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Issue:Modified and generalized correlation coefficient between intuitionistic fuzzy sets with applications: Difference between revisions

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{{issue/data
{{issue/data
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/26/1|Notes on Intuitionistic Fuzzy Sets, Volume 26 (2020), Number 1]], pages 8–22
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/26/1|Notes on Intuitionistic Fuzzy Sets, Volume 26 (2020), Number 1]], pages 8–22
  | doi            =  
  | doi            = https://doi.org/10.7546/nifs.2020.26.1.8-22
  | file            = NIFS-26-1-08-22.pdf
  | file            = NIFS-26-1-08-22.pdf
  | format          = PDF
  | format          = PDF
  | size            = 142
  | size            = 218
  | abstract        =  Intuitionistic fuzzy set (IFS) is a very interesting soft computing technique use to tackle/handle imprecisions embedded in multi-criteria decision-making (MCDM) problems.
  | abstract        =  Intuitionistic fuzzy set (IFS) is a very interesting soft computing technique use to tackle/handle imprecisions embedded in multi-criteria decision-making (MCDM) problems.
Correlation coefficient has proven to be an important measuring operator in an intuitionistic fuzzy setting with regard to its applications in solving MCDM problems. In this paper, Xu et al.’s method of correlation coefficient between IFSs is modified because it fails the axiomatic properties of correlation coefficient between IFSs, and hence generalized for a better output. That is, this paper is aimed at modifying and generalizing the triparametric correlation coefficient for IFSs proposed by Xu et al. with applications to some MCDM problems. Some numerical examples are supplied to authenticate the superiority of this new correlation coefficient for IFSs over some similar existing correlation coefficient measures. Subsequently, some MCDM problems such as medical diagnosis and pattern recognition problems represented in intuitionistic fuzzy pairs are determined with the aid of the novel correlation coefficient. An intuitionistic fuzzy clustering algorithm based on this novel correlation coefficient with applications could be an interesting research for future work.
Correlation coefficient has proven to be an important measuring operator in an intuitionistic fuzzy setting with regard to its applications in solving MCDM problems. In this paper, Xu et al.’s method of correlation coefficient between IFSs is modified because it fails the axiomatic properties of correlation coefficient between IFSs, and hence generalized for a better output. That is, this paper is aimed at modifying and generalizing the triparametric correlation coefficient for IFSs proposed by Xu et al. with applications to some MCDM problems. Some numerical examples are supplied to authenticate the superiority of this new correlation coefficient for IFSs over some similar existing correlation coefficient measures. Subsequently, some MCDM problems such as medical diagnosis and pattern recognition problems represented in intuitionistic fuzzy pairs are determined with the aid of the novel correlation coefficient. An intuitionistic fuzzy clustering algorithm based on this novel correlation coefficient with applications could be an interesting research for future work.
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# Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
# Atanassov, K. T. (1986). [[Issue:Intuitionistic fuzzy sets|Intuitionistic fuzzy sets]], Fuzzy Sets and Systems, 20, 87–96.
# Atanassov, K. T. (1994). New operations defined on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
# Atanassov, K. T. (1994). New operations defined on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
# Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg, 1999.
# Atanassov, K. T. (1999). [[Intuitionistic Fuzzy Sets: Theory and Applications]]. Physica-Verlag, Heidelberg, 1999.
# Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
# Atanassov, K. T. (2012). [[On Intuitionistic Fuzzy Sets Theory]]. Springer, Berlin.
# Chiang, D. A. & Lin, N. P. (1999). Correlation of fuzzy sets, Fuzzy Sets and Systems, 102 (2), 221–226.
# Chiang, D. A. & Lin, N. P. (1999). Correlation of fuzzy sets, Fuzzy Sets and Systems, 102 (2), 221–226.
# Davvaz, B. & Sadrabadi, E. H. (2016). An application of intuitionistic fuzzy sets in medicine, International Journal of Biomathematics, 9 (3), 1650037 (15 pages).
# Davvaz, B. & Sadrabadi, E. H. (2016). An application of intuitionistic fuzzy sets in medicine, International Journal of Biomathematics, 9 (3), 1650037 (15 pages).
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# Dumitrescu, D. (1978). Fuzzy correlation, Studia Univ. Babes-Bolyai Mathematics, 23, 41–44.
# Dumitrescu, D. (1978). Fuzzy correlation, Studia Univ. Babes-Bolyai Mathematics, 23, 41–44.
# Ejegwa, P. A. (2015). Intuitionistic fuzzy sets approach in appointment of positions in an organization via max-min-max rule, Global Journal of Science Frontier Research: F Mathematics and Decision Science, 15 (6), 1–6.
# Ejegwa, P. A. (2015). Intuitionistic fuzzy sets approach in appointment of positions in an organization via max-min-max rule, Global Journal of Science Frontier Research: F Mathematics and Decision Science, 15 (6), 1–6.
# Ejegwa, P. A. & Adamu, I. M. (2019). Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine, Notes on Intuitionistic Fuzzy Sets, 25 (3), 53–70.
# Ejegwa, P. A. & Adamu, I. M. (2019). [[Issue:Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine|Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine]], Notes on Intuitionistic Fuzzy Sets, 25 (3), 53–70.
# Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method, European Scientific Journal, 10 (15), 529–536.
# Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method, European Scientific Journal, 10 (15), 529–536.
# Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzzy sets in career determination, Journal of Information and Computing Science, 9 (4), 285–288.
# Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzy sets in career determination, Journal of Information and Computing Science, 9 (4), 285–288.
# Ejegwa, P. A. & Modom, E. S. (2015). Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets, International Journal of Fuzzy Mathematical Archive, 8 (1), 1–7.
# Ejegwa, P. A. & Modom, E. S. (2015). Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets, International Journal of Fuzzy Mathematical Archive, 8 (1), 1–7.
# Ejegwa, P. A. & Onasanya, B. O. (2019). Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process, Notes on Intuitionistic Fuzzy Sets, 25 (1), 43–58.
# Ejegwa, P. A. & Onasanya, B. O. (2019). [[Issue:Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process|Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process]], Notes on Intuitionistic Fuzzy Sets, 25 (1), 43–58.
# Ejegwa, P. A. & Onyeke, I. C. (2018). An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation, Annals of Communications in Mathematics, 1 (1), 38–47.  
# Ejegwa, P. A. & Onyeke, I. C. (2018). An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation, Annals of Communications in Mathematics, 1 (1), 38–47.  
# Garg, H. (2016). A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision making processes, International Journal of Intelligent Systems, 31(12), 1234–1252.
# Garg, H. (2016). A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision making processes, International Journal of Intelligent Systems, 31(12), 1234–1252.
Line 50: Line 50:
# Liu, B., Shen, Y., Mu, L., Chen, X. & Chen, L. (2016). A new correlation measure of the intuitionistic fuzzy sets, Journal of Intelligent and Fuzzy Systems, 30 (2), 1019–1028.
# Liu, B., Shen, Y., Mu, L., Chen, X. & Chen, L. (2016). A new correlation measure of the intuitionistic fuzzy sets, Journal of Intelligent and Fuzzy Systems, 30 (2), 1019–1028.
# Mitchell, H. B. (2004). A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems, 19 (5), 483–490.
# Mitchell, H. B. (2004). A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems, 19 (5), 483–490.
# Pavan, M.&Todeschini, R.(2009).Multi-criteriadecision-makingmethods, Computational Chemometric, 1, 591–629.
# Pavan, M.&Todeschini, R.(2009).Multi-criteria decision-making methods, Computational Chemometric, 1, 591–629.
# Szmidt, E. & Kacprzyk, J. (2001). Intuitionistic fuzzy sets in some medical applications, Notes on Intuitionistic Fuzzy Sets, 7 (4), 58–64.
# Szmidt, E. & Kacprzyk, J. (2001). [[Issue:Intuitionistic fuzzy sets in some medical applications|Intuitionistic fuzzy sets in some medical applications]], Notes on Intuitionistic Fuzzy Sets, 7 (4), 58–64.
# Szmidt, E. & Kacprzyk, J. (2004). Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 10 (4), 61–69.
# Szmidt, E. & Kacprzyk, J. (2004). [[Issue:Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets|Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets]], Notes on Intuitionistic Fuzzy Sets, 10 (4), 61–69.
# Szmidt, E. & Kacprzyk, J. (2010). Correlation of intuitionistic fuzzy sets, In: Hullermeier, E., Kruse, R. and Hoffmann, F. (eds.): Proc. of IPMU 2010, LNAI 6178, pp. 169–177, Springer-Verlag Berlin Heidelberg.
# Szmidt, E. & Kacprzyk, J. (2010). Correlation of intuitionistic fuzzy sets, In: Hullermeier, E., Kruse, R. and Hoffmann, F. (eds.): Proc. of IPMU 2010, LNAI 6178, pp. 169–177, Springer-Verlag Berlin Heidelberg.
# Thao, N. X. (2018). A new correlation coefficient of the intuitionistic fuzzy sets and its application, Journal of Intelligent and Fuzzy Systems, 35 (2), 1959–1968.
# Thao, N. X. (2018). A new correlation coefficient of the intuitionistic fuzzy sets and its application, Journal of Intelligent and Fuzzy Systems, 35 (2), 1959–1968.

Latest revision as of 14:03, 3 June 2020

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http://ifigenia.org/wiki/issue:nifs/26/1/8-22
Title of paper: Modified and generalized correlation coefficient between intuitionistic fuzzy sets with applications
Author(s):
Paul Augustine Ejegwa
Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
ejegwa.augustine@uam.edu.ng
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 26 (2020), Number 1, pages 8–22
DOI: https://doi.org/10.7546/nifs.2020.26.1.8-22
Download:  PDF (218  Kb, File info)
Abstract: Intuitionistic fuzzy set (IFS) is a very interesting soft computing technique use to tackle/handle imprecisions embedded in multi-criteria decision-making (MCDM) problems.

Correlation coefficient has proven to be an important measuring operator in an intuitionistic fuzzy setting with regard to its applications in solving MCDM problems. In this paper, Xu et al.’s method of correlation coefficient between IFSs is modified because it fails the axiomatic properties of correlation coefficient between IFSs, and hence generalized for a better output. That is, this paper is aimed at modifying and generalizing the triparametric correlation coefficient for IFSs proposed by Xu et al. with applications to some MCDM problems. Some numerical examples are supplied to authenticate the superiority of this new correlation coefficient for IFSs over some similar existing correlation coefficient measures. Subsequently, some MCDM problems such as medical diagnosis and pattern recognition problems represented in intuitionistic fuzzy pairs are determined with the aid of the novel correlation coefficient. An intuitionistic fuzzy clustering algorithm based on this novel correlation coefficient with applications could be an interesting research for future work.

Keywords: Fuzzy set, Intuitionistic fuzzy set, Correlation coefficient, Multi-criteria decision making.
AMS Classification: 03E72, 62H20, 62M10.
References:
  1. Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
  2. Atanassov, K. T. (1994). New operations defined on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
  3. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg, 1999.
  4. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  5. Chiang, D. A. & Lin, N. P. (1999). Correlation of fuzzy sets, Fuzzy Sets and Systems, 102 (2), 221–226.
  6. Davvaz, B. & Sadrabadi, E. H. (2016). An application of intuitionistic fuzzy sets in medicine, International Journal of Biomathematics, 9 (3), 1650037 (15 pages).
  7. De, S. K., Biswas, R. & Roy, A. R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117 (2), 209–213.
  8. Dumitrescu, D. (1977). A definition of an informational energy in fuzzy set theory, Studia Univ. Babes-Bolyai Mathematics, 22, 57–59.
  9. Dumitrescu, D. (1978). Fuzzy correlation, Studia Univ. Babes-Bolyai Mathematics, 23, 41–44.
  10. Ejegwa, P. A. (2015). Intuitionistic fuzzy sets approach in appointment of positions in an organization via max-min-max rule, Global Journal of Science Frontier Research: F Mathematics and Decision Science, 15 (6), 1–6.
  11. Ejegwa, P. A. & Adamu, I. M. (2019). Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine, Notes on Intuitionistic Fuzzy Sets, 25 (3), 53–70.
  12. Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method, European Scientific Journal, 10 (15), 529–536.
  13. Ejegwa, P. A., Akubo, A. J. & Joshua, O. M. (2014). Intuitionistic fuzzy sets in career determination, Journal of Information and Computing Science, 9 (4), 285–288.
  14. Ejegwa, P. A. & Modom, E. S. (2015). Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets, International Journal of Fuzzy Mathematical Archive, 8 (1), 1–7.
  15. Ejegwa, P. A. & Onasanya, B. O. (2019). Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process, Notes on Intuitionistic Fuzzy Sets, 25 (1), 43–58.
  16. Ejegwa, P. A. & Onyeke, I. C. (2018). An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation, Annals of Communications in Mathematics, 1 (1), 38–47.
  17. Garg, H. (2016). A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision making processes, International Journal of Intelligent Systems, 31(12), 1234–1252.
  18. Gerstenkorn, T. & Manko, J. (1991). Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 44 (1), 39–43.
  19. Hung, W. L. (2001). Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9 (4), 509–516.
  20. Hung, W. L. & Wu, J. W. (2002). Correlation of intuitionistic fuzzy sets by centroid method, Information Sciences, 144 (1), 219–225.
  21. Iqbal, M. N. & Rizwan, U. (in press). Some applications of intuitionistic fuzzy sets using new similarity measure, Journal of Ambient Intelligence and Humanized Computing, https://doi.org/10.1007/s12652-019-01516-7.
  22. Liu, B., Shen, Y., Mu, L., Chen, X. & Chen, L. (2016). A new correlation measure of the intuitionistic fuzzy sets, Journal of Intelligent and Fuzzy Systems, 30 (2), 1019–1028.
  23. Mitchell, H. B. (2004). A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems, 19 (5), 483–490.
  24. Pavan, M.&Todeschini, R.(2009).Multi-criteria decision-making methods, Computational Chemometric, 1, 591–629.
  25. Szmidt, E. & Kacprzyk, J. (2001). Intuitionistic fuzzy sets in some medical applications, Notes on Intuitionistic Fuzzy Sets, 7 (4), 58–64.
  26. Szmidt, E. & Kacprzyk, J. (2004). Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 10 (4), 61–69.
  27. Szmidt, E. & Kacprzyk, J. (2010). Correlation of intuitionistic fuzzy sets, In: Hullermeier, E., Kruse, R. and Hoffmann, F. (eds.): Proc. of IPMU 2010, LNAI 6178, pp. 169–177, Springer-Verlag Berlin Heidelberg.
  28. Thao, N. X. (2018). A new correlation coefficient of the intuitionistic fuzzy sets and its application, Journal of Intelligent and Fuzzy Systems, 35 (2), 1959–1968.
  29. Thao, N. X., Ali, M. & Smarandache, F. (2019). An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis, Journal of Intelligent and Fuzzy Systems, 36 (1), 189–198.
  30. Todorova, L., Atanassov, K. T., Hadjitodorov, S. & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decision-making in medicine (Part 1), International Electronic Journal of Bioautomation, 6,92–101.
  31. Todorova, L., Atanassov, K. T., Hadjitodorov, S. & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decision-making in medicine (Part 2), International Electronic Journal of Bioautomation, 7, 64–69.
  32. Xu, Z. (2006). On correlation measures of intuitionistic fuzzy sets, In: Corchado, E. et al. (eds.): Proc. of IDEAL 2006, LNCS 4224, pp. 16–24, Springer-Verlag Berlin Heidelberg.
  33. Xu, S., Chen, J. & Wu, J. J. (2008). Cluster algorithm for intuitionistic fuzzy sets, Information Sciences, 178, 3775–3790.
  34. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, pp. 338–353.
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