Research Article
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Year 2024, , 393 - 413, 01.03.2024
https://doi.org/10.35378/gujs.937205

Abstract

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(1): 87-96, (1986).
  • [3] Yager, R. R., “Pythagorean fuzzy subsets”, Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 57-61, (2013).
  • [4] Cuong, B. C., “Picture fuzzy sets,” Journal of Computer Science and Cybernetics, 30(4): 409-42. (2014).
  • [5] Kahraman, C., Kutlu Gündoğdu, F., “From 1D to 3D membership: spherical fuzzy sets”, BOS/SOR 2018, Polish Operational and Systems Research Society, September 24-26, 2018, Palais Staszic, Warsaw, Poland.
  • [6] Mahmood, T., Kifayat, U., Khan, Q., Jan, N., “An approach toward decision making and medical diagnosis problems using the concept of spherical fuzzy sets”, Neural Computing and Applications, 31: 7041-7053, (2018).
  • [7] Haque, T. S., Chakraborty, A., Mondal, S. P., Alam, S., “Approach to solve multi-criteria group decision-making problems by exponential operational law in generalized spherical fuzzy environment”, CAAI Transactions on Intelligence Technology, 5(2): 106-114, (2020).
  • [8] Harsanyi, J. C., “Cardinal welfare, individualistic ethics and interpersonal comparisons of utility”, Journal of Political Economy, 63: 309-321, (1955).
  • [9] Yager, R. R., “On ordered weighted averaging aggregation operators in multi-criteria decision making”, IEEE Transactions on Systems, Man and Cybernetics, 18: 183-19. (1988).
  • [10] Xu, Z., “Intuitionistic fuzzy aggregation operators”, IEEE Transactions on Fuzzy Systems, 15: 1179-1187, (2007).
  • [11] Wang, W., Liu, X., “Intuitionistic fuzzy information aggregation using Einstein operations”, IEEE Transactions on Fuzzy Systems, 20(5): 923-938, (2012).
  • [12] Yager, R. R., “Pythagorean membership grades in multicriteria decision making”, IEEE Transactions on Fuzzy Systems, 22(4): 958-965, (2013).
  • [13] 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): 886-92. (2016).
  • [14] Wei, G., “Picture fuzzy aggregation operators and their application to multiple attribute decision making”, Journal of Intelligent and Fuzzy Systems, 33(2): 713-724, (2017).
  • [15] Khan, S., Abdullah, S., Ashraf, S., “Picture fuzzy aggregation information based on Einstein operations and their application in decision making”, Mathematical Sciences, 13(3): 213-229, (2019).
  • [16] Munir, M., Kalsoom, H., Ullah, K., Mahmood, T., Chu, Y. M., “T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems”, Symmetry, 12(3): 365, (2020).
  • [17] Güner, E., Aygün, H., “Generalized spherical fuzzy Einstein aggregation operators: Application to multi-criteria group decision-making problems”, Conference Proceedings of Science and Technology, 3(2): 227-235, (2020).
  • [18] Güner, E., Aygün, H., “Generalized spherical fuzzy Hamacher aggregation operators”, 1st International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences (ISCDFAMS -2022), Erzurum, Turkey, 2022.
  • [19] Güner, E., Aygün, H., “An extension of TOPSIS method to the generalized spherical fuzzy environment”, 6th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Turkey, 2022.
  • [20] Güner, E., Aygün, H., "Generalized spherical fuzzy topological spaces with their applications to the multi-criteria decision-making problems", 6th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Turkey, 2022.
  • [21] Haque, T. S., Alam, S., Chakraborty, A., “Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment”, Computational and Applied Mathematics, 41(2): 1-23, (2022).
  • [22] Molodtsov, D., “Soft set theory-first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
  • [23] Maji, K., Biswas, R., Roy, A. R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9: 589–602, (2001).
  • [24] Maji, P. K., Roy, A. R., Biswas, R., “On intuitionistic fuzzy soft sets”, The Journal of Fuzzy Mathematics, 12(3): 669-683, (2004).
  • [25] Peng, X., Yang, Y., Song, J., Jiang, Y., “Pythagorean fuzzy soft set and its application”, Computer Engineering, 41: 224-229, (2015).
  • [26] Khan, M. J., Kumam, P., Ashraf, S., Kumam, W., “Generalized picture fuzzy soft sets and their application in decision support systems”, Symmetry, 11(3): 415, (2019).
  • [27] Güner, E., Aygün, H., “Spherical fuzzy soft sets: Theory and aggregation operator with its applications”, Iranian Journal of Fuzzy Systems, 19(2): 83-97, (2022).
  • [28] Guleria, A., Bajaj, R. K., “T-spherical fuzzy soft sets and its aggregation operators with application in decision making”, Scientia Iranica, 28(2): 1014-1029, (2021).
  • [29] Ramot, D., Milo, R., Friedman, M., Kandel, A., “Complex fuzzy sets”, IEEE Transactions on Fuzzy Systems, 10(2): 171-186, (2002).
  • [30] Alkouri, A. M. D. J. S., Salleh, A. R., “Complex intuitionistic fuzzy sets”, AIP Conference Proceedings, 1482(1): 464-47. (2012).
  • [31] Ullah, K., Mahmood, T., Ali, Z., Jan, N., “On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition”, Complex & Intelligent Systems, 6(1): 15-27, (2020).
  • [32] Akram, M., Bashir, A., Garg, H., “Decision-making model under complex picture fuzzy Hamacher aggregation operators”, Computational and Applied Mathematics, 39(3): 1-38, (2020).
  • [33] Akram, M., Kahraman, C., Zahid, K., “Group decision-making based on complex spherical fuzzy VIKOR approach”, Knowledge-Based Systems, 216: 106793, (2021).
  • [34] Ali, Z., Mahmood, T., Yang, M. S., “Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry, 12(8): 1311, (2020).
  • [35] Kumar, T., Bajaj, R. K., “On complex intuitionistic fuzzy soft sets with distance measures and entropies”, Journal of Mathematics, 2014: 1-12, (2014).
  • [36] Akram, M., Wasim, F., Al-Kenani, A. N., “A hybrid decision-making approach under complex Pythagorean fuzzy N-soft sets”, International Journal of Computational Intelligence Systems, 14(1): 1263-1291, (2021).
  • [37] Mahmood, T., Ahmmad, J., “Complex picture fuzzy N-soft sets and their decision-making algorithm”, Soft Computing, 25(21): 13657-13678, (2021).
  • [38] Akram, M., Shabir, M., Al-Kenani, A. N., Alcantud, J. C. R., “Hybrid decision-making frameworks under complex spherical fuzzy N-soft sets”, Journal of Mathematics, 2021: 1-46, (2021).
  • [39] Akram, M., Shabir, M., “Complex T-spherical fuzzy N-soft sets”, International Conference on Intelligent and Fuzzy Systems, Springer, Cham, 819-834, (2021).
  • [40] Akram, M., Shabir, M., Adeel, A., Al-Kenani, A. N., “A multiattribute decision-making framework: VIKOR method with complex spherical fuzzy N-soft sets”, Mathematical Problems in Engineering, 2021: 1-25, (2021).
  • [41] Akram, M., Al-Kenani, A. N., Shabir, M., “Enhancing ELECTRE I method with complex spherical fuzzy information”, International Journal of Computational Intelligence Systems, 14(1): 1-31, (2021).
  • [42] Aydoğdu, E., Güner, E., Aldemir, B., Aygün, H., “Complex spherical fuzzy TOPSIS based on entropy”, Expert Systems with Applications, 215: 119331, (2023).
  • [43] Khan, M. J., Kumam, P., Alreshidi, N. A., Kumam, W., “Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method”, Complex & Intelligent Systems, 7(5): 2679-2696, (2021).
  • [44] Khan, M. J., Ali, M. I., Kumam, P., Kumam, W., Al-Kenani, A. N., “q-Rung orthopair fuzzy modified dissimilarity measure based robust VIKOR method and its applications in mass vaccination campaigns in the context of COVID-19”, IEEE Access, 9: 93497-93515, (2021).
  • [45] Riaz, M., Habib, A., Khan, M. J., Kumam, P., “Correlation coefficients for cubic bipolar fuzzy sets with applications to pattern recognition and clustering analysis”, IEEE Access, 9: 109053-109066, (2021).
  • [46] Khan, M. J., Alcantud, J. C. R., Kumam, P., Kumam, W., Al‐Kenani, A. N., “An axiomatically supported divergence measures for q‐rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 36(10): 6133-6155, (2021).
  • [47] Khan, M. J., Kumam, P., Shutaywi, M., “Knowledge measure for the q‐rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 36(2): 628-655, (2021).

A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators

Year 2024, , 393 - 413, 01.03.2024
https://doi.org/10.35378/gujs.937205

Abstract

Generalized spherical fuzzy set theory is a powerful and useful tool that is capable to process uncertainty and vagueness. In this study, we investigate some induced aggregation operators under the generalized spherical fuzzy environment with the help of Einstein norms operations to merge the generalized spherical fuzzy information into a single one in the decision-making process. After we observe some properties of the presented aggregation operators, we establish an algorithm to use in the solution of the multiple criteria group decision-making problems by using these aggregation operators and also we give an illustrative example. Then, we compare the results under all defined generalized spherical fuzzy Einstein aggregation operators used within the decision-making process.

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(1): 87-96, (1986).
  • [3] Yager, R. R., “Pythagorean fuzzy subsets”, Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 57-61, (2013).
  • [4] Cuong, B. C., “Picture fuzzy sets,” Journal of Computer Science and Cybernetics, 30(4): 409-42. (2014).
  • [5] Kahraman, C., Kutlu Gündoğdu, F., “From 1D to 3D membership: spherical fuzzy sets”, BOS/SOR 2018, Polish Operational and Systems Research Society, September 24-26, 2018, Palais Staszic, Warsaw, Poland.
  • [6] Mahmood, T., Kifayat, U., Khan, Q., Jan, N., “An approach toward decision making and medical diagnosis problems using the concept of spherical fuzzy sets”, Neural Computing and Applications, 31: 7041-7053, (2018).
  • [7] Haque, T. S., Chakraborty, A., Mondal, S. P., Alam, S., “Approach to solve multi-criteria group decision-making problems by exponential operational law in generalized spherical fuzzy environment”, CAAI Transactions on Intelligence Technology, 5(2): 106-114, (2020).
  • [8] Harsanyi, J. C., “Cardinal welfare, individualistic ethics and interpersonal comparisons of utility”, Journal of Political Economy, 63: 309-321, (1955).
  • [9] Yager, R. R., “On ordered weighted averaging aggregation operators in multi-criteria decision making”, IEEE Transactions on Systems, Man and Cybernetics, 18: 183-19. (1988).
  • [10] Xu, Z., “Intuitionistic fuzzy aggregation operators”, IEEE Transactions on Fuzzy Systems, 15: 1179-1187, (2007).
  • [11] Wang, W., Liu, X., “Intuitionistic fuzzy information aggregation using Einstein operations”, IEEE Transactions on Fuzzy Systems, 20(5): 923-938, (2012).
  • [12] Yager, R. R., “Pythagorean membership grades in multicriteria decision making”, IEEE Transactions on Fuzzy Systems, 22(4): 958-965, (2013).
  • [13] 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): 886-92. (2016).
  • [14] Wei, G., “Picture fuzzy aggregation operators and their application to multiple attribute decision making”, Journal of Intelligent and Fuzzy Systems, 33(2): 713-724, (2017).
  • [15] Khan, S., Abdullah, S., Ashraf, S., “Picture fuzzy aggregation information based on Einstein operations and their application in decision making”, Mathematical Sciences, 13(3): 213-229, (2019).
  • [16] Munir, M., Kalsoom, H., Ullah, K., Mahmood, T., Chu, Y. M., “T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems”, Symmetry, 12(3): 365, (2020).
  • [17] Güner, E., Aygün, H., “Generalized spherical fuzzy Einstein aggregation operators: Application to multi-criteria group decision-making problems”, Conference Proceedings of Science and Technology, 3(2): 227-235, (2020).
  • [18] Güner, E., Aygün, H., “Generalized spherical fuzzy Hamacher aggregation operators”, 1st International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences (ISCDFAMS -2022), Erzurum, Turkey, 2022.
  • [19] Güner, E., Aygün, H., “An extension of TOPSIS method to the generalized spherical fuzzy environment”, 6th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Turkey, 2022.
  • [20] Güner, E., Aygün, H., "Generalized spherical fuzzy topological spaces with their applications to the multi-criteria decision-making problems", 6th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Turkey, 2022.
  • [21] Haque, T. S., Alam, S., Chakraborty, A., “Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment”, Computational and Applied Mathematics, 41(2): 1-23, (2022).
  • [22] Molodtsov, D., “Soft set theory-first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
  • [23] Maji, K., Biswas, R., Roy, A. R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9: 589–602, (2001).
  • [24] Maji, P. K., Roy, A. R., Biswas, R., “On intuitionistic fuzzy soft sets”, The Journal of Fuzzy Mathematics, 12(3): 669-683, (2004).
  • [25] Peng, X., Yang, Y., Song, J., Jiang, Y., “Pythagorean fuzzy soft set and its application”, Computer Engineering, 41: 224-229, (2015).
  • [26] Khan, M. J., Kumam, P., Ashraf, S., Kumam, W., “Generalized picture fuzzy soft sets and their application in decision support systems”, Symmetry, 11(3): 415, (2019).
  • [27] Güner, E., Aygün, H., “Spherical fuzzy soft sets: Theory and aggregation operator with its applications”, Iranian Journal of Fuzzy Systems, 19(2): 83-97, (2022).
  • [28] Guleria, A., Bajaj, R. K., “T-spherical fuzzy soft sets and its aggregation operators with application in decision making”, Scientia Iranica, 28(2): 1014-1029, (2021).
  • [29] Ramot, D., Milo, R., Friedman, M., Kandel, A., “Complex fuzzy sets”, IEEE Transactions on Fuzzy Systems, 10(2): 171-186, (2002).
  • [30] Alkouri, A. M. D. J. S., Salleh, A. R., “Complex intuitionistic fuzzy sets”, AIP Conference Proceedings, 1482(1): 464-47. (2012).
  • [31] Ullah, K., Mahmood, T., Ali, Z., Jan, N., “On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition”, Complex & Intelligent Systems, 6(1): 15-27, (2020).
  • [32] Akram, M., Bashir, A., Garg, H., “Decision-making model under complex picture fuzzy Hamacher aggregation operators”, Computational and Applied Mathematics, 39(3): 1-38, (2020).
  • [33] Akram, M., Kahraman, C., Zahid, K., “Group decision-making based on complex spherical fuzzy VIKOR approach”, Knowledge-Based Systems, 216: 106793, (2021).
  • [34] Ali, Z., Mahmood, T., Yang, M. S., “Complex T-spherical fuzzy aggregation operators with application to multi-attribute decision making. Symmetry, 12(8): 1311, (2020).
  • [35] Kumar, T., Bajaj, R. K., “On complex intuitionistic fuzzy soft sets with distance measures and entropies”, Journal of Mathematics, 2014: 1-12, (2014).
  • [36] Akram, M., Wasim, F., Al-Kenani, A. N., “A hybrid decision-making approach under complex Pythagorean fuzzy N-soft sets”, International Journal of Computational Intelligence Systems, 14(1): 1263-1291, (2021).
  • [37] Mahmood, T., Ahmmad, J., “Complex picture fuzzy N-soft sets and their decision-making algorithm”, Soft Computing, 25(21): 13657-13678, (2021).
  • [38] Akram, M., Shabir, M., Al-Kenani, A. N., Alcantud, J. C. R., “Hybrid decision-making frameworks under complex spherical fuzzy N-soft sets”, Journal of Mathematics, 2021: 1-46, (2021).
  • [39] Akram, M., Shabir, M., “Complex T-spherical fuzzy N-soft sets”, International Conference on Intelligent and Fuzzy Systems, Springer, Cham, 819-834, (2021).
  • [40] Akram, M., Shabir, M., Adeel, A., Al-Kenani, A. N., “A multiattribute decision-making framework: VIKOR method with complex spherical fuzzy N-soft sets”, Mathematical Problems in Engineering, 2021: 1-25, (2021).
  • [41] Akram, M., Al-Kenani, A. N., Shabir, M., “Enhancing ELECTRE I method with complex spherical fuzzy information”, International Journal of Computational Intelligence Systems, 14(1): 1-31, (2021).
  • [42] Aydoğdu, E., Güner, E., Aldemir, B., Aygün, H., “Complex spherical fuzzy TOPSIS based on entropy”, Expert Systems with Applications, 215: 119331, (2023).
  • [43] Khan, M. J., Kumam, P., Alreshidi, N. A., Kumam, W., “Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method”, Complex & Intelligent Systems, 7(5): 2679-2696, (2021).
  • [44] Khan, M. J., Ali, M. I., Kumam, P., Kumam, W., Al-Kenani, A. N., “q-Rung orthopair fuzzy modified dissimilarity measure based robust VIKOR method and its applications in mass vaccination campaigns in the context of COVID-19”, IEEE Access, 9: 93497-93515, (2021).
  • [45] Riaz, M., Habib, A., Khan, M. J., Kumam, P., “Correlation coefficients for cubic bipolar fuzzy sets with applications to pattern recognition and clustering analysis”, IEEE Access, 9: 109053-109066, (2021).
  • [46] Khan, M. J., Alcantud, J. C. R., Kumam, P., Kumam, W., Al‐Kenani, A. N., “An axiomatically supported divergence measures for q‐rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 36(10): 6133-6155, (2021).
  • [47] Khan, M. J., Kumam, P., Shutaywi, M., “Knowledge measure for the q‐rung orthopair fuzzy sets”, International Journal of Intelligent Systems, 36(2): 628-655, (2021).
There are 47 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Elif Güner 0000-0002-6969-400X

Halis Aygün 0000-0003-3263-3884

Early Pub Date August 23, 2023
Publication Date March 1, 2024
Published in Issue Year 2024

Cite

APA Güner, E., & Aygün, H. (2024). A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators. Gazi University Journal of Science, 37(1), 393-413. https://doi.org/10.35378/gujs.937205
AMA Güner E, Aygün H. A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators. Gazi University Journal of Science. March 2024;37(1):393-413. doi:10.35378/gujs.937205
Chicago Güner, Elif, and Halis Aygün. “A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators”. Gazi University Journal of Science 37, no. 1 (March 2024): 393-413. https://doi.org/10.35378/gujs.937205.
EndNote Güner E, Aygün H (March 1, 2024) A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators. Gazi University Journal of Science 37 1 393–413.
IEEE E. Güner and H. Aygün, “A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators”, Gazi University Journal of Science, vol. 37, no. 1, pp. 393–413, 2024, doi: 10.35378/gujs.937205.
ISNAD Güner, Elif - Aygün, Halis. “A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators”. Gazi University Journal of Science 37/1 (March 2024), 393-413. https://doi.org/10.35378/gujs.937205.
JAMA Güner E, Aygün H. A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators. Gazi University Journal of Science. 2024;37:393–413.
MLA Güner, Elif and Halis Aygün. “A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators”. Gazi University Journal of Science, vol. 37, no. 1, 2024, pp. 393-1, doi:10.35378/gujs.937205.
Vancouver Güner E, Aygün H. A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators. Gazi University Journal of Science. 2024;37(1):393-41.