Some New Techniques of Computing Correlation Coefficient between q-Rung Orthopair Fuzzy Sets and their Applications in Multi-Criteria Decision-Making

Year 2025, Early View

Paul Augustine Ejegwa , Arun Sarkar Idoko Charles Onyeke

https://doi.org/10.35378/gujs.1420424

Abstract

The term q-rung orthopair fuzzy set is an essential variant of fuzzy set with the capacity of tackling fuzziness and imprecision in the decision-making process. A fundamental concept in the decision-making process is the idea of correlation coefficient because of its wide applications. The process of decision-making is complex due to imprecisions, and as such the idea of correlation coefficient has been investigated under q-rung orthopair fuzzy setting. Some authors have constructed some techniques of correlation coefficient under q-rung orthopair fuzzy sets with practical applications. However, these existing techniques are defectives with several drawbacks in terms of precision and alignment with the conditions of correlation coefficient. In this work, two new techniques for estimating correlation coefficient under q-rung orthopair fuzzy sets are presented and theoretically discussed. Moreover, we apply the new techniques of correlation coefficient under q-rung orthopair fuzzy sets in disease diagnosis and employment process by using simulated q-rung orthopair fuzzy data based on multi-criteria decision-making approach and recognition principle. Some comparative analyses are provided to ascertain the benefits of the new techniques of correlation coefficient under q-rung orthopair fuzzy sets over the obtainable techniques with regard to reliability and performance rating.

Keywords

Pythagorean fuzzy set, q-Rung orthopair fuzzy set, Disease diagnosis, Intuitionistic fuzzy set, Fermatean fuzzy set

Ethical Statement

Not applicable

Supporting Institution

None

Thanks

Warm regards

References

• [1] Zadeh, L. A., “Fuzzy sets”, Information and Control, 8: 338-353, (1965).
• [2] Atanassov, K. T., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20: 87-96, (1986).
• [3] Atanassov, K. T., “Intuitionistic fuzzy sets: theory and applications”, Heidelberg: Physica-Verlag, (1999).
• [4] Yager, R. R., “Pythagorean membership grades in multicriteria decision making”, Technical Report MII-3301 Machine Intelligence Institute, Iona College, New Rochelle, (2013).
• [5] Begum, S. S., Srinivasan, R., “Some properties on intuitionistic fuzzy sets of third type”, Annals of Fuzzy Mathematics and Informatics, 10(5): 799-804, (2015).
• [6] Senapati, T., Yager, R. R., “Fermatean fuzzy sets”, Journal of Ambient and Intelligent and Humanized Computing, 11: 663-674, (2020).
• [7] Yager, R. R., “Generalized orthopair fuzzy sets”, IEEE Transactions on Fuzzy Systems, 25(5): 1222‐1230, (2017).
• [8] De, S. K., Biswas, R., Roy, A. R., “Some operations on intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 114(3): 477-484, (2000).
• [9] Ejegwa, P. A., “Novel correlation coefficient for intuitionistic fuzzy sets and its application to multi-criteria decision-making problems,” International Journal of Fuzzy Systems and Applications, 10(2): 39-58, (2021).
• [10] Ejegwa, P. A., Onyeke, I. C., “A novel intuitionistic fuzzy correlation algorithm and its applications in pattern recognition and student admission process”, International Journal of Fuzzy Systems and Applications 11(1): 1-20, (2022).
• [11] Li, D. F., Chen, C. T., “New similarity measures of intuitionistic fuzzy sets and application to pattern recognition”, Pattern Recognition Letters, 23(1-3): 221-225, (2002).
• [12] Yager, R. R., “Pythagorean membership grades in multicriteria decision making”, IEEE Transactions on Fuzzy Systems, 22: 958-965, (2014).
• [13] Zhang, X. L., Xu, Z. S., “Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets”, International Journal of Intelligent Systems, 29: 1061-1078, (2014).
• [14] 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, 132-139, Wanzhou, China, (2021).
• {15] Zeng, W., Li, D., Yin, Q., “Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making”, International Journal of Intelligent Systems, 33(11): 2236-2254, (2018).
• [16] Garg, H., “A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making”, International Journal of Intelligent Systems, 31(9): 886-920, (2016).
• [17] Garg, H., “Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision making process”, International Journal of Intelligent Systems, 32(6): 597-630, (2017).
• [18] Ejegwa, P. A., “Generalized triparametric correlation coefficient for Pythagorean fuzzy sets with application to MCDM problems”, Granular Computing, 6(3): 557-566, (2021).
• [19] Ejegwa, P. A., Awolola, J. A., “Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems”, Granular Computing, 6: 181-189, (2021).
• [20] Liu, D., Liu, Y., Chen, X., “Fermatean fuzzy linguistic set and its application in multicriteria decision making”, International Journal of Intelligent Systems, 34(5): 878-894, (2019).
• [21] Senapati, T., Yager, R. R., “Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods”. Engineering Applications and Artificial Intelligence, 85: 112-121, (2019).
• [22] Senapati, T., Yager, R. R., “Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making”, Informatica, 30(2): 391-412, (2019).
• [23] Mehdi, K. G., Maghsoud, A., Mohammad, H. T., Edmundas, K. Z., Arturas, K., “A new decision- making approach based on Fermatean fuzzy sets and WASPAS for green construction supplier evaluation”, Mathematics, 8(12): 2202, (2020).
• [24] Sahoo, L., “Some score functions on Fermatean fuzzy sets and its application to bride selection based on TOPSIS method”, International Journal of Fuzzy Systems Applications, 10(3): 18-29, (2021).
• [25] Aydin, S., “A fuzzy MCDM method based on new Fermatean fuzzy theories”, International Journal of Information Technology and Decision Making, 20(3): 881-902, (2021).
• [26] Krishankumar, R., Nimmagadda, S. S., Rani, P., Mishra, A. R., Ravichandran, K. S., Gandomi, A. H., “Solving renewable energy source selection problems using a q-rung orthopair fuzzy-based integrated decision-making approach”, Journal of Cleaner Production, 279: 123329 (2021).
• [27] Liu, P., Wang, Y., “Multiple attribute decision making based on q-rung orthopair fuzzy generalized Maclaurin symmetic mean operators”, Information Sciences, 518: 181-210, (2020).
• [28] Pen, X., Huang, H., Luo, Z., "q‐rung orthopair fuzzy decision‐making framework for integrating mobile edge caching scheme preferences”, International Journal of Intelligent Systems, 36(5): 2229-2266, (2021).
• [29] Sarkar, A., Biswas, A., “Dual hesitant q‐rung orthopair fuzzy Dombi t‐conorm and t-norm based Bonferroni mean operators for solving multicriteria group decision making problems”, International Journal of Intelligent Systems, 36(7): 3293-3338, (2021).
• [30] Garg, H., “A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐making”, International Journal of Intelligent Systems, 36(1): 526-557, (2021).
• [31] Khan, M. J., Kumam, P., Shutaywi, M., “Knowledge measure for the q-rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 36: 628- 655, (2021).
• [32] Akram, M., Alsulami, S., Karaaslan, F., Khan, A., “q-Rung orthopair fuzzy graphs under Hamacher operators”, International Journal of Intelligent Systems, 40(1): 1367-1390, (2021).
• [33] Sitara, M., Akram, M., Riaz, M., “Decision-making analysis based on q-rung picture fuzzy graphstructures”, Journal of Applied Mathematics and Computing, 67(1): 541-577, (2021).
• [34] Yin, S., Li, H., Yang, Y., “Product operations on q-rung orthopair fuzzy graphs”, Symmetry 11(4): 588, (2019).
• [35] Liu, P., Wang, P., “Some q-rung orthopair fuzzy aggregation operators and their applications to multiple attribute decision making”, International Journal of Intelligent Systems, 33(2): 259-280, (2017).
• [36] Gerstenkorn, T., Manko, J., “Correlation of intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 44(1): 39-43, (1991).
• [37] Xu, S., Chen, J., Wu, J., “Cluster algorithm for intuitionistic fuzzy sets”, Information Sciences, 178: 3775-3790, (2008).
• [38] Xu, Z. S., “On correlation measures of intuitionistic fuzzy sets”, In: Corchado, E. et al. (eds.): IDEAL 2006, LNCS 4224, Springer-Verlag Berlin Heidelberg, 16-24, (2006).
• [39] Xu, Z. S., Cai, X. Q., “Correlation, distance and similarity measures of intuitionistic fuzzy sets”, In: Intuitionistic Fuzzy Information Aggregation, Springer, Berlin, Heidelberg, 151-188, (2012).
• [40] Huang, H. L., Guo, Y., “An improved correlation coefficient of intuitionistic fuzzy sets”, Journal of Intelligent Systems, 28(2): 231-243, (2019).
• [41] Hung, W. L., “Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets”, International Journal of Uncertain, Fuzziness and Knowledge-Based Systems, 9(4): 509-516, (2001).
• [42] Park, J. H., Lim, K. M., Park, J. S., Kwun, Y. C., “Correlation coefficient between intuitionistic fuzzy sets”, In: Cao B, Li TF, Zhang CY (Eds.): Fuzzy Information and Engineering Volume 2, AISC 62, Springer, Berlin, Heidelberg, 601–610, (2009).
• [43] Szmidt, E., Kacprzyk, J., “Correlation of intuitionistic fuzzy sets”, In: Hullermeier E, Kruse R, Hoffmann (Eds.): IPMU, LNAI 6178, Springer, Berlin, Heidelberg, 169-177, (2010).
• [44] Liu, B., Shen, Y., Mu, L., Chen, X., Chen, L., “A new correlation measure of the intuitionistic fuzzy sets”, Journal of Intelligent and Fuzzy Systems, 30(2): 1019-1028, (2016).
• [45] Thao, N. X., “A new correlation coefficient of the intuitionistic fuzzy sets and its application”, Journal of Intelligent and Fuzzy Systems, 35(2): 1959-1968, (2018).
• [46] Ejegwa, P. A., Onyeke, I. C., “Intuitionistic fuzzy statistical correlation algorithm with applications to multi-criteria based decision-making processes”, International Journal of Intelligent Systems, 36(3): 1386-1407, (2021).
• [47] Garg, H., “A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision‐making processes”, International Journal of Intelligent Systems, 31(12): 1234-1252, (2016).
• [48] Thao, N. X., “A new correlation coefficient of the Pythagorean fuzzy sets and its applications”, Soft Computing, 24: 9467-9478, (2020).
• [49] Lin, M., Huang, C., Chen, R., Fujita, H., Wang, X., “Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis”, Complex Intelligent Systems, 7: 1025-1043, (2021).
• [50] Singh, S., Ganie, A. H., “On some correlation coefficients in Pythagorean fuzzy environment with applications”, International Journal of Intelligent Systems, 35: 682-717, (2020).
• [51] Ejegwa, P. A., Wen, S., Feng, Y., Zhang, W., Tang, N., “Novel Pythagorean fuzzy correlation measures via Pythagorean fuzzy deviation, variance and covariance with applications to pattern recognition and career placement”, IEEE Transaction on Fuzzy Systems, 30(6): 1660-1668, (2021).
• [52] 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”, Journal of Intelligent Fuzzy Systems, 40(5): 9873-9886, (2021).
• [53] Ejegwa, P. A., Feng, Y., Zhang, W., “Pattern recognition based on an improved Szmidt and Kacprzyk’s correlation coefficient in Pythagorean fuzzy environment”, In: Min, H., Sitian, Q., Nian, Z. (Eds.); Advances in Neural Networks, Lecture Notes in Computer Science (LNCS) 12557, Springer Nature, Switzerland, 190-206, (2020).
• [54] Du, W. S., “Correlation and correlation coefficient of generalized orthopair fuzzy sets”, International Journal of Intelligent Systems, 34(4): 564-583, (2019).
• [55] Li, H., Yang, Y., Yin, S., “Two λ-correlation coefficients of q-rung orthopair fuzzy sets and their application to clustering analysis”, Journal of Intelligent and Fuzzy Systems, 39(1): 581-591, (2020).
• [56] Singh, S., Ganie, A. H., “Some novel q-rung orthopair fuzzy correlation coefficients based on the statistical viewpoint with their applications”, Journal of Ambient of Intelligence and Humanized Computing, 13: 2227-2252, (2022).
• [57] Bashir, H., Inayatullah, S., Alsanad, A., Anjum, R., Mosleh, M., Ashraf, P., “Some improved correlation coefficients for q-rung orthopair fuzzy sets and their applications in cluster analysis”, Mathematical Problems in Engineering, Article ID 4745068, 11, (2021).
• [58] Ejegwa, P. A., Davvaz, B., “An improved composite relation and its application in deciding patients’ medical status based on a q-rung orthopair fuzzy information”, Computational and Applied Mathematics, 41: 303, (2022).
• [59] Ejegwa, P. A., “Decision-making on patients’ medical status based on a q-rung orthopair fuzzy max-min-max composite relation”, In: Garg, H. (eds) q-Rung Orthopair Fuzzy Sets: Theory and Applications, Springer, 47-66, (2022).
• [60] Utku, A., Akcayol, M. A., “Hybrid deep learning model for earthquake time prediction”, Gazi University Journal of Science, 37(3): 1172-1188, (2024).
• [61] Berkol, A., Tümer Sivri, T., Erdem, H., “Lip reading using various deep learning models with visual Turkish data”, Gazi University Journal of Science, 37(3): 1190-1203, (2024).
• [62] Kocaoğlu, B., Bulut, M., “Circular supply chain network design for e-commerce”, Gazi University Journal of Science, 37(2): 840-852, (2024).
• [63] Petchımuthu, S., Kamacı, H., “Exponential function-based similarity measures for q-rung linear diophantine fuzzy sets and their application to clustering problem”, Gazi University Journal of Science, 37(1): 415-425, (2024).