Pythagorean fuzzy Muirhead mean operators in multiple attribute decision making for evaluating of emerging technology commercialization

References

• Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. doi:10.1016/S0165-0114(86)80034-3
   Web of Science ®Google Scholar
• Atanassov, K. (2000). Two theorems for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 110(2), 267–269. doi:10.1016/S0165-0114(99)00112-8
   Web of Science ®Google Scholar
• Beliakov, G., & James, S. (2014). Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs. FUZZ-IEEE, pp. 298–305.
   Google Scholar
• Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners. Berlin. Springer.
   Google Scholar
• Bonferroni, C. (1950). Sulle medie multiple di potenze. Bolletino Matematica Italiana, 5, 267–270.
   Google Scholar
• Chen, T. Y. (2017). Multiple criteria decision analysis using prioritised interval type-2 fuzzy aggregation operators and its application to site selection. Technological and Economic Development of Economy, 23(1), 1–21. doi:10.3846/20294913.2016.1209249
   Web of Science ®Google Scholar
• Chen, T.-Y. (2015). The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making. Applied Soft Computing, 26, 57–73. doi:10.1016/j.asoc.2014.09.015
   Web of Science ®Google Scholar
• Chu, Y. C., & Liu, P. D. (2015). Some two-dimensional uncertain linguistic Heronian mean operators and their application in multiple-attribute decision making. Neural Computing and Applications, 26(6), 1461–1480. doi:10.1007/s00521-014-1813-8
   Web of Science ®Google Scholar
• De, S. K., & Sana, S. S. (2014). A multi-periods production-inventory model with capacity constraints for multi-manufacturers-A global optimality in intuitionistic fuzzy environment. Applied Mathematics and Computation, 242, 825–841. doi:10.1016/j.amc.2014.06.075
   Web of Science ®Google Scholar
• Deng, X. M., Wei, G. W., Gao, H., & Wang, J. (2018). Models for safety assessment of construction project with some 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators. IEEE Access, 6, 52105–52137. doi:10.1109/ACCESS.2018.2869414
   Web of Science ®Google Scholar
• Gao, H. (2018). Pythagorean fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 35(2), 2229–2245. doi:10.3233/JIFS-172262
   Web of Science ®Google Scholar
• Gao, H., Wei, G. W., & Huang, Y. H. (2018). Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access, 6(1), 11508–11522. doi:10.1109/ACCESS.2017.2784963
   Web of Science ®Google Scholar
• Garg, H. (2016a). 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. doi:10.1002/int.21809
   Web of Science ®Google Scholar
• Garg, H. (2016b). A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. Journal of Intelligent & Fuzzy Systems, 31(1), 529–540. doi:10.3233/IFS-162165
   Web of Science ®Google Scholar
• Gou, X., Xu, Z., & Ren, P. (2016). The properties of continuous Pythagorean fuzzy information. International Journal of Intelligent Systems, 31(5), 401–424. doi:10.1002/int.21788
   Web of Science ®Google Scholar
• Huang, Y. H., & Wei, G. W. (2018). TODIM method for Pythagorean 2-tuple linguistic multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 35(1), 901–915. doi:10.3233/JIFS-171636
   Web of Science ®Google Scholar
• Liu, P. D., Liu, Z. M., & Zhang, X. (2014). Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Applied Mathematics and Computation, 230, 570–586. doi:10.1016/j.amc.2013.12.133
   Web of Science ®Google Scholar
• Liu, P.-D., Chen, S.-M., & Liu, J. (2017). Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators. Information Sciences., 411, 98–121. doi:10.1016/j.ins.2017.05.016
   Web of Science ®Google Scholar
• Liu, X. D., Zhu, J. J., Liu, G. D., & Hao, J. J. (2013). A multiple attribute decision making method based on uncertain linguistic Heronian mean. Mathematical Problems in Engineering, 2013, 1–11. doi:10.1155/2013/597671
   Web of Science ®Google Scholar
• Lu, M., & Wei, G. W. (2017). Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making. International Journal of Knowledge-Based and Intelligent Engineering Systems, 21(3), 165–179. doi:10.3233/KES-170361
   Web of Science ®Google Scholar
• Lu, M., Wei, G. W., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2017). Hesitant Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 33(2), 1105–1117. doi:10.3233/JIFS-16554
   Web of Science ®Google Scholar
• Ma, Z., & Xu, Z. (2016). Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. International Journal of Intelligent Systems, 31(12), 1198–1219. no. doi:10.1002/int.21823
   Web of Science ®Google Scholar
• Maclaurin, C. (1729). A second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philosophical Transactions of the Royal Society of London Series A, 36, 59–96.
   Google Scholar
• Mardani, A., Jusoh, A., Nor, K. M., Khalifah, Z., Zakwan, N., & Valipour, A. (2015). Multiple criteria decision-making techniques and their applications-a review of the literature from 2000 to 2014. Economic Research-Ekonomska Istraživanja, 28(1), 516–571. doi:10.1080/1331677X.2015.1075139
   Web of Science ®Google Scholar
• Mardani, A., Nilashi, M., Zavadskas, E. K., Awang, S. R., Zare, H., & Jamal, N. M. (2018). Decision-making methods based on fuzzy aggregation operators: Three decades review from 1986 to 2017. International Journal of Information Technology & Decision Making, 17, 391–466. doi:10.1142/S021962201830001X
   Web of Science ®Google Scholar
• Muirhead, R. F. (1902). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21(3), 144–162. doi:10.1017/S001309150003460X
   Google Scholar
• Peng, X. D., & Yang, Y. (2016). Pythagorean fuzzy choquet integral based MABAC method for multiple attribute group decision making. International Journal of Intelligent Systems, 31(10), 989–1020. doi:10.1002/int.21814
   Web of Science ®Google Scholar
• Peng, X., & Selvachandran, G. (2017). Pythagorean fuzzy set: State of the art and future directions. Artificial Intelligence Review, 1, 1–55.
   Google Scholar
• Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30(11), 1133–1160. doi:10.1002/int.21738
   Web of Science ®Google Scholar
• Qin, J. Q., & Liu, X. W. (2016). 2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection. Kybernetes, 45(1), 2–29. doi:10.1108/K-11-2014-0271
   Web of Science ®Google Scholar
• Reformat, M., & Yager, R. R. (2014). Suggesting recommendations using Pythagorean fuzzy sets illustrated using Netflix movie data. IPMU, 1, 546–556.
   Google Scholar
• Ren, P., Xu, Z., & Gou, X. (2016). Pythagorean fuzzy TODIM approach to multi-criteria decision making. Applied Soft Computing, 42, 246–259. doi:10.1016/j.asoc.2015.12.020
   Web of Science ®Google Scholar
• Rostamzadeh, R., Esmaeili, A., Nia, A. S., Saparauskas, J., & Ghorabaee, M. K. (2017). A fuzzy Aras method for supply chain management performance measurement in SMEs under uncertainty. Transformations in Business & Economics, 16(2A), 319–348.
   Web of Science ®Google Scholar
• Tang, X. Y., & Wei, G. W. (2018). Models for green supplier selection in green supply chain management with Pythagorean 2-tuple linguistic information. IEEE Access, 6, 18042–18060. doi:10.1109/ACCESS.2018.2817551
   Web of Science ®Google Scholar
• Wang, J., Wei, G. W., & Wei, Y. (2018b). Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators. Symmetry, 10(5), 131. doi:10.3390/sym10050131
   Google Scholar
• Wang, J., Wei, G., & Gao, H. (2018d). Approaches to multiple attribute decision making with interval-valued 2-tuple linguistic pythagorean fuzzy information. Mathematics, 6(10), 201. doi:10.3390/math6100201
   Web of Science ®Google Scholar
• Wang, J., Wei, G., & Lu, M. (2018a). TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Symmetry, 10(10), 486. doi:10.3390/sym10100486
   Google Scholar
• Wang, J., Wei, G., & Lu, M. (2018c). An extended VIKOR method for multiple criteria group decision making with triangular fuzzy neutrosophic numbers. Symmetry, 10(10), 497. doi:10.3390/sym10100497
   Google Scholar
• Wei, G. W. (2017a). Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 33(4), 2119–2132. doi:10.3233/JIFS-162030
   Web of Science ®Google Scholar
• Wei, G. W. (2017b). Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making. Kybernetes, 46(10), 1777–1800. doi:10.1108/K-01-2017-0025
   Web of Science ®Google Scholar
• Wei, G. W. (2017c). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 28(3), 547–564. doi:10.15388/Informatica.2017.144
   Web of Science ®Google Scholar
• Wei, G. W. (2018a). Some similarity measures for picture fuzzy sets and their applications. Iranian Journal of Fuzzy Systems, 15(1), 77–89.
   Web of Science ®Google Scholar
• Wei, G. W. (2018b). Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fundamenta Informaticae, 157(3), 271–320. doi:10.3233/FI-2018-1628
   Web of Science ®Google Scholar
• Wei, G. W. (2018c). TODIM method for picture fuzzy multiple attribute decision making. Informatica, 29(3), 555–566. doi:10.15388/Informatica.2018.181
   Web of Science ®Google Scholar
• Wei, G. W., & Lu, M. (2017a). Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making. Archives of Control Sciences, 27(3), 365–395. doi:10.1515/acsc-2017-0024
   Web of Science ®Google Scholar
• Wei, G. W., & Lu, M. (2017b). Pythagorean hesitant fuzzy Hamacher aggregation operators in multiple attribute decision making. Journal of Intelligent Systems. DOI: doi:10.1515/jisys-2017-0106
   Web of Science ®Google Scholar
• Wei, G. W., & Lu, M. (2018a). Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(5), 1043–1070. doi:10.1002/int.21911
   Web of Science ®Google Scholar
• Wei, G. W., & Lu, M. (2018b). Pythagorean fuzzy power aggregation operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(1), 169–186. doi:10.1002/int.21946
   Web of Science ®Google Scholar
• Wei, G. W., Gao, H., & Wei, Y. (2018a). Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(7), 1426–1458. doi:10.1002/int.21985
   Web of Science ®Google Scholar
• Wei, G. W., Gao, H., Wang, J., & Huang, Y. H. (2018c). Research on risk evaluation of enterprise human capital investment with interval-valued bipolar 2-tuple linguistic information. IEEE Access, 6, 35697–35712. doi:10.1109/ACCESS.2018.2836943
   Web of Science ®Google Scholar
• Wei, G. W., Lu, M., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2017a). Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 33(2), 1129–1142. doi:10.3233/JIFS-16715
   Web of Science ®Google Scholar
• Wei, G. W., Lu, M., Tang, X. Y., & Wei, Y. (2018b). Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Intelligent Systems, 33(6), 1197–1233. doi:10.1002/int.21978
   Web of Science ®Google Scholar
• Wei, G., & Wei, Y. (2018). Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 35(2), 2001–2013. doi:10.3233/JIFS-171741
   Web of Science ®Google Scholar
• Wei, Y., Liu, J., Lai, X., & Hu, Y. (2017b). Which determinant is the most informative in forecasting crude oil market volatility: Fundamental, speculation, or uncertainty? Energy Economics, 68, 141–150. doi:10.1016/j.eneco.2017.09.016
   Web of Science ®Google Scholar
• Wei, Y., Yu, Q., Liu, J., & Cao, Y. (2018d). Hot money and China’s stock market volatility: Further evidence using the GARCH-MIDAS model. Physica A: Statistical Mechanics and Its Applications, 492, 923–930. doi:10.1016/j.physa.2017.11.022
   Web of Science ®Google Scholar
• Wu, S. J., & Wei, G. W. (2017). Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Knowledge-Based and Intelligent Engineering Systems, 21(3), 189–201. doi:10.3233/KES-170363
   Web of Science ®Google Scholar
• Wu, S., Wang, J., Wei, G., & Wei, Y. (2018). Research on construction engineering project risk assessment with some 2-tuple linguistic neutrosophic Hamy mean operators. Sustainability, 10(5), 1536. doi:10.3390/su10051536
   Web of Science ®Google Scholar
• Yager, R. R. (2001). The power average operator. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 31(6), 724–731. doi:10.1109/3468.983429
   Web of Science ®Google Scholar
• Yager, R. R. (2013). Pythagorean fuzzy subsets. Proceeding of The Joint IFSA Wprld Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp. 57–61.
   Google Scholar
• Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. doi:10.1109/TFUZZ.2013.2278989
   Web of Science ®Google Scholar
• Yu, D. J. (2013). Intuitionistic fuzzy geometric Heronian mean aggregation operators. Applied Soft Computing, 13(2), 1235–1246. doi:10.1016/j.asoc.2012.09.021
   Web of Science ®Google Scholar
• Yu, S. M., Zhou, H., Chen, X. H., & Wang, J. Q. (2015). A multi-criteria decision-making method based on Heronian mean operators under a linguistic hesitant fuzzy environment. Asia-Pacific Journal of Operational Research, 32(05), 1550035. doi:10.1142/S0217595915500359
   Web of Science ®Google Scholar
• Yue, Z., & Jia, Y. (2013). A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making. Applied Soft Computing, 13(5), 2304–2317. doi:10.1016/j.asoc.2012.12.032
   Web of Science ®Google Scholar
• Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–356. doi:10.1016/S0019-9958(65)90241-X
   Google Scholar
• Zeng, S. Z., Mu, Z. M., & Balezentis, T. (2018). A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. International Journal of Intelligent Systems, 33(3), 573–585. doi:10.1002/int.21953
   Web of Science ®Google Scholar
• Zeng, S., Chen, J., & Li, X. (2016). A hybrid method for Pythagorean fuzzy multiple-criteria decision making. International Journal of Information Technology & Decision Making, 15(02), 403–422. doi:10.1142/S0219622016500012
   Web of Science ®Google Scholar
• Zhang, R. T., Wang, J., Zhu, X. M., Xia, M. M., & Yu, M. (2017). Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multiattribute group decision-making. Complexity, 2017, 1–16. Volume Article ID 5937376, pages. doi:10.1155/2017/5937376
   Web of Science ®Google Scholar
• Zhang, X. L., & Xu, Z. S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. doi:10.1002/int.21676
   Web of Science ®Google Scholar
• Zhu, B., Xu, Z. S., & Xia, M. M. (2012). Hesitant fuzzy geometric Bonferroni means. Information Sciences, 205, 72–85. doi:10.1016/j.ins.2012.01.048
   Web of Science ®Google Scholar