Abstract
Fermatean fuzzy set (FFS) is an advance variant of fuzzy set applicable in curbing uncertainties and vagueness in complex decision making scenarios. Correlation coefficient is a measure of relationship between two variables or data with a significant importance in decision-making involving different areas of human endeavours. Several methods for calculating the correlation coefficient between FFSs have been developed and used to discuss sundry real-world problems. Albeit, these existing methods lack reliability, precision and give mispleading interpretations during real-life applications. Due to these setbacks, this work constructs a new method of Fermatean fuzzy correlation coefficient (FFCC) with practicable application potentials. This new method of FFCC is demonstrated to show accuracy, reliability, and superiority over the existing methods of FFCC through comparative studies. More so, the new method is applied to determine students’ academic performance via clustering analysis and selection process. This new method of FFCC could be used to discuss technique for order preference by similarity to ideal solutions and multiple attributes decision-making.
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inf. Cont. 8, 338–353 (1965)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Set. Syst. 20, 87–96 (1986)
Todorova, L., Atanasasov, K.T., Hadjitodorov, S., Vassilev, P.: On an intuitionistic fuzzy approach for decision-making in medicine: part 1. Bioautomat. 6, 92–101 (2007)
Xu, Z., Chen, J., Wu, J.: Clustering algorithm for intuitionistic fuzzy sets. Inf. Sci. 178(19), 3775–3790 (2008)
Davvaz, B., Sadrabadi, E.H.: An application of intuitionistic fuzzy sets in medicine. Int. Biomath. 9(3), 1650037 (2016)
Ejegwa, P.A., Ahemen, S.: Enhanced intuitionistic fuzzy similarity operator with applications in emergency management and pattern recognition. Granul. Comput. 8, 361–372 (2023)
Zhou, Y., Ejegwa, P.A., Johnny, S.E.: Generalized similarity operator for intuitionistic fuzzy sets and its applications based on recognition principle and multiple criteria decision making technique. Int. J. Comput. Intell. Syst. 16, 85 (2023)
Atanassov, K.T.: More on intuitionistic fuzzy sets. Fuzzy Set. Syst. 33(1), 37–45 (1989)
Yager, R.R.: Pythagorean membership grades in multi-criteria decision-making. IEEE Trans. Fuzzy Set Syst. 22(4), 958–956 (2014)
Zhang, X.L., Xu, Z.S.: Extension of TOPSIS to multiple criteria decision-making with Pythagorean fuzzy sets. Int. J. Intell. Syst. 29, 1061–1078 (2014)
Yager, R.R.: Properties and applications of Pythagorean fuzzy sets. In: Angelov, Sotirov, S. (eds) Imprecision and Uncertainty in Information Representation and Processing, Studies in Fuzziness and Soft Computing, Springer, vol. 332, pp. 119–136 (2016).
He, X., Du, Y., Liu, W.: Pythagorean fuzzy power average operators. Fuzzy Syst. Math. 30, 116–124 (2016)
Gou, X., Xu, Z., Ren, P.: The properties of continuous Pythagorean fuzzy information. Int. J. Intell. Syst. 31, 401–424 (2016)
Wei, G., Wei, Y.: Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int. J. Intell. Syst. 33(3), 634–652 (2018)
Zhou, F., Chen, T.: A novel distance measure for Pythagorean fuzzy sets and its applications to the technique for order preference by similarity to ideal solutions. Int. J. Intell. Syst. 12(2), 955–969 (2019)
Ejegwa, P.A., Feng, Y., Tang, S., Agbetayo, J.M., Dai, X.: New Pythagorean fuzzy-based distance operators and their applications in pattern classification and disease diagnostic analysis. Neural Comput. Appl. 35(14), 10083–10095 (2023)
Wu, K., Ejegwa, P.A., Feng, Y., Onyeke, I.C., Johnny, S.E., Ahemen, S.: Some enhanced distance measuring approaches based on Pythagorean fuzzy information with applications in decision making. Symmet. 14, 2669 (2022)
Ejegwa, P.A.: Pythagorean fuzzy set and its application in career placements based on academic performance using max-min-max composition. Complex Intell. Syst. 5, 165–175 (2019)
Senapati, T., Yager, R.R.: Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision-making. Informat 30(2), 391–412 (2019)
Senapati, T., Yager, R.R.: Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng. Appl. Artif. Intell. 85, 112–121 (2019)
Aydin, S.: A fuzzy MCDM method based on the new Fermatean fuzzy theories. Int. J. Inf. Tech. Dec. 20(3), 881–902 (2021)
Ejegwa, P.A., Muhiuddin, G., Algehyne, E.A., Agbetayo, J.M., Al-Kadi, D.: An enhanced Fermatean fuzzy composition relation based on a maximum-average approach and its application in diagnostic analysis. J. Math. 1786221, 12 (2022)
Sahoo, L.: Some score function on Fermatean fuzzy sets and its application in bride selection based on TOPSIS method. Int. J. Fuzzy Syst. Appl. 10(3), 18–29 (2021)
Sahoo, L.: A new score function based Fermatean fuzzy transportation problem. Res. Contr. Optimiz. 4(11), 100040 (2021)
Akram, M., Muhiuddin, G., Santos-Garcia, G.: An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets. Math. Biosci. Eng. 19(7), 7201–7231 (2022)
Sahoo, L.: Similarity measure for Fermatean fuzzy sets and its application in group decision-making. Dec. Sci. Lett. 11(2), 167–180 (2022)
Sindhu, M.S., Siddique, I., Yager, R.R.: Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision-making. Informat 30(2), 391–412 (2019)
Ejegwa, P.A., Onyeke, I.C.: Fermatean fuzzy similarity measure and its application in students’ admission process. Int. J. Fuzzy Comput. Modell. 4(1), 34–50 (2022)
Onyeke, I.C., Ejegwa, P.A.: Modified Senapati and Yager’s Fermatean fuzzy distance and its application in students’ course placement in tertiary institution. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain, Studies in Fuzziness and Soft Computing, Springer, vol. 420, pp. 237–253 (2023).
Dumitrescu, D.: Fuzzy correlation. Studia Univ. Babe-Bolyai Math. 23, 41–44 (1978)
Gerstenkorn, T., Manko, J.: Correlation of intuitionistic fuzzy sets. Fuzzy Set. Syst. 8, 23–43 (1991)
Hung, W.L.: Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. Int. J. Uncert. Fuzz. Knowl. Syst. 9(4), 509–516 (2001)
Ejegwa, P.A., Ajogwu, C.F., Sarkar, A.: A hybridized correlation coefficient technique and its application in classification process under intuitionistic fuzzy setting. Iranian J. Fuzzy Syst. 20(4), 103–120 (2023)
Ejegwa, P.A., Onyeke, I.C.: Intuitionistic fuzzy statistical correlation algorithm with application to multi-criteria based decision-making processes. Int. J. Intell. Syst. 36(3), 1386–1407 (2021)
Ejegwa, P.A., Onyeke, I.C., Kausar, N., Kattel, P.: A new partial correlation coefficient technique based on intuitionistic fuzzy information and its pattern recognition application. Int. J. Intell. Syst. 5540085, 14 (2023)
Garg, H.: A novel correlation coefficients between pythagorean fuzzy sets and its application to decision-making. Int. J. Intell. Syst. 31, 1234–1252 (2016)
Ejegwa, P.A., Feng, Y., Zhang, W.: Pattern recognition based on an improved Szmidt and Kacprzyk’s correlation coefficient in Pythagorean fuzzy environment. In: Han, M. et al. (Eds.) Advances in Neural Networks–17th International Symposium on Neural Networks, Lecture Notes in Computer Science 12557, Springer pp. 190–206 (2021).
Thao, N.X.: A new correlation coefficient of the pythagorean fuzzy sets and its applications. Soft. Comput. 24, 9467–9478 (2020)
Ejegwa, P.A., Wen, S., Feng, Y., Zhang, W., Chen, J.: Some new Pythagorean fuzzy correlation techniques via statistical viewpoint with applications to decision-making problems. J. Intell. Fuzzy Syst. 40(5), 9873–9886 (2021)
Ejegwa, P.A., Wen, S., Feng, Y., Zhang, W.: Determination of pattern recognition problems based on a Pythagorean fuzzy correlation measure from statistical viewpoint. In: Proceedings of the 13th International Conference of Advanced Computational Intelligence, Wanzhou, China, pp. 132–139 (2021).
Ejegwa, P.A., Sarkar, A., Onyeke, I.C.: New methods of computing correlation coefficient based on Pythagorean fuzzy information and their applications in disaster control and diagnostic analysis. In: Jana, C., Pal, M., Muhiuddin, G., Liu, P. (eds.) Fuzzy Optimization, pp. 473–498. Springer, Decision-making and Operations Research (2023)
Yan, D., Wu, K., Ejegwa, P.A., Xie, X., Feng, Y.: Pythagorean fuzzy partial correlation measure and its application. Symmet 15, 216 (2023)
Kirisci, M.: Correlation coefficient of Fermatean fuzzy sets with a medical application. J. Math. Sci. Modell. 5(1), 16–23 (2022)
Bhatia, M., Arora, H.D., Anjali, N.: Some new correlation coefficient measures based on Fermatean fuzzy sets using decision-making approach in pattern analysis and supplier selection. Int. J. Math. Eng. Manag. Sci. 8(2), 245–263 (2023)
Ejegwa, P.A., Sarkar, A.: Fermatean fuzzy approach of diseases diagnosis based on new correlation coefficient operators. In: Garg, H., Chatterjee, J.M. (eds) Deep learning in personalized healthcare and decision support, Academic Press, pp. 23–38 (2023).
Gouli, S., Mahapatra, B.S., Mahapatra, G.S.: A new correlation based measure on Fermatean fuzzy applied on multi-criteria decision-making for electric vehicle selection. Expert Syst. Applic. 23(7), 121–605 (2023)
Amman, M., Rashid, T., Ali, A.: Fermatean fuzzy multi-criteria decision-making based on Spearman rank correlation coefficient. Granul. Comput. 8, 2005–2019 (2023)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ejegwa, P.A., Wanzenke, T.D., Ogwuche, I.O. et al. A robust correlation coefficient for fermatean fuzzy sets based on spearman’s correlation measure with application to clustering and selection process. J. Appl. Math. Comput. 70, 1747–1770 (2024). https://doi.org/10.1007/s12190-024-02019-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-024-02019-1
Keywords
- Fermatean fuzzy set
- Fermatean fuzzy correlation coefficient
- Clustering analysis
- Selection process
- Decision-making