Novel multiple criteria decision-making analysis under $ m $-polar fuzzy aggregation operators with application

Ghous Ali; Adeel Farooq; Mohammed M. Ali Al-Shamiri; Ghous Ali; Adeel Farooq; Mohammed M. Ali Al-Shamiri

doi:10.3934/mbe.2023166

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3566-3593. doi: 10.3934/mbe.2023166

Previous Article Next Article

Research article Special Issues

Novel multiple criteria decision-making analysis under $ m $-polar fuzzy aggregation operators with application

1.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
3.
Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha, Saudi Arabia
4.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen

Received: 03 September 2022 Revised: 30 October 2022 Accepted: 24 November 2022 Published: 06 December 2022

Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of $ m $-polar fuzzy ($ m $F) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an $ m $-polar fuzzy environment, including $ m $-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with $ m $-polar information under Yager's operations (that is, Yager's $ t $-norm and $ t $-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an $ m $F information environment through the use of Yager's operations. Our proposed AOs are named as the $ m $F Yager weighted averaging ($ m $FYWA) operator, $ m $F Yager ordered weighted averaging operator, $ m $F Yager hybrid averaging operator, $ m $F Yager weighted geometric ($ m $FYWG) operator, $ m $F Yager ordered weighted geometric operator and $ m $F Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing $ m $F information, an innovative algorithm for MCDM is established under the under the condition of $ m $FYWA and $ m $FYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated $ m $F Yager AOs are compared with existing $ m $F Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.
- accuracy function,
- algorithm,
- $ m $-polar fuzzy set,
- score function,
- Yager's $ t $-norm,
- Yager's $ t $-conorm
Citation: Ghous Ali, Adeel Farooq, Mohammed M. Ali Al-Shamiri. Novel multiple criteria decision-making analysis under $ m $-polar fuzzy aggregation operators with application[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3566-3593. doi: 10.3934/mbe.2023166

Related Papers:

Abstract

Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of $ m $-polar fuzzy ($ m $F) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an $ m $-polar fuzzy environment, including $ m $-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with $ m $-polar information under Yager's operations (that is, Yager's $ t $-norm and $ t $-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an $ m $F information environment through the use of Yager's operations. Our proposed AOs are named as the $ m $F Yager weighted averaging ($ m $FYWA) operator, $ m $F Yager ordered weighted averaging operator, $ m $F Yager hybrid averaging operator, $ m $F Yager weighted geometric ($ m $FYWG) operator, $ m $F Yager ordered weighted geometric operator and $ m $F Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing $ m $F information, an innovative algorithm for MCDM is established under the under the condition of $ m $FYWA and $ m $FYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated $ m $F Yager AOs are compared with existing $ m $F Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.

References

[1]	L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[2]	B. Zhao, H. Chen, D. Gao, L. Xu, Risk assessment of refinery unit maintenance based on fuzzy second generation curvelet neural network, Alexandria Eng. J., 59 (2020), 1823–1831. https://doi.org/10.1016/j.aej.2020.04.052 doi: 10.1016/j.aej.2020.04.052
[3]	B. Zhao, Y. Ren, D. Gao, L. Xu, Performance ratio prediction of photovoltaic pumping system based on grey clustering and second curvelet neural network, Energy, 171 (2019), 360–371. https://doi.org/10.1016/j.energy.2019.01.028 doi: 10.1016/j.energy.2019.01.028
[4]	B. Zhao, H. Song, Fuzzy Shannon wavelet finite element methodology of coupled heat transfer analysis for clearance leakage flow of single screw compressor, Eng. Comput., 37 (2021), 2493–2503. https://doi.org/10.1007/s00366-020-01259-6 doi: 10.1007/s00366-020-01259-6
[5]	Q. Song, A. Kandel, M. Schneider, Parameterized fuzzy operators in fuzzy decision making, Int. J. Intell. Syst., 18 (2003), 971–987. https://doi.org/10.1002/int.10124 doi: 10.1002/int.10124
[6]	J. M. Merigo, A. M. Gil-Lafuente, Fuzzy induced generalized aggregation operators and its application in multi-person decision making, Expert Syst. Appl., 38 (2011), 9761–9772. https://doi.org/10.1016/j.eswa.2011.02.023 doi: 10.1016/j.eswa.2011.02.023
[7]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
[8]	Z. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
[9]	Z. Xu, Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators, Knowl. Based Syst., 24 (2011), 749–760. https://doi.org/10.1016/j.knosys.2011.01.011 doi: 10.1016/j.knosys.2011.01.011
[10]	S. Zeng, W. Su, Intuitionistic fuzzy ordered weighted distance operator, Knowl. Based Syst., 24 (2011), 1224–1232. https://doi.org/10.1016/j.knosys.2011.05.013 doi: 10.1016/j.knosys.2011.05.013
[11]	Z. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. General Syst., 35 (2006), 417–433. https://doi.org/10.1080/03081070600574353 doi: 10.1080/03081070600574353
[12]	G. Wei, Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Appl. Soft Comput., 10 (2010), 423–431. https://doi.org/10.1016/j.asoc.2009.08.009 doi: 10.1016/j.asoc.2009.08.009
[13]	C. Tan, W. Yi, X. Chen, Generalized intuitionistic fuzzy geometric aggregation operators and their application to multi-criteria decision making, J. Oper. Res. Soc., 66 (2015), 1919–1938. https://doi.org/10.1057/jors.2014.104 doi: 10.1057/jors.2014.104
[14]	R. R. Yager, Pythagorean fuzzy subsets, in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, (2013), 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
[15]	X. Peng, Y. Yang, Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators, Int. J. Intell. Syst., 31 (2016), 444–487. https://doi.org/10.1002/int.21790 doi: 10.1002/int.21790
[16]	H. Garg, K. Kumar, Power geometric aggregation operators based on connection number of set pair analysis under intuitionistic fuzzy environment, Arabian J. Sci. Eng., 45 (2020), 2049–2063. https://doi.org/10.1007/s13369-019-03961-0 doi: 10.1007/s13369-019-03961-0
[17]	G. Shahzadi, M. Akram, A. N. Al-Kenani, Decision-making approach under Pythagorean fuzzy Yager weighted operators, Mathematics, 8 (2020), 70. https://doi.org/10.3390/math8010070 doi: 10.3390/math8010070
[18]	Z. Ali, T. Mahmood, M. S. Yang, Complex $T$-spherical fuzzy aggregation operators with application to multi-attribute decision making, Symmetry, 12 (2020), 1311. https://doi.org/10.3390/sym12081311 doi: 10.3390/sym12081311
[19]	S. Ashraf, S. Abdullah, T. Mahmood, Spherical fuzzy Dombi aggregation operators and their application in group decision making problems, J. Ambient Intell. Humaniz. Comput., 11 (2020), 2731–2749. https://doi.org/10.1007/s12652-019-01333-y} doi: 10.1007/s12652-019-01333-y
[20]	G. Wei, F. E. Alsaadi, T. Hayat, A. Alsaedi, Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making, Int. J. Fuzzy Syst., 20 (2018), 1–12. https://doi.org/10.1007/s40815-017-0338-6 doi: 10.1007/s40815-017-0338-6
[21]	C. Jana, M. Pal, J. Q. Wang, Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process, J. Ambient Intell. Humaniz. Comput., 10 (2019), 3533–3549. https://doi.org/10.1007/s12652-018-1076-9 doi: 10.1007/s12652-018-1076-9
[22]	C. Jana, M. Pal, J. Q. Wang, Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making, Soft Comput., 24 (2020), 3631–3646. https://doi.org/10.1007/s00500-019-04130-z doi: 10.1007/s00500-019-04130-z
[23]	J. Chen, S. Li, S. Ma, X. Wang, $m$-polar fuzzy sets: An extension of bipolar fuzzy sets, The Scientific World Journal, 2014 (2014), 416530. https://doi.org/10.1155/2014/416530 doi: 10.1155/2014/416530
[24]	N. Waseem, M. Akram, J. C. R. Alcantud, Multi-attribute decision-making based on $m$-polar fuzzy Hamacher aggregation operators, Symmetry, 11 (2019), 1498. https://doi.org/10.3390/sym11121498 doi: 10.3390/sym11121498
[25]	A. Z. Khameneh, A. Kilicman, $m$-polar fuzzy soft weighted aggregation operators and their applications in group decision-making, Symmetry, 10 (2018), 636. https://doi.org/10.3390/sym10110636 doi: 10.3390/sym10110636
[26]	M. Akram, N. Yaqoob, G. Ali, W. Chammam, Extensions of Dombi aggregation operators for decision making under $m$-polar fuzzy information, J. Math., 2020 (2020), 4739567. https://doi.org/10.1155/2020/4739567 doi: 10.1155/2020/4739567
[27]	S. Naz, M. Akram, M. M. A. Al-Shamiri, M. M. Khalaf, G. Yousaf, A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators, Math. Biosci. Eng., 19 (2022), 3843–3878. https://doi.org/10.3934/mbe.2022177 doi: 10.3934/mbe.2022177
[28]	H. Garg, G. Shahzadi, M. Akram, Decision-making analysis based on Fermatean fuzzy Yager aggregation operators with application in COVID-19 testing facility, Math. Prob. Eng., 2020 (2020), 7279027. https://doi.org/10.1155/2020/7279027 doi: 10.1155/2020/7279027
[29]	P. Liu, G. Shahzadi, M. Akram, Specific types of $q$-rung picture fuzzy Yager aggregation operators for decision-making, Int. J. Comput. Intell. Syst., 13 (2020), 1072–1091. https://doi.org/10.2991/ijcis.d.200717.001 doi: 10.2991/ijcis.d.200717.001
[30]	M. Akram, X. Peng, A. Sattar, Multi-criteria decision-making model using complex Pythagorean fuzzy Yager aggregation operators, Arabian J. Sci. Eng., 46 (2021), 1691–1717. https://doi.org/10.1007/s13369-020-04864-1 doi: 10.1007/s13369-020-04864-1
[31]	M. Akram, $m-$polar fuzzy graphs, in Studies in Fuzziness and Soft Computing, Springer, 371 (2019). https://doi.org/10.1007/978-3-030-03751-2
[32]	M. Akram, G. Ali, M. A. Butt, J. C. R. Alcantud, Novel MCGDM analysis under $m$-polar fuzzy soft expert sets, Neural Comput. Appl., 33 (2021), 12051–12071. https://doi.org/10.1007/s00521-021-05850-w doi: 10.1007/s00521-021-05850-w
[33]	M. Akram, G. Ali, J. C. R. Alcantud, Parameter reduction analysis under interval-valued $m$-polar fuzzy soft information, Artif. Intell. Rev., 54 (2021), 5541–5582. https://doi.org/10.1007/s10462-021-10027-x doi: 10.1007/s10462-021-10027-x
[34]	G. Ali, M. Akram, Decision-making method based on fuzzy $N$-soft expert sets, Arabian J. Sci. Eng., 45 (2020), 10381–10400. https://doi.org/10.1007/s13369-020-04733-x doi: 10.1007/s13369-020-04733-x
[35]	P. Liu, Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 83–97. https://doi.org/10.1109/TFUZZ.2013.2248736 doi: 10.1109/TFUZZ.2013.2248736
[36]	T. Mahmood, Z. Ali, K. Ullah, Q. Khan, H. AlSalman, A. Gumaei, S. M. M. Rahman, Complex Pythagorean fuzzy aggregation operators based on confidence levels and their applications, Math. Biosci. Eng., 19 (2022), 1078–1107. https://doi.org/10.3934/mbe.2022050 doi: 10.3934/mbe.2022050
[37]	Z. Xu, Q. L. Da, An overview of operators for aggregating information, Int. J. Intell. Syst., 18 (2003), 953–969. https://doi.org/10.1002/int.10127 doi: 10.1002/int.10127
[38]	R. Sahu, S. R. Dash, S. Das, Career selection of students using hybridized distance measure based on picture fuzzy set and rough set theory, Decis. Making Appl. Manage. Eng., 4 (2021), 104–126. https://doi.org/10.31181/dmame2104104s doi: 10.31181/dmame2104104s
[39]	N. Vojinović, Ž. Stević, I. Tanackov, A novel IMF SWARA-FDWGA-PESTEL analysis for assessment of healthcare system, Oper. Res. Eng. Sci. Theory Appl., 5 (2022), 139–151. https://doi.org/10.31181/oresta070422211v} doi: 10.31181/oresta070422211v
[40]	R. R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision-making, IEEE Trans. Syst. Man Cybern., 18 (1988), 183–190. https://doi.org/10.1109/21.87068 doi: 10.1109/21.87068
[41]	R. R. Yager, Aggregation operators and fuzzy systems modeling, Fuzzy Sets Syst., 67 (1994), 129–145. https://doi.org/10.1016/0165-0114(94)90082-5 doi: 10.1016/0165-0114(94)90082-5
[42]	A. Khan, M. Akram, U. Ahmad, M. M. A. Al-Shamiri, A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on 2-tuple spherical fuzzy linguistic sets, Math. Biosci. Eng., 20 (2023), 456–488. https://doi.org/10.3934/mbe.2023021 doi: 10.3934/mbe.2023021
[43]	M. Deveci, V. Simic, S. Karagoz, J. Antucheviciene, An interval type-2 fuzzy sets based Delphi approach to evaluate site selection indicators of sustainable vehicle shredding facilities, Appl. Soft Comput., 118 (2022), 108465. https://doi.org/10.1016/j.asoc.2022.108465 doi: 10.1016/j.asoc.2022.108465
[44]	M. Deveci, Site selection for hydrogen underground storage using interval type-2 hesitant fuzzy sets, Int. J. Hydrogen Energy, 43 (2018), 9353–9368. https://doi.org/10.1016/j.ijhydene.2018.03.127 doi: 10.1016/j.ijhydene.2018.03.127
[45]	X. Wang, E. Triantaphyllou, Ranking irregularities when evaluating alternatives by using aome ELECTRE methods, Omega, 36 (2008), 45–63. https://doi.org/10.1016/j.omega.2005.12.003 doi: 10.1016/j.omega.2005.12.003

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)