# A MAGDM ALGORITHM FOR DECISION-MAKING PROBLEMS ON FUZZY SOFT SETS USING A COEFFICIENT CORRELATION AND AN ENTROPY MEASURE FOR DETERMINING THE WEIGHT OF PARAMETERS

• Latifa Khairunnisa Department of Mathematics, Faculty of Mathematics and Natural Science, Andalas University, Indonesia
• Admi Nazra Department of Mathematics, Faculty of Mathematics and Natural Science, Andalas University, Indonesia
• Izzati Rahmi HG Department of Mathematics, Faculty of Mathematics and Natural Science, Andalas University, Indonesia
Keywords: correlation coefficient, Fuzzy soft set, MAGDM, Entropy measure

### Abstract

In statistics, the correlation coefficient concept aims to show how strong the linear relationship between two variables is. Sometimes the data collected relates to everyday life problems whose value is uncertain. Therefore, the concept of correlation coefficient must be developed on the fuzzy sets and the fuzzy soft sets environment. In this study, a decision-making algorithm was designed on fuzzy soft sets using the concept of the correlation coefficient. The method used is MAGDM, where the parameter weights are determined using entropy measures. Using this method, the algorithm of our decision-making problem is more realistic and general. The final section gives an example of a decision-making problem and a numerical illustration using the designed algorithm.

### References

L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, Jun. 1965, doi: 10.1016/S0019-9958(65)90241-X.

D. Molodtsov, “Soft set theory—First results,” Computers & Mathematics with Applications, vol. 37, no. 4–5, pp. 19–31, Feb. 1999, doi: 10.1016/S0898-1221(99)00056-5.

A. R. Roy and P. K. Maji, “A fuzzy soft set theoretic approach to decision making problems,” J Comput Appl Math, vol. 203, no. 2, pp. 412–418, Jun. 2007, doi: 10.1016/j.cam.2006.04.008.

Q. Zhang, J. Liu, J. Hu, Z. Yao, and J. Yang, “New correlation coefficients of Pythagorean fuzzy set and its application to extended TODIM method,” Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 509–523, Jun. 2022, doi: 10.3233/JIFS-212323.

Q. Zhang, J. Liu, J. Hu, Z. Yao, and J. Yang, “New correlation coefficients of Pythagorean fuzzy set and its application to extended TODIM method,” Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 509–523, Jun. 2022, doi: 10.3233/JIFS-212323.

W. Ali et al., “A New Correlation Coefficient for T -Spherical Fuzzy Sets and Its Application in Multicriteria Decision-Making and Pattern Recognition,” J Sens, vol. 2022, pp. 1–11, Jul. 2022, doi: 10.1155/2022/4471945.

M. KİRİSCİ, “Correlation Coefficients of Fermatean Fuzzy Sets with a Medical Application,” Journal of Mathematical Sciences and Modelling, pp. 16–23, Apr. 2021, doi: 10.33187/jmsm.1039613.

X. Liu, Z. Tao, Q. Liu, and L. Zhou, “Correlation Coefficient of Probabilistic Hesitant Fuzzy Soft Set and Its Applications in Decision Making,” in 2021 3rd International Conference on Industrial Artificial Intelligence (IAI), Nov. 2021, pp. 1–6. doi: 10.1109/IAI53119.2021.9619297.

S. Das, D. Malakar, S. Kar, and T. Pal, “Correlation measure of hesitant fuzzy soft sets and their application in decision making,” Neural Comput Appl, vol. 31, no. 4, pp. 1023–1039, Apr. 2019, doi: 10.1007/s00521-017-3135-0.

S. Singh and S. Lalotra, “Generalized correlation coefficients of the hesitant fuzzy sets and the hesitant fuzzy soft sets with application in group decision-making,” Journal of Intelligent & Fuzzy Systems, vol. 35, no. 3, pp. 3821–3833, Oct. 2018, doi: 10.3233/JIFS-18719.

D. Malakar, S. Gope, and S. Das, “Correlation Measure of Hesitant Fuzzy Linguistic Term Soft Set and Its Application in Decision Making,” 2016, pp. 413–423. doi: 10.1007/978-81-322-2695-6_35.

P. Singh, “Correlation coefficients for picture fuzzy sets,” Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 591–604, 2015, doi: 10.3233/IFS-141338.

B. Farhadinia, “Correlation for Dual Hesitant Fuzzy Sets and Dual Interval-Valued Hesitant Fuzzy Sets,” International Journal of Intelligent Systems, vol. 29, no. 2, pp. 184–205, Feb. 2014, doi: 10.1002/int.21633.

N. Chen, Z. Xu, and M. Xia, “Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis,” Appl Math Model, vol. 37, no. 4, pp. 2197–2211, Feb. 2013, doi: 10.1016/j.apm.2012.04.031.

J. Ye, “Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making,” Appl Math Model, vol. 38, no. 2, pp. 659–666, Jan. 2014, doi: 10.1016/j.apm.2013.07.010.

H. Liao, Z. Xu, X.-J. Zeng, and J. M. Merigó, “Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets,” Knowl Based Syst, vol. 76, pp. 127–138, Mar. 2015, doi: 10.1016/j.knosys.2014.12.009.

F. Meng and X. Chen, “Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures,” Cognit Comput, vol. 7, no. 4, pp. 445–463, Aug. 2015, doi: 10.1007/s12559-014-9313-9.

H. Liao, Z. Xu, and X.-J. Zeng, “Novel correlation coefficients between hesitant fuzzy sets and their application in decision making,” Knowl Based Syst, vol. 82, pp. 115–127, Jul. 2015, doi: 10.1016/j.knosys.2015.02.020.

P. Singh, “Correlation coefficients for picture fuzzy sets,” Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 591–604, 2015, doi: 10.3233/IFS-141338.

S. Singh and A. H. Ganie, “On a new picture fuzzy correlation coefficient with its applications to pattern recognition and identification of an investment sector,” Computational and Applied Mathematics, vol. 41, no. 1, p. 8, Feb. 2022, doi: 10.1007/s40314-021-01699-w.

S. Singh and A. H. Ganie, “Applications of a picture fuzzy correlation coefficient in pattern analysis and decision-making,” Granular Computing, vol. 7, no. 2, pp. 353–367, Apr. 2022, doi: 10.1007/s41066-021-00269-z.

P. A. Ejegwa and I. C. Onyeke, “Intuitionistic fuzzy statistical correlation algorithm with applications to multicriteria‐based decision‐making processes,” International Journal of Intelligent Systems, vol. 36, no. 3, pp. 1386–1407, Mar. 2021, doi: 10.1002/int.22347.

S. Sharma and S. Singh, “On some generalized correlation coefficients of the fuzzy sets and fuzzy soft sets with application in cleanliness ranking of public health centres,” Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3671–3683, Apr. 2019, doi: 10.3233/JIFS-181838.

A. De Luca and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory,” Information and Control, vol. 20, no. 4, pp. 301–312, May 1972, doi: 10.1016/S0019-9958(72)90199-4.

R. R. YAGER, “ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval,” Int J Gen Syst, vol. 5, no. 4, pp. 221–229, Jan. 1979, doi: 10.1080/03081077908547452.

Published
2023-09-30
How to Cite

L. Khairunnisa, A. Nazra, and I. HG, “A MAGDM ALGORITHM FOR DECISION-MAKING PROBLEMS ON FUZZY SOFT SETS USING A COEFFICIENT CORRELATION AND AN ENTROPY MEASURE FOR DETERMINING THE WEIGHT OF PARAMETERS”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1503-1512, Sep. 2023.
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Articles