Approaches to multi-attribute group decision-making based on picture fuzzy prioritized Aczel–Alsina aggregation information

Saba Ijaz; Kifayat Ullah; Maria Akram; Dragan Pamucar; Saba Ijaz; Kifayat Ullah; Maria Akram; Dragan Pamucar

doi:10.3934/math.2023847

AIMS Mathematics

2023, Volume 8, Issue 7: 16556-16583. doi: 10.3934/math.2023847

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Approaches to multi-attribute group decision-making based on picture fuzzy prioritized Aczel–Alsina aggregation information

1.
Department of Mathematics, Riphah International University (Lahore Campus), 54000, Lahore, Pakistan
2.
Department of Operations Research and Statistics, Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia
3.
College of Engineering, Yuan Ze University, Taiwan

Received: 29 November 2022 Revised: 21 February 2023 Accepted: 21 March 2023 Published: 10 May 2023
MSC : 03E52, 03E72, 28E10, 68T27, 94D05

The Aczel-Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982. They are modified forms of the algebraic t-norm and t-conorm. Furthermore, the theory of picture fuzzy values is a very valuable and appropriate technique for describing awkward and unreliable information in a real-life scenario. In this research, we analyze the theory of averaging and geometric aggregation operators (AOs) in the presence of the Aczel-Alsina operational laws and prioritization degree based on picture fuzzy (PF) information, such as the prioritized PF Aczel-Alsina average operator and prioritized PF Aczel-Alsina geometric operator. Moreover, we examine properties such as idempotency, monotonicity and boundedness for the derived operators and also evaluated some important results. Furthermore, we use the derived operators to create a system for controlling the multi-attribute decision-making problem using PF information. To show the approach's effectiveness and the developed operators' validity, a numerical example is given. Also, a comparative analysis is presented.
- picture fuzzy sets,
- Aczel-Alsina operational laws,
- prioritized aggregation operators,
- decision-making processes
Citation: Saba Ijaz, Kifayat Ullah, Maria Akram, Dragan Pamucar. Approaches to multi-attribute group decision-making based on picture fuzzy prioritized Aczel–Alsina aggregation information[J]. AIMS Mathematics, 2023, 8(7): 16556-16583. doi: 10.3934/math.2023847

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Abstract

The Aczel-Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982. They are modified forms of the algebraic t-norm and t-conorm. Furthermore, the theory of picture fuzzy values is a very valuable and appropriate technique for describing awkward and unreliable information in a real-life scenario. In this research, we analyze the theory of averaging and geometric aggregation operators (AOs) in the presence of the Aczel-Alsina operational laws and prioritization degree based on picture fuzzy (PF) information, such as the prioritized PF Aczel-Alsina average operator and prioritized PF Aczel-Alsina geometric operator. Moreover, we examine properties such as idempotency, monotonicity and boundedness for the derived operators and also evaluated some important results. Furthermore, we use the derived operators to create a system for controlling the multi-attribute decision-making problem using PF information. To show the approach's effectiveness and the developed operators' validity, a numerical example is given. Also, a comparative analysis is presented.

References

[1]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[2]	K. T. Atanasov, Intuitionistic fuzzy sets, Fuzzy set syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
[3]	K. T. Atanassov, Two theorems for intuitionistic fuzzy sets, Fuzzy set syst., 110 (2000), 267–269.
[4]	R. E. Gergin, İskender Peker, A. C. Gök Kısa, Supplier selection by integrated IFDEMATEL-IFTOPSIS Method: A case study of automotive supply industry, Decis. Making Appl. Manag. Eng., 5 (2022), 169–193.
[5]	K. Pandey, A. Mishra, P. Rani, J. Ali, R. Chakrabortty, Selecting features by utilizing intuitionistic fuzzy Entropy method, Decis. Making Appl. Manag. Eng., 6 (2023), 111–133.
[6]	M. R. Khan, K. Ullah, Q. Khan, Multi-attribute decision-making using Archimedean aggregation operator in T-spherical fuzzy environment, Rep. Mech. Eng., 4 (2023), 18–38.
[7]	R. R. Yager, Pythagorean fuzzy subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375 doi: 10.1109/IFSA-NAFIPS.2013.6608375
[8]	H. Garg, A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem, J. Intell. Fuzzy Syst., 31 (2016), 529–540.
[9]	A. Ashraf, K. Ullah, A. Hussain, M. Bari, Interval-valued picture fuzzy maclaurin symmetric mean operator with application in multiple attribute decision-making, Rep. Mech. Eng., 3 (2022), 210–226.
[10]	H. Fazlollahtabar, Mathematical modeling for sustainability evaluation in a multi-layer supply chain, J. Eng. Manag. Syst. Eng., 1 (2022), 2–14.
[11]	K. Ullah, T. Mahmood, Z. Ali, N. Jan, On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition, Complex Intell. Syst., 6 (2020), 15–27. https://doi.org/10.1007/s40747-019-0103-6 doi: 10.1007/s40747-019-0103-6
[12]	R. R. Yager, Generalized orthopair fuzzy sets, IEEE T. Fuzzy Syst., 25 (2017), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
[13]	D. Liu, X. Chen, D. Peng, Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets, Int. J. Intell. Syst., 34 (2019), 1572–1587.
[14]	H. Garg, S. M. Chen, Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets, Inform. Sci., 517 (2020), 427–447, https://doi.org/10.1016/j.ins.2019.11.035 doi: 10.1016/j.ins.2019.11.035
[15]	G. Wei, H. Gao, Y. Wei, Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 1426–1458. https://doi.org/10.1002/int.21985 doi: 10.1002/int.21985
[16]	D. Liu, D. Peng, Z. Liu, The distance measures between q-rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making, Int. J. Intell. Syst., 34 (2019), 2104–2121. https://doi.org/10.1002/int.22133 doi: 10.1002/int.22133
[17]	G. Wei, C. Wei, J. Wang, H. Gao, Y. Wei, Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization, Int. J. Intell. Syst., 34 (2019), 50–81. https://doi.org/10.1002/int.22042 doi: 10.1002/int.22042
[18]	B. C. Cuong, V. Kreinovich, Picture fuzzy sets-A new concept for computational intelligence problems, Third World Congress on Information and Communication Technologies, 2013, 1–6. https://doi.org/10.1109/WICT.2013.7113099 doi: 10.1109/WICT.2013.7113099
[19]	P. Liu, M. Munir, T. Mahmood, K. Ullah, Some similarity measures for interval-valued picture fuzzy sets and their applications in decision making, Information, 10 (2019), 369. https://doi.org/10.3390/info10120369 doi: 10.3390/info10120369
[20]	K. Ullah, Z. Ali, N. Jan, T. Mahmood, S. Maqsood, Multi-attribute decision making based on averaging aggregation operators for picture hesitant fuzzy sets, Tech. J., 23 (2018), 84–95.
[21]	I. Alshammari, P. Mani, C. Ozel, H. Garg, Multiple attribute decision making algorithm via picture fuzzy nano topological spaces, Symmetry, 13 (2021), 69. https://doi.org/10.3390/sym13010069 doi: 10.3390/sym13010069
[22]	P. Dutta, S. Ganju, Some aspects of picture fuzzy set, T. A Razmadze Math. In., 172 (2018), 164–175. https://doi.org/10.1016/j.trmi.2017.10.006 doi: 10.1016/j.trmi.2017.10.006
[23]	K. Menger, Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America, 28 (1942), 535.
[24]	I. Silambarasan, Generalized orthopair fuzzy sets based on Hamacher T-norm and T-conorm, Open J. Math. Sci., 5 (2021), 44–64. https://doi.org/10.30538/oms2021.0144 doi: 10.30538/oms2021.0144
[25]	S. Ashraf, S. Abdullah, M. Aslam, M. Qiyas, M. A. Kutbi, Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms, J. Intell. Fuzzy Syst., 36 (2019), 6089–6102. https://doi.org/10.3233/JIFS-181941 doi: 10.3233/JIFS-181941
[26]	H. Garg, Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making, Comput. Ind. Eng., 101 (2016), 53–69.
[27]	M. Xia, Z. Xu, B. Zhu, Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm, Knowl. Based Syst., 31 (2012), 78–88. https://doi.org/10.1016/j.knosys.2012.02.004 doi: 10.1016/j.knosys.2012.02.004
[28]	M. R. Seikh, U. Mandal, Some picture fuzzy aggregation operators based on Frank t-norm and t-conorm: Application to MADM process, Informatica, 45 (2021), 447–461.
[29]	P. Drygaś, On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums, Fuzzy Set Syst., 161 (2010), 149–157. https://doi.org/10.1016/j.fss.2009.09.017 doi: 10.1016/j.fss.2009.09.017
[30]	J. Aczél, C. Alsina, Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements, Aeq. Math., 25 (1982), 313–315. https://doi.org/10.1007/BF02189626 doi: 10.1007/BF02189626
[31]	T. Senapati, G. Chen, R. R. Yager, Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making, Int. J. Intell. Syst., 37 (2021), 1529–1551.
[32]	T. Senapati, G. Chen, R. Mesiar, R. R. Yager, Novel Aczel–Alsina operations-based interval-valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision-making process, Int. J. Intell. Syst., 37 (2021), 5059–5081 https://doi.org/10.1002/int.22751 doi: 10.1002/int.22751
[33]	T. Senapati, Approaches to multi-attribute decision-making based on picture fuzzy Aczel–Alsina average aggregation operators, Comput. Appl. Math., 41 (2022), 40.
[34]	A. Hussain, K. Ullah, M. N. Alshahrani, M. S. Yang, D. Pamucar, Novel Aczel–Alsina operators for pythagorean fuzzy sets with application in multi-attribute decision making, Symmetry, 14 (2022), 940. https://doi.org/10.3390/sym14050940 doi: 10.3390/sym14050940
[35]	A. Hussain, K. Ullah, M. S. Yang, D. Pamucar, Aczel-Alsina aggregation operators on t-spherical fuzzy (TSF) information with application to TSF multi-attribute decision making, IEEE Access, 10 (2022), 26011–26023.
[36]	R. R. Yager, Prioritized aggregation operators, Int. J. Approx. Reason., 48 (2008), 263–274. https://doi.org/10.1016/j.ijar.2007.08.009 doi: 10.1016/j.ijar.2007.08.009
[37]	R. R. Yager, Prioritized OWA aggregation, Fuzzy Optim. Decis Making, 8 (2009), 245–262. https://doi.org/10.1007/s10700-009-9063-4 doi: 10.1007/s10700-009-9063-4
[38]	H.-B. Yan, V.-N. Huynh, Y. Nakamori, T. Murai, On prioritized weighted aggregation in multi-criteria decision making, Expert Syst. Appl., 38 (2011), 812–823. https://doi.org/10.1016/j.eswa.2010.07.039 doi: 10.1016/j.eswa.2010.07.039
[39]	G. Wei, Picture fuzzy hamacher aggregation operators and their application to multiple attribute decision making, Fund. Inform., 157 (2018), 271–320. https://doi.org/10.3233/FI-2018-1628 doi: 10.3233/FI-2018-1628
[40]	G. Wei, Picture fuzzy aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 33 (2017), 713–724. https://doi.org/10.3233/JIFS-161798 doi: 10.3233/JIFS-161798
[41]	C. Jana, T. Senapati, M. Pal, R. R. Yager, Picture fuzzy Dombi aggregation operators: Application to MADM process, Appl. Soft Comput., 74 (2019), 99–109. https://doi.org/10.1016/j.asoc.2018.10.021 doi: 10.1016/j.asoc.2018.10.021

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