Multi-attribute Group Decision Making Method with Unknown Attribute Weights Based on the Q-rung Orthopair Uncertain Linguistic Power Muirhead Mean Operators
Keywords:
q-rung orthopair uncertain linguistic set, cross -entropy, attribute weights, q-rung orthopair uncertain linguistic power Muirhead mean, multi-attribute group decision makingAbstract
Q-rung orthopair uncertain linguistic sets (q-ROULSs) are a powerful tool for describing ambiguity and uncertainty of linguistic information. In this study, considering that in most multi-attribute group decision making (MAGDM) problems, not only the quantitative evaluation information of decision makers but also the qualitative evaluation opinions should be considered. Therefore, we develop a novel MAGDM method with unknown attribute weights under the q-rung orthopair uncertain linguistic environments. We firstly propose the cross-entropy of q-ROULSs, which is utilized to solve the optimal attribute weights by a linear programming model. In order to effectively summarize the unclear language information of q-ROULSs, we extend the power Muirhead mean (PMM) operator to q-ROULSs, and propose a family of q-rung othpair uncertain linguistic power Muirhead mean (q-ROULPMM) operators. The advantage of the PMM operator is that it not only mitigates the adverse effects of too high or too low attribute values on the results, but also takes into account the interrelationships between attribute values. At the same time, some ideal properties and special cases of the q-ROULPMM operator are also studied. Further, a new method based on the proposed cross-entropy and aggregation operators is developed for solving the MAGDM problem under q-ROULSs. Finally, we carried out numerical experiments to prove the effectiveness and superiority of the method
References
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[22] Adem Pınar, Rouyendegh Babak Daneshvar, and Yavuz Selim í–zdemir. q-rung orthopair fuzzy topsis method for green supplier selection problem. Sustainability, 13(2):985, 2021. https://doi.org/10.3390/su13020985
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[26] Dejian Yu, Deng-Feng Li, Jose M Merigo, and Lincong Fang. Mapping development of linguistic decision making studies. Journal of Intelligent & Fuzzy Systems, 30(5):2727-2736, 2016. https://doi.org/10.3233/IFS-152026
[27] Zeshui Xu. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information sciences, 168(1-4):171-184, 2004. https://doi.org/10.1016/j.ins.2004.02.003
[28] Peide Liu and Fang Jin. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Information Sciences, 205:58-71, 2012. https://doi.org/10.1016/j.ins.2012.04.014
[29] Peide Liu. Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Applied Mathematical Modelling, 37(4):2430-2444, 2013. https://doi.org/10.1016/j.apm.2012.05.032
[30] Yushui Geng, Peide Liu, Fei Teng, and Zhengmin Liu. Pythagorean fuzzy uncertain linguistic todim method and their application to multiple criteria group decision making. Journal of Intelligent & Fuzzy Systems, 33(6):3383-3395, 2017. https://doi.org/10.3233/JIFS-162175
[31] Kaiyuan Bai, Xiaomin Zhu, Jun Wang, and Runtong Zhang. Power partitioned heronian mean operators for q-rung orthopair uncertain linguistic sets with their application to multiattribute group decision making. International Journal of Intelligent Systems, 35(1):3-37, 2020. https://doi.org/10.1002/int.22196
[32] Jun Wang, Runtong Zhang, Li Li, Xiaomin Zhu, and Xiaopu Shang. A novel approach to multiattribute group decision making based on q-rung orthopair uncertain linguistic information. Journal of Intelligent & Fuzzy Systems, 36(6):5565-5581, 2019. https://doi.org/10.3233/JIFS-181425
[33] Ronald R Yager. The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31(6):724-731, 2001. https://doi.org/10.1109/3468.983429
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[38] Li Li, Runtong Zhang, Jun Wang, Xiaomin Zhu, and Yuping Xing. Pythagorean fuzzy power muirhead mean operators with their application to multi-attribute decision making. Journal of Intelligent & Fuzzy Systems, 35(2):2035-2050, 2018. https://doi.org/10.3233/JIFS-171907
[39] Wuhuan Xu, Xiaopu Shang, Jun Wang, and Weizi Li. A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power muirhead mean. Symmetry, 11(3):441, 2019. https://doi.org/10.3390/sym11030441
[40] Peide Liu, Qaisar Khan, and Tahir Mahmood. Some single-valued neutrosophic power muirhead mean operators and their application to group decision making. Journal of Intelligent & Fuzzy Systems, 37(2):2515-2537, 2019. https://doi.org/10.3233/JIFS-182774
[41] Zhengmin Liu, Hongxue Xu, Yuannian Yu, and Junqing Li. Some q-rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making. International Journal of Intelligent Systems, 34(10):2521-2555, 2019. https://doi.org/10.1002/int.22159
[42] Zhengmin Liu, Lin Li, and Junqing Li. q-rung orthopair uncertain linguistic partitioned bonferroni mean operators and its application to multiple attribute decision-making method. International Journal of Intelligent Systems, 34(10):2490-2520, 2019. https://doi.org/10.1002/int.22158
[43] Xiaowen Qi, Changyong Liang, and Junling Zhang. Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment. Computers & Industrial Engineering, 79:52-64, 2015. https://doi.org/10.1016/j.cie.2014.10.017
[44] Peide Liu, Zhengmin Liu, and Xin Zhang. Some intuitionistic uncertain linguistic heronian mean operators and their application to group decision making. Applied Mathematics and Computation, 230:570-586, 2014. https://doi.org/10.1016/j.amc.2013.12.133
[45] Peide Liu, Yubao Chen, and Yanchang Chu. Intuitionistic uncertain linguistic weighted bonferroni owa operator and its application to multiple attribute decision making. Cybernetics and Systems, 45(5):418-438, 2014. https://doi.org/10.1080/01969722.2014.929348
[46] Chao Liu, Guolin Tang, and Peide Liu. An approach to multicriteria group decision-making with unknown weight information based on pythagorean fuzzy uncertain linguistic aggregation operators. Mathematical problems in Engineering, 2017, 2017. https://doi.org/10.1155/2017/6414020
[47] Rosa M Rodriguez, Luis Martinez, and Francisco Herrera. Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on fuzzy systems, 20(1):109-119, 2011. https://doi.org/10.1109/TFUZZ.2011.2170076
[48] Qi Pang, Hai Wang, and Zeshui Xu. Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369:128-143, 2016. https://doi.org/10.1016/j.ins.2016.06.021
[2] Krassimir Atanassov. Intuitionistic fuzzy sets. International Journal Bioautomation, 20:1, 2016. https://doi.org/10.1016/S0165-0114(86)80034-3
[3] Ronald R Yager. Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4):958-965, 2013. https://doi.org/10.1109/TFUZZ.2013.2278989
[4] Shikha Maheshwari and Amit Srivastava. Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis. Journal of Applied Analysis & Computation, 6(3):772-789, 2016. https://doi.org/10.11948/2016050
[5] Mahatab Uddin Molla, Bibhas C Giri, and Pranab Biswas. Extended promethee method with pythagorean fuzzy sets for medical diagnosis problems. Soft Computing, pages 1-10, 2021.
[6] Wen-Sheng Chou. New algorithm of similarity measures for pattern-recognition problems. Journal of Testing and Evaluation, 44(4):1473-1484, 2016. https://doi.org/10.1520/JTE20140319
[7] Shyi-Ming Chen, Shou-Hsiung Cheng, and Tzu-Chun Lan. A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Information Sciences, 343:15-40, 2016. https://doi.org/10.1016/j.ins.2016.01.040
[8] Murat Olgun, Mehmet íœnver, and Seyhmus Yardımcı. Pythagorean fuzzy points and applications in pattern recognition and pythagorean fuzzy topologies. Soft Computing, pages 1-8, 2021. https://doi.org/10.1007/s00500-020-05522-2
[9] Zhong Wang, Zeshui Xu, Shousheng Liu, and Zeqing Yao. Direct clustering analysis based on intuitionistic fuzzy implication. Applied Soft Computing, 23:1-8, 2014. https://doi.org/10.1016/j.asoc.2014.03.037
[10] Zhong Wang, Zeshui Xu, Shousheng Liu, and Jian Tang. A netting clustering analysis method under intuitionistic fuzzy environment. Applied Soft Computing, 11(8):5558-5564, 2011. https://doi.org/10.1016/j.asoc.2011.05.004
[11] Zhenhua Zhang, Yong Hu, Chao Ma, Jinhui Xu, Shenguo Yuan, and Zhao Chen. Incentivepunitive risk function with interval valued intuitionistic fuzzy information for outsourced software project risk assessment. Journal of Intelligent & Fuzzy Systems, 32(5):3749-3760, 2017. https://doi.org/10.3233/JIFS-169307
[12] Ningxin Xie, Zhaowen Li, and Gangqiang Zhang. An intuitionistic fuzzy soft set method for stochastic decision-making applying prospect theory and grey relational analysis. Journal of Intelligent & Fuzzy Systems, 33(1):15-25, 2017. https://doi.org/10.3233/JIFS-16013
[13] Xiaomin Zhu, Kaiyuan Bai, Jun Wang, Runtong Zhang, and Yuping Xing. Pythagorean fuzzy interaction power partitioned bonferroni means with applications to multi-attribute group decision making. Journal of Intelligent & Fuzzy Systems, 36(4):3423-3438, 2019. https://doi.org/10.3233/JIFS-181171
[14] Liguo Fei and Yong Deng. Multi-criteria decision making in pythagorean fuzzy environment. Applied Intelligence, 50(2):537-561, 2020. https://doi.org/10.1007/s10489-019-01532-2
[15] Ronald R Yager. Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5):1222-1230, 2016. https://doi.org/10.1109/TFUZZ.2016.2604005
[16] Peide Liu and Peng Wang. Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems, 33(2):259-280, 2018. https://doi.org/10.1002/int.21927
[17] Peide Liu and Peng Wang. Multiple-attribute decision-making based on archimedean bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Transactions on Fuzzy systems, 27(5):834- 848, 2018. https://doi.org/10.1109/TFUZZ.2018.2826452
[18] Adjei Peter Darko and Decui Liang. 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, 2020. https://doi.org/10.1016/j.engappai.2019.103259
[19] Wen Sheng Du. Minkowski-type distance measures for generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 33(4):802-817, 2018. https://doi.org/10.1002/int.21968
[20] Decui Liang, Yinrunjie Zhang, and Wen Cao. q-rung orthopair fuzzy choquet integral aggregation and its application in heterogeneous multicriteria two-sided matching decision making. International Journal of Intelligent Systems, 34(12):3275-3301, 2019. https://doi.org/10.1002/int.22194
[21] Liuxin Chen, Nanfang Luo, and Xiaoling Gou. A novel q-rung orthopair fuzzy todim approach for multi-criteria group decision making based on shapley value and relative entropy. Journal of Intelligent & Fuzzy Systems, (Preprint):1-16.
[22] Adem Pınar, Rouyendegh Babak Daneshvar, and Yavuz Selim í–zdemir. q-rung orthopair fuzzy topsis method for green supplier selection problem. Sustainability, 13(2):985, 2021. https://doi.org/10.3390/su13020985
[23] Jia-Wei Gong, Qiang Li, Linsen Yin, and Hu-Chen Liu. Undergraduate teaching audit and evaluation using an extended mabac method under q-rung orthopair fuzzy environment. International Journal of Intelligent Systems, 35(12):1912-1933, 2020. https://doi.org/10.1002/int.22278
[24] Xindong Peng and Zhigang Luo. A review of q-rung orthopair fuzzy information: bibliometrics and future directions. Artificial Intelligence Review, pages 1-70, 2021. https://doi.org/10.1007/s10462-020-09926-2
[25] Kaiyuan Bai, Xiaomin Zhu, Jun Wang, and Runtong Zhang. Some partitioned maclaurin symmetric mean based on q-rung orthopair fuzzy information for dealing with multi-attribute group decision making. Symmetry, 10(9):383, 2018. https://doi.org/10.3390/sym10090383
[26] Dejian Yu, Deng-Feng Li, Jose M Merigo, and Lincong Fang. Mapping development of linguistic decision making studies. Journal of Intelligent & Fuzzy Systems, 30(5):2727-2736, 2016. https://doi.org/10.3233/IFS-152026
[27] Zeshui Xu. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information sciences, 168(1-4):171-184, 2004. https://doi.org/10.1016/j.ins.2004.02.003
[28] Peide Liu and Fang Jin. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Information Sciences, 205:58-71, 2012. https://doi.org/10.1016/j.ins.2012.04.014
[29] Peide Liu. Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Applied Mathematical Modelling, 37(4):2430-2444, 2013. https://doi.org/10.1016/j.apm.2012.05.032
[30] Yushui Geng, Peide Liu, Fei Teng, and Zhengmin Liu. Pythagorean fuzzy uncertain linguistic todim method and their application to multiple criteria group decision making. Journal of Intelligent & Fuzzy Systems, 33(6):3383-3395, 2017. https://doi.org/10.3233/JIFS-162175
[31] Kaiyuan Bai, Xiaomin Zhu, Jun Wang, and Runtong Zhang. Power partitioned heronian mean operators for q-rung orthopair uncertain linguistic sets with their application to multiattribute group decision making. International Journal of Intelligent Systems, 35(1):3-37, 2020. https://doi.org/10.1002/int.22196
[32] Jun Wang, Runtong Zhang, Li Li, Xiaomin Zhu, and Xiaopu Shang. A novel approach to multiattribute group decision making based on q-rung orthopair uncertain linguistic information. Journal of Intelligent & Fuzzy Systems, 36(6):5565-5581, 2019. https://doi.org/10.3233/JIFS-181425
[33] Ronald R Yager. The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31(6):724-731, 2001. https://doi.org/10.1109/3468.983429
[34] Carlo Bonferroni. Sulle medie multiple di potenze. Bollettino dell'Unione Matematica Italiana, 5(3-4):267-270, 1950.
[35] Stanislav S'ykora. Mathematical means and averages: Generalized heronian means. Stan's Library: Castano Primo, Italy, 2009.
[36] Robert Franklin Muirhead. Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21:144-162, 1902. https://doi.org/10.1017/S001309150003460X
[37] Colin Maclaurin. A second letter to martin folkes, esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans Roy Soc London Ser A, 36(1729):59-96, 1729. https://doi.org/10.1098/rstl.1729.0011
[38] Li Li, Runtong Zhang, Jun Wang, Xiaomin Zhu, and Yuping Xing. Pythagorean fuzzy power muirhead mean operators with their application to multi-attribute decision making. Journal of Intelligent & Fuzzy Systems, 35(2):2035-2050, 2018. https://doi.org/10.3233/JIFS-171907
[39] Wuhuan Xu, Xiaopu Shang, Jun Wang, and Weizi Li. A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power muirhead mean. Symmetry, 11(3):441, 2019. https://doi.org/10.3390/sym11030441
[40] Peide Liu, Qaisar Khan, and Tahir Mahmood. Some single-valued neutrosophic power muirhead mean operators and their application to group decision making. Journal of Intelligent & Fuzzy Systems, 37(2):2515-2537, 2019. https://doi.org/10.3233/JIFS-182774
[41] Zhengmin Liu, Hongxue Xu, Yuannian Yu, and Junqing Li. Some q-rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making. International Journal of Intelligent Systems, 34(10):2521-2555, 2019. https://doi.org/10.1002/int.22159
[42] Zhengmin Liu, Lin Li, and Junqing Li. q-rung orthopair uncertain linguistic partitioned bonferroni mean operators and its application to multiple attribute decision-making method. International Journal of Intelligent Systems, 34(10):2490-2520, 2019. https://doi.org/10.1002/int.22158
[43] Xiaowen Qi, Changyong Liang, and Junling Zhang. Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment. Computers & Industrial Engineering, 79:52-64, 2015. https://doi.org/10.1016/j.cie.2014.10.017
[44] Peide Liu, Zhengmin Liu, and Xin Zhang. Some intuitionistic uncertain linguistic heronian mean operators and their application to group decision making. Applied Mathematics and Computation, 230:570-586, 2014. https://doi.org/10.1016/j.amc.2013.12.133
[45] Peide Liu, Yubao Chen, and Yanchang Chu. Intuitionistic uncertain linguistic weighted bonferroni owa operator and its application to multiple attribute decision making. Cybernetics and Systems, 45(5):418-438, 2014. https://doi.org/10.1080/01969722.2014.929348
[46] Chao Liu, Guolin Tang, and Peide Liu. An approach to multicriteria group decision-making with unknown weight information based on pythagorean fuzzy uncertain linguistic aggregation operators. Mathematical problems in Engineering, 2017, 2017. https://doi.org/10.1155/2017/6414020
[47] Rosa M Rodriguez, Luis Martinez, and Francisco Herrera. Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on fuzzy systems, 20(1):109-119, 2011. https://doi.org/10.1109/TFUZZ.2011.2170076
[48] Qi Pang, Hai Wang, and Zeshui Xu. Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369:128-143, 2016. https://doi.org/10.1016/j.ins.2016.06.021
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