefficients in Pythagorean fuzzy environment with applications, Int. J. Intell. Syst., 35 (2020), 682-717.
  • [43] T. Senapati, R. R. Yager, Fermatean fuzzy sets, Journal of Ambient Intelligence and Humanized Computing, 11(2) (2020), 663-674.
  • [44] T. Senapati, R. R. Yager, Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making, Informatica 30(2) (2019), 391-412.
  • [45] T. Senapati, R. R. Yager, Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods, Eng. Appl. Artif. Intell., 85 (2019) 112-121, doi:10.1016/j.engappai.2019.05.012.
  • [46] D. Liu, Y. Liu, X. Chen, Fermatean fuzzy linguistic set and its application in multicriteria decision making,Int. J. Intell. Syst., 34(5) (2019), 878-894, doi: 10.1002/int.22079.
  • [47] D. Liu, Y. Liu, L. Wang, Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods, J. Intell. Syst. 34(11) (2019), 2807-2834, doi:10.1002/int.22162.
  • [48] M. Kiris¸ci, Fermatean fuzzy soft set with enttropy measure, Journal of Ambient Intelligence & Humanized Computing, (2021).
  • [49] M. Kiris¸ci, Fermatean hesitant fuzzy sets with medical decision making application, Computers and Structures, (2021).
  • [50] M. Kiris¸ci, I. Demir, N. S¸ims¸ek, Fermatean fuzzy ELECTRE multi-criteria group decision-making and most suitable biomedical material selection, Artificial Intelligence in Medicine, (2021).
  • [51] N. S¸ims¸ek, M. Kiris¸ci, Incomplete fermatean fuzzy preference relations and group decision making, Applied Mathematical Modelling, (2021).
There are 51 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Murat Kirisci 0000-0003-4938-5207

Publication Date April 30, 2022
Submission Date December 21, 2021
Acceptance Date March 6, 2022
Published in Issue Year 2022 Volume: 5 Issue: 1

Cite

APA Kirisci, M. (2022). Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application. Journal of Mathematical Sciences and Modelling, 5(1), 16-23. https://doi.org/10.33187/jmsm.1039613
AMA Kirisci M. Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application. Journal of Mathematical Sciences and Modelling. April 2022;5(1):16-23. doi:10.33187/jmsm.1039613
Chicago Kirisci, Murat. “Correlation Coefficients of Fermatean Fuzzy Sets With a Medical Application”. Journal of Mathematical Sciences and Modelling 5, no. 1 (April 2022): 16-23. https://doi.org/10.33187/jmsm.1039613.
EndNote Kirisci M (April 1, 2022) Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application. Journal of Mathematical Sciences and Modelling 5 1 16–23.
IEEE M. Kirisci, “Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application”, Journal of Mathematical Sciences and Modelling, vol. 5, no. 1, pp. 16–23, 2022, doi: 10.33187/jmsm.1039613.
ISNAD Kirisci, Murat. “Correlation Coefficients of Fermatean Fuzzy Sets With a Medical Application”. Journal of Mathematical Sciences and Modelling 5/1 (April 2022), 16-23. https://doi.org/10.33187/jmsm.1039613.
JAMA Kirisci M. Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application. Journal of Mathematical Sciences and Modelling. 2022;5:16–23.
MLA Kirisci, Murat. “Correlation Coefficients of Fermatean Fuzzy Sets With a Medical Application”. Journal of Mathematical Sciences and Modelling, vol. 5, no. 1, 2022, pp. 16-23, doi:10.33187/jmsm.1039613.
Vancouver Kirisci M. Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application. Journal of Mathematical Sciences and Modelling. 2022;5(1):16-23.

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