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MATERIALS ENGINEERING

A novel aggregation method for generating Pythagorean fuzzy numbers in multiple criteria group decision making: An application to materials selection

ORCID Icon & | (Reviewing editor)
Article: 1905230 | Received 12 Nov 2020, Accepted 07 Mar 2021, Published online: 11 Apr 2021

References

  • Abdullah, L., & Goh, P. (2019). Decision making method based on Pythagorean fuzzy sets and its application to solid waste management. Complex & Intelligent Systems, 5(2), 185–23. https://doi.org/10.1007/s40747-019-0100-9
  • Akram, M., Dudek, W. A., & Ilyas, F. (2019). Group decision‐making based on Pythagorean fuzzy TOPSIS method. International Journal of Intelligent Systems, 34(7), 1455–1475. https://doi.org/10.1002/int.22103
  • Akram, M., Garg, H., & Zahid, K. (2020). Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment. Iranian Journal of Fuzzy Systems, 17(5), 147–164. http://search.ebscohost.com.sdl.idm.oclc.org/login.aspx?direct=true&db=asn&AN=144759524&site=eds-live
  • Akram, M., Ilyas, F., & Garg, H. (2020). Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Computing - A Fusion of Foundations, Methodologies & Applications, 24(5), 3425. https://doi.org/10.1007/s00500-019-04105-0
  • Akram, M., Kahraman, C., & Zahid, K. (2021). Group decision-making based on complex spherical fuzzy VIKOR approach. Knowledge-Based Systems, 216, 106793. https://doi.org/10.1016/j.knosys.2021.106793
  • Ali Khan, M. S., Abdullah, S., & Ali, A. (2019). Multiattribute group decision‐making based on Pythagorean fuzzy Einstein prioritized aggregation operators. International Journal of Intelligent Systems, 34(5), 1001–1033. https://doi.org/10.1002/int.22084
  • An, X., Wang, Z., Li, H., & Ding, J. (2018). Project delivery system selection with interval-valued intuitionistic fuzzy set group decision-making method. Group Decision and Negotiation, 27(4), 689–707. https://doi.org/10.1007/s10726-018-9581-y
  • Ashraf, S., Abdullah, S., & Aslam, M. (2020). Symmetric sum based aggregation operators for spherical fuzzy information: Application in multi-attribute group decision making problem. Journal of Intelligent & Fuzzy Systems, 38(4), 5241–5255. https://doi.org/10.3233/JIFS-191819
  • Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B141. https://doi.org/10.1287/mnsc.17.4.B141
  • Biswas, A., & Sarkar, B. (2018). Pythagorean fuzzy multicriteria group decision making through similarity measure based on point operators. International Journal of Intelligent Systems, 33(8), 1731–1744. https://doi.org/10.1002/int.21994
  • Bryniarska, A. (2020). The n-Pythagorean fuzzy sets. Symmetry (20738994), 12(11), 1772. https://doi.org/10.3390/sym12111772
  • Chakraborty, S., & Chatterjee, P. (2013). Selection of materials using multi-criteria decision-making methods with minimum data. Decision Science Letters, 2(3), 135–148. https://doi.org/10.5267/j.dsl.2013.03.005
  • Darko, A. P., & Liang, D. (2020). Some q-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Engineering Applications of Artificial Intelligence, 87, 103259. https://doi.org/10.1016/j.engappai.2019.103259
  • Das, S., Kar, M. B., Pal, T., & Kar, S. (2014). Multiple attribute group decision making using interval-valued intuitionistic fuzzy soft matrix. 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Fuzzy Systems (FUZZ-IEEE), 2014 IEEE International Conference On, 2222–2229. https://doi.org/10.1109/FUZZ-IEEE.2014.6891687
  • Fatima, S. S., Wooldridge, M., & Jennings, N. R. (2008). A linear approximation method for the Shapley value. Artificial Intelligence, 172(14), 1673–1699. https://doi.org/10.1016/j.artint.2008.05.003
  • Feng, F., Fujita, H., Ali, M. I., Yager, R. R., & Liu, X. (2019). Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods. IEEE Transactions on Fuzzy Systems, 27(3), 474–488. https://doi.org/10.1109/TFUZZ.2018.2860967
  • Feng, F., Xu, Z., Fujita, H., & Liang, M. (2020). Enhancing PROMETHEE method with intuitionistic fuzzy soft sets. International Journal of Intelligent Systems, 35(7), 1071–1104. https://doi.org/10.1002/int.22235
  • 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. https://doi.org/10.1002/int.21827
  • Garg, H. (2017). Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Computational & Mathematical Organization Theory, 23(4), 546–571. https://doi.org/10.1007/s10588-017-9242-8
  • 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. https://doi.org/10.1016/j.ins.2019.11.035.
  • Garg, H., & Kaur, G. (2020). Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment. Scientia Iranica. Transaction D, Computer Science & Engineering & Electrical Engineering, 27(1), 396–410. https://doi.org/10.24200/sci.2018.5307.1194
  • Garg, H., & Kumar, K. (2020). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. The Artificial Intelligence Review, 53(1), 595–624. https://doi.org/10.1007/s10462-018-9668-5
  • Garg, H., & Kumar, K. (2020). Linguistic interval-valued Atanassov Intuitionistic Fuzzy Sets and their applications to group decision making problems. IEEE Transactions on Fuzzy Systems, 27(12), 2302–2311. https://doi.org/10.1109/TFUZZ.2019.2897961
  • Guo, J. (2013). Hybrid multicriteria group decision making method for information system project selection based on intuitionistic fuzzy theory. Mathematical Problems in Engineering. https://doi.org/10.1155/2013/859537
  • Hashemi, S. S., Hajiagha, S. H. R., Zavadskas, E. K., & Mahdiraji, H. A. (2016). Multicriteria group decision making with ELECTRE III method based on interval-valued intuitionistic fuzzy information. Applied Mathematical Modelling, 40(2), 1554–1564. https://doi.org/10.1016/j.apm.2015.08.011
  • Jahan, A., Ismail, M. Y., Mustapha, F., & Sapuan, S. M. (2010). Material selection based on ordinal data. Materials and Design, 31(7), 3180–3187. https://doi.org/10.1016/j.matdes.2010.02.024
  • Jahan, A., Ismail, M. Y., Sapuan, S. M., & Mustapha, F. (2010). Material screening and choosing methods - A review. Materials and Design, 31(2), 696–705. https://doi.org/10.1016/j.matdes.2009.08.013
  • Jih-Chang, W., & Ting-Yu, C. (2020). A novel Pythagorean Fuzzy LINMAP-based compromising approach for multiple criteria group decision-making with preference over alternatives. International Journal of Computational Intelligence Systems, 13(1), 444-463. https://doi.org/10.2991/ijcis.d.200408.001
  • Khan, M. S. A., Khan, F., Lemley, J., Abdullah, S., & Hussain, F. (2020). Extended topsis method based on Pythagorean cubic fuzzy multi-criteria decision making with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 38(2), 2285–2296. https://doi.org/10.3233/JIFS-191089
  • Kuei-Hu, C. (2019). A novel supplier selection method that integrates the intuitionistic fuzzy weighted averaging method and a soft set with imprecise data. Annals of Operations Research, 272(1–2), 139. https://doi.org/10.1007/s10479-017-2718-6
  • Kumar, K., & Garg, H. (2018). Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Applied Intelligence, 48(8), 2112–2119. https://doi.org/10.1007/s10489-017-1067-0
  • Leszczyński, K., Penczek, P., & Grochulski, W. (1985). Sugeno’s fuzzy measure and fuzzy clustering. Fuzzy Sets and Systems, 15(2), 147–158. https://doi.org/10.1016/0165-0114(85)90043-0
  • Li, H., Wu, P., Zhou, L., & Chen, H. (2021). A new approach for multicriteria group decision making under interval type-2 fuzzy environment. Measurement, 172, 108818. https://doi.org/10.1016/j.measurement.2020.108818
  • Li, Y., Deng, Y., Chan, F. T. S., Liu, J., & Deng, X. (2014). An improved method on group decision making based on interval-valued intuitionistic fuzzy prioritized operators. Applied Mathematical Modelling, 38(9), 2689–2694. https://doi.org/10.1016/j.apm.2014.02.028
  • Liang, W., Zhang, X., & Liu, M. (2015). The maximizing deviation method based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dynamics in Nature and Society, 2015, 1–15. https://doi.org/10.1155/2015/746572
  • Liangli, D., Ying, P., Junjun, M., & Dengbao, Y. (2017). Multiple attribute group decision making based on interval type-2 fuzzy cross-entropy and ranking value. 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), Automation (YAC), 2017 32nd Youth Academic Annual Conference of Chinese Association Of, 791–796. Hefei, China. https://doi.org/10.1109/YAC.2017.7967517
  • Lin, J., & Zhang, Q. (2016). Note on aggregating crisp values into intuitionistic fuzzy number. Applied Mathematical Modelling, 40(23–24), 10800–10808. https://doi.org/10.1016/j.apm.2016.07.020
  • Liou, J. J. H., & Chuang, Y.-T. (2010). Developing a hybrid multi-criteria model for selection of outsourcing providers. Expert Systems With Applications, 37(5), 3755–3761. https://doi.org/10.1016/j.eswa.2009.11.048
  • Liu, S. L., & Qiu, W. H. (1998). Studies on the basic theories for multiple attribute decision making. Systems Engineering-Theory & Practice, 18(1), 38–43
  • Liu, X., Kim, H. S., Feng, F., & Alcantud, J. C. R. (2018). Centroid transformations of intuitionistic fuzzy values based on aggregation operators. Mathematics, 6(11), 215. https://doi.org/10.3390/math6110215
  • Liu, Y., & Du, J. (2020). A multi criteria decision support framework for renewable energy storage technology selection. Journal of Cleaner Production, 277, 122183. https://doi.org/10.1016/j.jclepro.2020.122183
  • Mohamed, M. A., & Xiao, W. (2003). Q-measures: An efficient extension of the Sugeno/spl lambda/-measure. IEEE Transactions on Fuzzy Systems, 11(3), 419–426. https://doi.org/10.1109/TFUZZ.2003.812701
  • Montajabiha, M. (2016). An extended PROMETHE II multi-criteria group decision making technique based on intuitionistic fuzzy logic for sustainable energy planning. Group Decision and Negotiation, 25(2), 221–244. http://dx.doi.org/10.1007/s10726-015-9440-z
  • Pérez-Domínguez, L., Alvarado-Iniesta, A., García-Alcaraz, J. L., & Valles-Rosales, D. J. (2018). Intuitionistic Fuzzy dimensional analysis for multi-criteria decision making. Iranian Journal of Fuzzy Systems, 15(6), 17–40. http://search.ebscohost.com.sdl.idm.oclc.org/login.aspx?direct=true&db=asn&AN=134211306&site=eds-live
  • Remadi, F. D., & Frikha, H. M. (2020). The triangular intuitionistic fuzzy extension of the CODAS method for solving multi-criteria group decision making. 2020 International Multi-Conference on: “Organization of Knowledge and Advanced Technologies” (OCTA), “Organization of Knowledge and Advanced Technologies” (OCTA), 2020 International Multi-Conference On, 1–6, Tunis, Tunisia. https://doi.org/10.1109/OCTA49274.2020.9151786
  • Ren, P., Xu, Z., Liao, H., & Zeng, X.-J. (2017). A thermodynamic method of intuitionistic fuzzy MCDM to assist the hierarchical medical system in China. Information Sciences, 420, 490–504. https://doi.org/10.1016/j.ins.2017.08.070
  • Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Tokyo Institute of Technology. https://dds.crl.edu/crldelivery/19112
  • Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, SMC-15(1), 116–132. https://doi.org/10.1109/TSMC.1985.6313399
  • Wan, S. P., Xu, J., & Dong, J. Y. (2016). Aggregating decision information into interval-valued intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making. Knowledge-Based Systems, 113, 155–170. https://doi.org/10.1016/j.knosys.2016.09.026.
  • Wu, J., Huang, H., & Cao, Q. (2013). Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Applied Mathematical Modelling, 37(24), 9898–9906. https://doi.org/10.1016/j.apm.2013.05.035
  • Xindong, P. (2019). Algorithm for Pythagorean Fuzzy multi-criteria decision making based on WDBA with new score function. Fundamenta Informaticae, 165(2), 99–137. https://doi.org/10.3233/FI-2019-1778
  • Xu, Z. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678
  • Xu, Z., & Yager, R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems - INT J GEN SYSTEM, 35(4), 417–433. https://doi.org/10.1080/03081070600574353
  • Xue, Y.-X., You, J.-X., Lai, X.-D., & Liu, H.-C. (2016). An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information. Applied Soft Computing, 38, 703–713. https://doi.org/10.1016/j.asoc.2015.10.010
  • Yager, R. R. (2013). Pythagorean fuzzy subsets. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
  • Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
  • Yager, R. R. (2017). Generalized Orthopair Fuzzy Sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005
  • Yue, Z. (2008). The comprehensive evaluation of urban environmental quality based on intuitionistic fuzzy set. Mathematics in Practice and Theory, 8. https://www.researchgate.net/publication/265917025_The_comprehensive_evaluation_of_urban_environmental_quality_based_on_intuitionistic_fuzzy_set
  • Yue, Z. (2011). An approach to aggregating interval numbers into interval-valued intuitionistic fuzzy information for group decision making. Expert Systems with Applications, 38(5), 6333–6338. https://doi.org/10.1016/j.eswa.2010.11.108
  • Yue, Z. (2014a). A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information. Applied Mathematical Modelling, 38(2), 683–698. https://doi.org/10.1016/j.apm.2013.07.007
  • Yue, Z. (2014b). Aggregating crisp values into intuitionistic fuzzy number for group decision making. Applied Mathematical Modelling, 38(11–12), 2969–2982. https://doi.org/10.1016/j.apm.2013.11.020
  • 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. https://doi.org/10.1016/j.asoc.2012.12.032
  • Yue, Z., Jia, Y., & Ye, G. (2009). An approach for multiple attribute group decision making based on intuitionistic fuzzy information. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 17(3), 317–332. https://doi.org/10.1142/S0218488509005899
  • Yue, Z., Jia, Y., & Zhu, C. (2008). Interval multiple attribute decision making based on interval-valued intuitionistic fuzzy set. 2008 Congress on Image and Signal Processing, 4, 403–407. https://doi.org/10.1109/CISP.2008.228
  • Zhang, L. (2018). Multiple attributes group decision making under intuitionistic fuzzy preference settings. 2018 Chinese Control And Decision Conference (CCDC), Chinese Control And Decision Conference (CCDC), 2018, 2202–2206. Shenyang, China. https://doi.org/10.1109/CCDC.2018.8407492
  • Zhang, X. (2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent Systems, 31(6), 593–611. https://doi.org/10.1002/int.21796
  • Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676
  • Zhang, Z., Wang, C., Tian, D., & Li, K. (2014). A novel approach to interval-valued intuitionistic fuzzy soft set based decision making. Applied Mathematical Modelling, 38(4), 1255–1270. https://doi.org/10.1016/j.apm.2013.08.019
  • Zhao, J., You, X.-Y., Liu, H.-C., & Wu, S.-M. (2017). An extended VIKOR method using intuitionistic fuzzy sets and combination weights for supplier selection. Symmetry, 9(9), 169. https://doi.org/10.3390/sym9090169
  • Zhou, F., & Chen, T.-Y. (2020). Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures. Computers & Industrial Engineering, 148, 106670. https://doi.org/10.1016/j.cie.2020.106670
  • Zhou, L., Tao, Z., Chen, H., & Liu, J. (2014). Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making. Applied Mathematical Modelling, 38(7), 2190–2205. https://doi.org/10.1016/j.apm.2013.10.036