Correlation Measures for q-rung Orthopair m-polar Fuzzy Sets with Application to Pattern Recognition

Tahir Hamid Ch; Muhammad Abid; Khalid Naeem; Rana Muhammad Zulqarnain

doi:10.31181/dma31202560

Authors

Tahir Hamid Ch Department of Mathematics, Garrison Postgraduate College, Lahore Cantt., 58810, Lahore, Pakistan https://orcid.org/0000-0002-4547-1506
Muhammad Abid Department of Mathematics, North Carolina State University, 27695 NC Raleigh, USA https://orcid.org/0009-0006-8619-6666
Khalid Naeem Department of Mathematics, Federal Government Degree College for Men, 50070, Kharian Cantt., Pakistan https://orcid.org/0000-0003-4614-5689
Rana Muhammad Zulqarnain Department of Mathematics, Saveetha School of Engineering, SIMATS Thandalam, Chennai, 602105 Tamilnadu, India https://orcid.org/0000-0002-2656-8679

DOI:

https://doi.org/10.31181/dma31202560

Keywords:

Correlation and Weighted Correlation Measures, Pattern Recognition, Optimization and Decision Making, q-Rung Orthopair m-Polar Fuzzy Set

Abstract

Correlation provides a relationship between two quantities with the help of certain statistical data. It shows the strength of the relationship amongst different alternatives. q-rung orthopair fuzzy setting offers extended space for the selection of values of the two components. There is no iota in the fact that the multipolarity factor reduces the chances of error. We study correlation in the framework of q-rung orthopair m-polar fuzzy set to judge the efficiency of this system in real-life problems and decision-making. We present some major characteristics of the correlation measure in the said setting. An application to pattern recognition is also incorporated. To elaborate on the ideas of correlation measures and q-rung orthopair m-polar fuzzy set, we instigate a comparison analysis to probe the supremacy and dominance of propound abstraction.

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References

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1), 3-28.

Feng, F., Zheng, Y., Sun, B., & Akram, M. (2022). Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making. Granular Computing, 7(1), 95-111.

Akram, M., Ali, G., & Shabir, M. (2021). A hybrid decision-making framework using rough m F bipolar soft environment. Granular Computing, 6, 539-555.

Arya, V., & Kumar, S. (2021). Knowledge measure and entropy: a complementary concept in fuzzy theory. Granular Computing, 6(3), 631-643.

Atanassov, K. T. (1999). Intuitionistic fuzzy sets (pp. 1-137). Physica-Verlag HD.

Atanassov K. T., & Stoeva, S. (1983). Intuitionistic fuzzy sets. In Polish Symposium on Interval & Fuzzy Mathematics, Poznan.

Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE.

Farhadinia, B., Effati, S., & Chiclana, F. (2021). A family of similarity measures for q‐rung orthopair fuzzy sets and their applications to multiple criteria decision making. International Journal of Intelligent Systems, 36(4), 1535-1559.

Peng, X., Yuan, H., & Yang, Y. (2017). Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems, 32(10), 991-1029.

Garg, H., & Chen, S. M. (2020). Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets. Information Sciences, 517, 427-447.

Gupta, R., & Kumar, S. (2022). A new similarity measure between picture fuzzy sets with applications to pattern recognition and clustering problems. Granular Computing, 7(3), 561-576.

Kadian, R., & Kumar, S. (2022). New fuzzy mean codeword length and similarity measure. Granular Computing, 7(3), 461-478.

Liu, S., Wang, B., & Liu, J. (2020). Group decision making under social influences based on information entropy. Granular Computing, 5, 303-308.

Naeem, K., Riaz, M., & Afzal, D. (2019). Pythagorean m-polar fuzzy sets and TOPSIS method for the selection of advertisement mode. Journal of Intelligent & Fuzzy Systems, 37(6), 8441-8458.

Zhang, S., Hou, Y., Zhang, S., & Zhang, M. (2017). Fuzzy control model and simulation for nonlinear supply chain system with lead times. Complexity, 2017(1), 2017634.

Haq, H. B. U., Akram, W., Irshad, M. N., Kosar, A., & Abid, M. (2024). Enhanced real-time facial expression recognition using deep learning. Acadlore Transactions on AI and Machine Learning, 3(1), 24-35.

Naeem, K., & Divvaz, B. (2023). Information measures for MADM under m-polar neutrosophic environment. Granular Computing, 8(3), 597-616.

Kumam, W., Naeem, K., Riaz, M., Khan, M. J., & Kumam, P. (2023). Comparison measures for Pythagorean m-polar fuzzy sets and their applications to robotics and movie recommender system. Applied Mathematics for Modern Challenges, 8(5).

Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE transactions on fuzzy systems, 25(5), 1222-1230.

Rani, P., Jain, D., & Hooda, D. S. (2019). Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on shapley weighted divergence measure. Granular Computing, 4, 407-420.

Riaz, M., Naeem, K., & Afzal, D. (2020). A similarity measure under pythagorean fuzzy soft environment with applications. Computational and Applied Mathematics, 39(4), 269.

Singh, S., & Ganie, A. H. (2020). On some correlation coefficients in Pythagorean fuzzy environment with applications. International Journal of Intelligent Systems, 35(4), 682-717.

Singh, S., & Ganie, A. H. (2022). Generalized hesitant fuzzy knowledge measure with its application to multi-criteria decision-making. Granular Computing, 7(2), 239-252.

Riaz, M., Garg, H., Hamid, M. T., & Afzal, D. (2022). Modelling uncertainties with TOPSIS and GRA based on q‐rung orthopair m‐polar fuzzy soft information in COVID‐19. Expert Systems, 39(5), e12940.

Abid, M., & Shahid, M. (2024). Tumor Detection in MRI Data using Deep Learning Techniques for Image Classification and Semantic Segmentation. Sustainable Machine Intelligence Journal, 9, 1-13.

Hamid, M. T., Riaz, M., & Naeem, K. (2022). q-Rung orthopair fuzzy soft topology with multi-attribute decision-making. In q-Rung Orthopair Fuzzy Sets: Theory and Applications (pp. 17-46). Singapore: Springer Nature Singapore.

Riaz, M., Hamid, M. T., Afzal, D., Pamucar, D., & Chu, Y. M. (2021). Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets. PLoS one, 16(2), e0246485.

Hamid, M. T., Riaz, M., & Naeem, K. (2022). A study on weighted aggregation operators for q‐rung orthopair m‐polar fuzzy set with utility to multistage decision analysis. International Journal of Intelligent Systems, 37(9), 6354-6387.

Mitchell, H. (2004). A correlation coefficient for intuitionistic fuzzy sets. International journal of intelligent systems, 19(5), 483-490.

Meharunnisa, M. S., Abid, M., Awais, M., & Stevic, Z. (2023). Analysis of software effort estimation by machine learning techniques. Ingénierie des Systèmes d’Information, 28(6), 1445-1457.

Zhang, S., Zhang, P., & Zhang, M. (2019). Fuzzy emergency model and robust emergency strategy of supply chain system under random supply disruptions. Complexity, 2019(1), 3092514.

Ejegwa, P. A., Onyeke, I. C., & Adah, V. (2020). An algorithm for an improved intuitionistic fuzzy correlation measure with medical diagnostic application. Annals of Optimization Theory and Practice, 3(3), 51-66.

Lin, M., Huang, C., Chen, R., Fujita, H., & Wang, X. (2021). Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis. Complex & Intelligent Systems, 7, 1025-1043.

Thao, N. X. (2020). A new correlation coefficient of the Pythagorean fuzzy sets and its applications. Soft Computing, 24(13), 9467-9478.

Mahmood, T., & Ali, Z. (2021). Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making. Soft Computing, 25, 1249-1275.

Sarwar, M., & Li, T. (2019). Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces. Hacettepe Journal of Mathematics and Statistics, 48(6), 1712-1728.

Zulqarnain, R. M., Siddique, I., Jarad, F., Ali, R., & Abdeljawad, T. (2021). Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID‐19 Pandemic. Complexity, 2021(1), 6634991.

Abid, M., & Saqlain, M. (2023). Utilizing edge cloud computing and deep learning for enhanced risk assessment in China’s international trade and investment. International Journal of Knowledge and Innovation Studies, 1(1), 1-9.

Peng, X., & Liu, L. (2019). Information measures for q‐rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(8), 1795-1834.

Xia, Y., Wang, J., Meng, B., & Chen, X. (2020). Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems. Applied Mathematics and Computation, 379, 125225.

Garg, H., & Arora, R. (2020). TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information. AIMS mathematics, 5(4), 2944-2966.

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.

Ejegwa, P. A., Adah, V., & Onyeke, I. C. (2022). Some modified Pythagorean fuzzy correlation measures with application in determining some selected decision-making problems. Granular Computing, 7(2), 381-391.

Abid, M., & Saqlain, M. (2023). Decision-making for the bakery product transportation using linear programming. Spectrum of Engineering and Management Sciences, 1(1), 1-12.

Khan, M. J., Alcantud, J. C. R., Kumam, P., Kumam, W., & Al‐Kenani, A. N. (2021). An axiomatically supported divergence measures for q‐rung orthopair fuzzy sets. International Journal of Intelligent Systems, 36(10), 6133-6155.

Alahmadi, R. A., Ganie, A. H., Al-Qudah, Y., Khalaf, M. M., & Ganie, A. H. (2023). Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure. Granular Computing, 8(6), 1385-1405.

Li, H., Yang, Y., & Yin, S. (2020). Two λ-correlation coefficients of q-rung orthopair fuzzy sets and their application to clustering analysis. Journal of Intelligent & Fuzzy Systems, 39(1), 581-591.

Zhang, S., & Zhang, M. (2020). Mitigation of Bullwhip Effect in Closed‐Loop Supply Chain Based on Fuzzy Robust Control Approach. Complexity, 2020(1), 1085870.

Ejegwa, P. A., Onyeke, I. C., & Adah, V. (2020). An algorithm for an improved intuitionistic fuzzy correlation measure with medical diagnostic application. Annals of Optimization Theory and Practice, 3(3), 51-66.

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.

Hung, W. L., & Wu, J. W. (2002). Correlation of intuitionistic fuzzy sets by centroid method. Information sciences, 144(1-4), 219-225.

Ge, J., & Zhang, S. (2020). Adaptive inventory control based on fuzzy neural network under uncertain environment. Complexity, 2020(1), 6190936.

Young, G. O. (1964). Synthetic structure of industrial plastics. In Plastics, 2nd edition, pp. 15-64. New York: McGraw-Hill.

Zhang, N., Qi, W., Pang, G., Cheng, J., & Shi, K. (2022). Observer-based sliding mode control for fuzzy stochastic switching systems with deception attacks. Applied Mathematics and Computation, 427, 127153.

Khan, M. J., Alcantud, J. C. R., Kumam, P., Kumam, W., & Al‐Kenani, A. N. (2021). An axiomatically supported divergence measures for q‐rung orthopair fuzzy sets. International Journal of Intelligent Systems, 36(10), 6133-6155.

Lin, M., Huang, C., Chen, R., Fujita, H., & Wang, X. (2021). Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis. Complex & Intelligent Systems, 7, 1025-1043.

Naeem, K., Riaz, M., & Afzal, D. (2019). Pythagorean m-polar fuzzy sets and TOPSIS method for the selection of advertisement mode. Journal of Intelligent & Fuzzy Systems, 37(6), 8441-8458.

Riaz, M., Naeem, K., & Afzal, D. (2020). A similarity measure under pythagorean fuzzy soft environment with applications. Computational and Applied Mathematics, 39(4), 269.

Hamid, M. T. & Abid, M (2024). Decision Support System for Mobile Phone Selection Utilizing Fuzzy Hypersoft Sets and Machine Learning. Journal of Intelligent Management Decision, 3(2), 104-115.

Abid, M., & Shahid, M. (2024). Data-driven evaluation of background radiation safety using machine learning and statistical analysis. Big Data and Computing Visions, 4(2), 110-134.

Szmidt, E., & Kacprzyk, J. (2010). Correlation of intuitionistic fuzzy sets. In International conference on information processing and management of uncertainty in knowledge-based systems (pp. 169-177). Berlin, Heidelberg: Springer Berlin Heidelberg.

Duan, Z. X., Liang, J. L., & Xiang, Z. R. (2022). H∞ control for continuous-discrete systems in TS fuzzy model with finite frequency specifications. Discrete and Continuous Dynamical Systems, 64(1), 1-18.

Thao, N. X. (2020). A new correlation coefficient of the Pythagorean fuzzy sets and its applications. Soft Computing, 24(13), 9467-9478.

Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE.

Zhang, S., Li, S., Zhang, S., & Zhang, M. (2017). Decision of Lead‐Time Compression and Stable Operation of Supply Chain. Complexity, 2017(1), 7436764.

Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230.

Joshi, R. (2022). Multi-criteria decision-making based on bi-parametric exponential fuzzy information measures and weighted correlation coefficients. Granular Computing, 7, 49-62.

Diao, Y., & Zhang, Q. (2021). Optimization of Management Mode of Small‐and Medium‐Sized Enterprises Based on Decision Tree Model. Journal of Mathematics, 2021(1), 2815086.

Riaz, M., Naeem, K., & Afzal, D. (2020). Pythagorean m-polar fuzzy soft sets with TOPSIS method for MCGDM. Punjab University Journal of Mathematics, 52(3), 21-46.

Gao, M., Zhang, L., Qi, W., Cao, J., Cheng, J., Kao, Y., et al. (2020). SMC for semi-Markov jump TS fuzzy systems with time delay. Applied Mathematics and Computation, 374, 125001.

Gerstenkorn, T., & Mańko, J. (1991). Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems, 44(1), 39-43.

Huang, B., Miao, J., & Li, Q. (2022). A Vetoed Multi-objective Grey Target Decision Model with Application in Supplier Choice. Journal of Grey System, 34(4), 15-27.