Multi-attribute decision-making based on q-rung dual hesitant power dual Maclaurin symmetric mean operator and a new ranking method

• Autorzy: Li Li , Wang Jun , Ji Chunliang

Identyfikatory

DOI

10.24425/acs.2022.142852

• Języki publikacji: EN

Abstrakty

EN

The ability of q-rung dual hesitant fuzzy sets (q-RDHFSs) in dealing with decision makers’ fuzzy evaluation information has received much attention. This main aim of this paper is to propose new aggregation operators of q-rung dual hesitant fuzzy elements and employ them in multi-attribute decision making (MADM). In order to do this, we first propose the power dual Maclaurin symmetric mean (PDMSM) operator by integrating the power geometric (PG) operator and the dual Maclaurin symmetric mean (DMSM). The PG operator can reduce or eliminate the negative influence of decision makers’ extreme evaluation values, making the final decision results more reasonable. The DMSM captures the interrelationship among multiple attributes. The PDMSM takes the advantages of both PG and DMSM and hence it is suitable and powerful to fuse decision information. Further, we extend the PDMSM operator to q-RDHFSs and propose q-rung dual hesitant fuzzy PDMSM operator and its weighted form. Properties of these operators are investigated. Afterwards, a new MADM method under q-RDHFSs is proposed on the basis on the new operators. Finally, the effectiveness of the new method is testified through numerical examples.

Słowa kluczowe

EN

q-rung dual hesitant fuzzy sets; power geometric; dual Maclaurin symmetric mean; power dual Maclaurin symmetric mean; multi-attribute decision-making

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2022
• Tom: Vol. 32, No. 3
• Strony: 627--658
• Opis fizyczny: Bibliogr. 57 poz., tab., wzory

Twórcy

autor

Li Li

• School of Economics and Management, Beihang University, Beijing 100191, China

autor

Wang Jun

• School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China

autor

Ji Chunliang

• School of Economics and Management, Beijing Jiaotong University, Beijing100044, China

Bibliografia

• [1] A. Biswas and A. Sarkar: Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multi-criteria group decision making. Archives of Control Sciences, 28(4), (2018), 527-549. DOI: 10.24425/acs.2018.125482.
• [2] J. Wang, X.P. Shang, K.Y. Bai and Y. Xu: A new approach to cubic q-rung orthopair fuzzy multiple attribute group decision-making based on power Muirhead mean. Neural Computing and Applications, 32 (2020), 14087-14112. DOI: 10.1007/s00521-020-04807-9.
• [3] L. Li, R.T. Zhang, J. Wang and X.P. Shang: Some q-rung orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making. Archives of Control Sciences, 28(4), (2018), 551-583. DOI: 10.24425/acs.2018.125483.
• [4] J. Wang, R.T. Zhang, X.M. Zhu, X.P. Shang and W.Z. Li: Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. Journal of Intelligent and Fuzzy Systems, 36(2), (2019), 1599-1614. DOI: 10.3233/JIFS-18607.
• [5] G.W. Wei and M. Lu: Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making. Archives of Control Sciences, 27(3), (2017), 365-395. DOI: 10.1515/acsc-2017-0024.
• [6] J. Wang, X.P. Shang, X. Feng and M.Y. Sun: A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean. Archives of Control Sciences, 30(2), (2020), 233-272. DOI: 10.24425/acs.2020.133499.
• [7] R.R. Yager: The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31 (2001), 724-731. DOI: 10.1109/3468.983429.
• [8] K.T. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1986), 87-96.
• [9] V. Torra: Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), (2010), 529-539. DOI: 10.1002/int.20418.
• [10] B. Zhu, Z.X. Xu and M.M Xia: Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012 (2012), Article ID 879629. DOI: 10.1155/2012/879629.
• [11] R.R. Yager: Pythagorean membership grades in multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), (2014), 958-965. DOI: 10.1109/TFUZZ.2013.2278989.
• [12] R.R. Yager: Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), (2017), 1222-1230. DOI: 10.1109/TFUZZ.2016.2604005.
• [13] Z.S. Xu: Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Systems, 24(6), (2011), 749-760. DOI: 10.1016/j.knosys.2011.01.011.
• [14] Z.M. Zhang: Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234 (2013), 150-181. DOI: 10.1016/j.ins.2013.01.002.
• [15] L. Wang, Q.G. Shen and L. Zhu: Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making. Applied Soft Computing, 38 (2016), 23-50. DOI: 10.1016/j.asoc.2015.09.012.
• [16] G.W. Wei and M. Lu: Pythagorean fuzzy power aggregation operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(1), (2018), 169-186. DOI: 10.1002/int.21946.
• [17] W.H. Xu, X.P. Shang, J. Wang and W.Z. Li: A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean. Symmetry, 11(3), (2019). DOI: 10.3390/sym11030441.
• [18] C. Maclaurin: 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 (1729), 59-96.
• [19] J.D. Qin and X.W. Liu: An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. Journal of Intelligent & Fuzzy Systems, 27(5), (2014), 2177-2190. DOI: 10.3233/IFS-141182.
• [20] P. Wang and P.D. Liu: Some Maclaurin symmetric mean aggregation operators based on Schweizer-Sklar operations for intuitionistic fuzzy numbers and their application to decision making. Journal of Intelligent & Fuzzy Systems, 36(4), (2019), 3801-3824. DOI: 10.3233/JIFS-18801.
• [21] P.D. Liu and W.Q. Liu: Intuitionistic fuzzy interaction Maclaurin symmetric means and their application to multiple-attribute decision-making. Technological and Economic Development of Economy, 24(4), (2018), 1533-1559. DOI: 10.3846/tede.2018.3698.
• [22] G. Sun and W.L. Xia: Evaluation method for innovation capability and efficiency of high technology enterprises with interval-valued intuitionistic fuzzy information. Journal of Intelligent & Fuzzy Systems, 31(3), (2016), 1419-1425. DOI: 10.3233/IFS-162208.
• [23] G.W. Wei and M. Lu: Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(5), (2018), 1043-1070. DOI: 10.1002/int.21911.
• [24] G.W. Wei, H. Garg, H. Gao and C. Wei: Interval-valued Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. IEEE Access 6 (2018), 67866-67884. DOI: 10.1109/ACCESS.2018.2877725.
• [25] G.W. Wei, C. Wei, J. Wang, H. Gao and Y. Wei: Some q-rung orthopair fuzzy Maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. International Journal of Intelligent Systems, 34(1), (2019), 50-81. DOI: 10.1002/int.22042.
• [26] J. Wang, G.W. Wei, R. Wang, et al.: Some q-rung interval-valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making. International Journal of Intelligent Systems, 34(11), (2019), 2769-2806. DOI: 10.1002/int.22156.
• [27] P.D. Liu and Y. Li: A novel decision-making method based on probabilistic linguistic information. Cognitive Computation, 11(5), (2019), 735-747. DOI: 10.1007/s12559-019-09648-w.
• [28] P.D. Liu, Y. Li and M.C. Zhang: Some Maclaurin symmetric mean aggregation operators based on two-dimensional uncertain linguistic information and their application to decision making. Neural Computing and Applications, 31(8), (2019), 4305-4318. DOI: 10.1007/s00521-018-3350-3.
• [29] F. Teng, Z.M. Liu and P.D. Liu: Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making. International Journal of Intelligent Systems, 33(9), (2018), 1949-1985. DOI: 10.1002/int.22005.
• [30] Z.M. Liu, F. Teng, P.D. Liu and G. Qian: Interval-valued intuitionistic fuzzy power Maclaurin symmetric mean aggregation operators and their application to multiple attribute group decision-making. International Journal for Uncertainty Quantification, 8(3), (2018), 211-232. DOI: 10.1615/Int.J.UncertaintyQuantification.2018020702.
• [31] P.D. Liu, S.M. Chen and P. Wang: Multiple-attribute group decision-making based on q-rung orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(10), (2020), 3741-3756. DOI: 10.1109/TSMC.2018.2852948.
• [32] C. Bonferroni: Sulle medie multiple di potenze. Bolletino Matematica Italiana, 5(3-4), (1950), 267-270. In Italian.
• [33] M.M. Xia, Z.S. Xu and B. Zhu: Geometric Bonferroni means with their application in multi-criteria decision making. Knowledge-Based Systems, 40 (2013), 88-100. DOI: 10.1016/j.knosys.2012.11.013.
• [34] S. Sykora: Mathematical means and averages: generalized Heronian means (2009). DOI: 10.3247/SL3Math09.002.
• [35] D.J. Yu: Intuitionistic fuzzy geometric Heronian mean aggregation operators. Applied Soft Computing, 13(2), (2013), 1235-1246. DOI: 10.1016/j.asoc.2012.09.021.
• [36] Y.D. He, Z. He, G.D. Wang and H.Y. Chen: Hesitant fuzzy power Bonferroni means and their application to multiple attribute decision making. IEEE Transactions on Fuzzy Systems, 23(5), (2014), 1655-1668. DOI: 10.1109/TFUZZ.2014.2372074.
• [37] Y.D. He, Z. He, C. Jin and H.Y. Chen: Intuitionistic fuzzy power geometric Bonferroni means and their application to multiple attribute group decision making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(2), (2015), 285-315. DOI: 10.1142/s0218488515500129.
• [38] P.D. Liu: Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Computers & Industrial Engineering, 108 (2017), 199-212. DOI: 10.1016/j.cie.2017.04.033.
• [39] M.H. Shi, F. Yang and Y.W. Xiao: Intuitionistic fuzzy power geometric Heronian mean operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 37(2), (2019), 2651-2669. DOI: 10.3233/JIFS-182903.
• [40] Z.S. Xu and R.R. Yager: Power geometric operators and their use in group decision making. IEEE Transaction of Fuzzy Systems, 18(1), (2010), 94-105. DOI: 10.1109/TFUZZ.2009.2036907.
• [41] J.D. Qin, and X.W. Liu: Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. Journal of Intelligent & Fuzzy Systems, 29(1), (2015), 171-186. DOI: 10.3233/IFS-151584.
• [42] Y. Xu, X.P. Shang, J. Wang, W. Wu and H.Q. Huang: Some q-rung dual hesitant fuzzy Heronian mean operators with their application to multiple attribute group decision-making. Symmetry, 10 (2018), 472. DOI: 10.3390/sym10100472.
• [43] Y.D. He, Z. He, C. Jin and H.Y. Chen: Intuitionistic fuzzy power geometric Bonferroni means and their application to multiple attribute group decision making. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 23(2), (2015), 285-315. DOI: 10.1142/s0218488515500129.
• [44] H.J. Wang, X.F. Zhao and G.W. Wei: Dual hesitant fuzzy aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 26(5), (2014), 2281-2290. DOI: 10.3233/IFS-130901.
• [45] M. Tang, J. Wang, J.P. Liu, G.W. Wei, C. Wei and Y. Wei: Dual hesitant Pythagorean fuzzy Heronian mean operators in multiple attribute decision making. Mathematics, 7(4), (2019). DOI: 10.3390/math7040344.
• [46] C. Jana and and M. Pal: Multi-criteria decision making process based on some single-valued neutrosophic Dombi power aggregation operators. Soft Computing, 25 (2021), 5055-5072. DOI: 10.1007/s00500-020-05509-z.
• [47] G.W. Wei and M. Lu: Pythagorean fuzzy power aggregation operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(1), (2018), 169-186. DOI: 10.1002/int.21946.
• [48] X.W. Qi, C.Y. Liang and J.L Zhang: Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment. International Journal of Machine Learning and Cybernetics, 7(6), (2016), 1147-1193. DOI: 10.1007/s13042-015-0445-3.
• [49] H. Garg and R. Arora: Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multicriteria decision-making. International Journal of Intelligent Systems, 34(2), (2019), 215-246. DOI: 10.1002/int.22048.
• [50] Y.D. He, Z. He and H.Y. Chen: Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE Transactions on Cybernetics, 45(1), (2015), 116-128. DOI: 10.1109/TCYB.2014.2320910.
• [51] X.J. Gou, Z.S. Xu and H.C. Liao: Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Computing, 21(21), (2017), 6515-6529. DOI: 10.1007/s00500-016-2211-1.
• [52] P.D. Liu and P. Wang: Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy Systems, 27(5), (2019), 834-848. DOI: 10.1109/TFUZZ.2018.2826452.
• [53] R.T. Zhang, J. Wang, X.M. Zhu, M.M. Xia and M. Yu: Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multiattribute group decision-making. Complexity, 2017 (2017). DOI: 10.1155/2017/5937376.
• [54] C. Jana, M. Pal and G.W. Wei: Multiple Attribute decision making method based on intuitionistic Dombi operators and its application in mutual fund evaluation. Archives of Control Sciences, 30(3), (2020), 437-470. DOI: 10.24425/acs.2020.134673.
• [55] X. Feng, X.P. Shang, J. Wang and Y. Xu: A multiple attribute decision-making method based on interval-valued q-rung dual hesitant fuzzy power Hamy mean and novel score function. Computational and Applied Mathematics, 40(1), (2021), 1-32. DOI: 10.1007/s40314-020-01384-4.
• [56] Y. Yang, Z.S. Chen, R.M. Rodriguez, W. Pedrycz and K.S. Chin: Novel fusion strategies for continuous interval-valued q-rung orthopair fuzzy information: a case study in quality assessment of SmartWatch appearance design. International Journal of Machine Learning and Cybernetics, 13(3), (2022), 609-632. DOI: 10.1007/s13042-020-01269-2.
• [57] R. Krishankumar, S.S. Nimmagadda, P. Rani, A.R. Mishra, K.S. Ravichandran and A.H. Gandomi: Solving renewable energy source selection problems using a q-rung orthopair fuzzy-based integrated decision-making approach. Journal of Cleaner Production, 279 (2021). DOI: 10.1016/j.jclepro.2020.123329.

Uwagi

1. This work was supported by Project funded by China Postdoctoral Science Foundation (2020M680315) and Funds for First-class Discipline Construction (XK1802-5)

2. Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)