Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making

Shahzaib Ashraf; Harish Garg; Muneeba Kousar; Sameh Askar; Shahid Abbas; Shahzaib Ashraf; Harish Garg; Muneeba Kousar; Sameh Askar; Shahid Abbas

doi:10.3934/math.2023907

AIMS Mathematics

2023, Volume 8, Issue 8: 17765-17802. doi: 10.3934/math.2023907

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Research article

Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making

1.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan
2.
School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India
3.
Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, Uttarakhand, India
4.
Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
5.
College of Technical Engineering, The Islamic University, Najaf, Iraq
6.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
7.
Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, Australia

Received: 18 April 2023 Revised: 12 May 2023 Accepted: 16 May 2023 Published: 24 May 2023
MSC : 03B52, 03E72

Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work.
- complex probabilistic hesitant fuzzy soft set,
- soft max-AND,
- soft min-OR operators,
- properties,
- algorithms,
- decision-making
Citation: Shahzaib Ashraf, Harish Garg, Muneeba Kousar, Sameh Askar, Shahid Abbas. Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making[J]. AIMS Mathematics, 2023, 8(8): 17765-17802. doi: 10.3934/math.2023907

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Abstract

Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work.

References

[1]	S. Song, G. Paulino, W. Buttlar, Simulation of crack propagation in asphalt concrete using an intrinsic cohesive zone model, J. Eng. Mech., 132 (2006), 1215–1223. http://dx.doi.org/10.1061/(ASCE)0733-9399(2006)132:11(1215) doi: 10.1061/(ASCE)0733-9399(2006)132:11(1215)
[2]	S. Abar, G. Theodoropoulos, P. Lemarinier, G. O'Hare, Agent based modelling and simulation tools: a review of the state-of-art software, Comput. Sci. Rev., 24 (2017), 13–33. http://dx.doi.org/10.1016/j.cosrev.2017.03.001 doi: 10.1016/j.cosrev.2017.03.001
[3]	F. Haan, P. Sarkar, W. Gallus, Design, construction and performance of a large tornado simulator for wind engineering applications, Eng. Struct., 30 (2008), 1146–1159. http://dx.doi.org/10.1016/j.engstruct.2007.07.010 doi: 10.1016/j.engstruct.2007.07.010
[4]	L. Zadeh, Fuzzy sets, In: Fuzzy sets, fuzzy logic, and fuzzy systems, New York: World scientific, 1996,394–432. http://dx.doi.org/10.1142/9789814261302_0021
[5]	H. Ibrahim, T. Al-Shami, A. Mhemdi, Applications of n^th power root fuzzy sets in multicriteria decision making, J. Math., 2023 (2023), 1487724. http://dx.doi.org/10.1155/2023/1487724
[6]	T. Al-shami, A. Mhemdi, Generalized frame for orthopair fuzzy sets: (m, n)-fuzzy sets and their applications to multi-criteria decision-making methods, Information, 14 (2023), 56. http://dx.doi.org/10.3390/info14010056} doi: 10.3390/info14010056
[7]	S. Ashraf, S. Abdullah, S. Khan, Fuzzy decision support modeling for internet finance soft power evaluation based on sine trigonometric Pythagorean fuzzy information, J. Ambient Intell. Human. Comput., 12 (2021), 3101–3119. http://dx.doi.org/10.1007/s12652-020-02471-4 doi: 10.1007/s12652-020-02471-4
[8]	A. Almagrabi, S. Abdullah, M. Shams, Y. Al-Otaibi, S. Ashraf, A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19, J. Ambient Intell. Human. Comput., 13 (2022), 1687–1713. http://dx.doi.org/10.1007/s12652-021-03130-y doi: 10.1007/s12652-021-03130-y
[9]	S. Ashraf, S. Abdullah, S. Zeng, H. Jin, F. Ghani, Fuzzy decision support modeling for hydrogen power plant selection based on single valued neutrosophic sine trigonometric aggregation operators, Symmetry, 12 (2020), 298. http://dx.doi.org/10.3390/sym12020298 doi: 10.3390/sym12020298
[10]	S. Ali, M. Kousar, Q. Xin, D. Pamucar, M. Hameed, R. Fayyaz, Belief and possibility belief interval-valued N-soft set and their applications in multi-attribute decision-making problems, Entropy, 23 (2021), 1498. http://dx.doi.org/10.3390/e23111498 doi: 10.3390/e23111498
[11]	J. Gong, A. Rezaeipanah, A fuzzy delay-bandwidth guaranteed routing algorithm for video conferencing services over SDN networks, Multimed. Tools Appl., in press. http://dx.doi.org/10.1007/s11042-023-14349-6
[12]	A. Taghieh, C. Zhang, K. Alattas, Y. Bouteraa, S. Rathinasamy, A. Mohammadzadeh, A predictive type-3 fuzzy control for underactuated surface vehicles, Ocean Eng., 266 (2022), 113014. http://dx.doi.org/10.1016/j.oceaneng.2022.113014 doi: 10.1016/j.oceaneng.2022.113014
[13]	D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. http://dx.doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
[14]	F. Feng, J. Cho, W. Pedrycz, H. Fujita, T. Herawan, Soft set based association rule mining, Knowl.-Based Syst., 111 (2016), 268–282. http://dx.doi.org/10.1016/j.knosys.2016.08.020 doi: 10.1016/j.knosys.2016.08.020
[15]	F. Feng, Y. Li, Soft subsets and soft product operations, Inform. Sci., 232 (2013), 44–57. http://dx.doi.org/10.1016/j.ins.2013.01.001 doi: 10.1016/j.ins.2013.01.001
[16]	A. Roy, P. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203 (2007), 412–418. http://dx.doi.org/10.1016/j.cam.2006.04.008 doi: 10.1016/j.cam.2006.04.008
[17]	Y. Zou, Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowl.-Based Syst., 21 (2008), 941–945. http://dx.doi.org/10.1016/j.knosys.2008.04.004 doi: 10.1016/j.knosys.2008.04.004
[18]	P. Maji, R. Biswas, A. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 589–602.
[19]	P. Maji, R. Biswas, A. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562. http://dx.doi.org/10.1016/S0898-1221(03)00016-6
[20]	S. Ashraf, M. Kousar, M. Hameed, Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information, Soft Comput., in press. https://doi.org/10.1007/s00500-023-08083-2
[21]	M. Shazib Hameed, S. Mukhtar, H. Khan, S. Ali, M. Haris Mateen, M. Gulzar, Pythagorean fuzzy N-Soft groups, Indonesian Journal of Electrical Engineering and Computer Science, 21 (2021), 1030–1038. http://dx.doi.org/10.11591/ijeecs.v21i2.pp1030-1038 doi: 10.11591/ijeecs.v21i2.pp1030-1038
[22]	A. Meghdadi, M. Akbarzadeh-T, Probabilistic fuzzy logic and probabilistic fuzzy systems, Proceedings of 10th IEEE International Conference on Fuzzy Systems, 2001, 1127–1130. http://dx.doi.org/10.1109/FUZZ.2001.1008853
[23]	J. Pidre, C. Carrillo, A. Lorenzo, Probabilistic model for mechanical power fluctuations in asynchronous wind parks, IEEE T. Power Syst., 18 (2003), 761–768. http://dx.doi.org/10.1109/TPWRS.2003.811201 doi: 10.1109/TPWRS.2003.811201
[24]	K. Valavanis, G. Saridis, Probabilistic modeling of intelligent robotic systems, IEEE Transactions on Robotics and Automation, 7 (1991), 164–171. http://dx.doi.org/10.1109/70.68080 doi: 10.1109/70.68080
[25]	D. Huang, S. Ma, A new radial basis probabilistic neural network model, Proceedings of Third International Conference on Signal Processing, 1996, 1449–1452. http://dx.doi.org/10.1109/ICSIGP.1996.571134
[26]	Attaullah, S. Ashraf, N. Rehman, H. AlSalman, A. Gumaei, A decision-making framework using q-rung orthopair probabilistic hesitant fuzzy rough aggregation information for the drug selection to treat COVID-19, Complexity, 2022 (2022), 5556309. http://dx.doi.org/10.1155/2022/5556309 doi: 10.1155/2022/5556309
[27]	Z. Liu, H. Li, A probabilistic fuzzy logic system for modeling and control, IEEE T. Fuzzy Syst., 13 (2005), 848–859. http://dx.doi.org/10.1109/TFUZZ.2005.859326 doi: 10.1109/TFUZZ.2005.859326
[28]	S. Chen, E. Nikolaidis, H. Cudney, R. Rosca, R. Haftka, Comparison of probabilistic and fuzzy set methods for designing under uncertainty, Proceedings of 40th structures, structural dynamics, and materials conference and exhibit, (1999), 2860–2874. http://dx.doi.org/10.2514/6.1999-1579
[29]	D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE T. Fuzzy Syst., 10 (2002), 171–186. http://dx.doi.org/10.1109/91.995119
[30]	O. Yazdanbakhsh, S. Dick, A systematic review of complex fuzzy sets and logic, Fuzzy Set. Syst., 338 (2018), 1–22. http://dx.doi.org/10.1016/j.fss.2017.01.010 doi: 10.1016/j.fss.2017.01.010
[31]	A. Alkouri, A. Salleh, Complex intuitionistic fuzzy sets, AIP Conference Proceedings, 1482 (2012), 464–470. http://dx.doi.org/10.1063/1.4757515 doi: 10.1063/1.4757515
[32]	A. Alkouri, A. Salleh, Complex Atanassov's intuitionistic fuzzy relation, Abstr. Appl. Anal., 2013 (2013), 287382. http://dx.doi.org/10.1155/2013/287382 doi: 10.1155/2013/287382
[33]	A. Alkouri, A. Salleh, Some operations on complex Atanassov's intuitionistic fuzzy sets, AIP Conference Proceedings, 1571 (2013), 987–993. http://dx.doi.org/10.1063/1.4858782 doi: 10.1063/1.4858782
[34]	M. Akram, A. Khan, J. Alcantud, G. Santos-Garcia, A hybrid decision-making framework under complex spherical fuzzy prioritized weighted aggregation operators, Expert Syst., 38 (2021), 12712. http://dx.doi.org/10.1111/exsy.12712 doi: 10.1111/exsy.12712
[35]	M. Akram, U. Amjad, J. Alcantud, G. Santos-Garcia, Complex fermatean fuzzy N-soft sets: a new hybrid model with applications, J. Ambient Intell. Human. Comput., in press. http://dx.doi.org/10.1007/s12652-021-03629-4
[36]	M. Akram, K. Zahid, J. Alcantud, A new outranking method for multicriteria decision making with complex Pythagorean fuzzy information, Neural Comput. Appl., 34 (2022), 8069–8102. http://dx.doi.org/10.1007/s00521-021-06847-1 doi: 10.1007/s00521-021-06847-1
[37]	X. Xie, Y. Tian, G. Wei, Deduction of sudden rainstorm scenarios: integrating decision makers' emotions, dynamic Bayesian network and DS evidence theory, Nat. Hazards, 116 (2023), 2935–2955. http://dx.doi.org/10.1007/s11069-022-05792-z doi: 10.1007/s11069-022-05792-z
[38]	V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529–539. http://dx.doi.org/10.1002/int.20418
[39]	Q. Pang, H. Wang, Z. Xu, Probabilistic linguistic term sets in multi-attribute group decision making, Inform. Sci., 369 (2016), 128–143. http://dx.doi.org/10.1016/j.ins.2016.06.021 doi: 10.1016/j.ins.2016.06.021
[40]	Z. Xu, W. Zhou, Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment, Fuzzy Optim. Decis. Making, 16 (2017), 481–503. http://dx.doi.org/10.1007/s10700-016-9257-5} doi: 10.1007/s10700-016-9257-5
[41]	J. Alcantud, Ranked hesitant fuzzy sets for multi-criteria multi-agent decisions, Expert Syst. Appl., 209 (2022), 118276. http://dx.doi.org/10.1016/j.eswa.2022.118276 doi: 10.1016/j.eswa.2022.118276
[42]	B. Zhu, Z. Xu, M. Xia, Dual hesitant fuzzy sets, J. Appl. Math., 2012 (2012), 879629. http://dx.doi.org/10.1155/2012/879629
[43]	N. Zhang, G. Wei, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Appl. Math. Model., 37 (2013), 4938–4947. http://dx.doi.org/10.1016/j.apm.2012.10.002 doi: 10.1016/j.apm.2012.10.002
[44]	N. Liao, H. Gao, R. Lin, G. Wei, X. Chen, An extended EDAS approach based on cumulative prospect theory for multiple attributes group decision making with probabilistic hesitant fuzzy information, Artif. Intell. Rev., 56 (2023), 2971–3003. http://dx.doi.org/10.1007/s10462-022-10244-y doi: 10.1007/s10462-022-10244-y
[45]	Z. Xu, W. Zhou, Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment, Fuzzy Optim. Decis. Making, 16 (2017), 481–503. http://dx.doi.org/10.1007/s10700-016-9257-5 doi: 10.1007/s10700-016-9257-5
[46]	F. Fatimah, D. Rosadi, R. Fajriya Hakim, J. Alcantud, N-soft sets and their decision making algorithms, Soft Comput., 22 (2018), 3829–3842. http://dx.doi.org/10.1007/s00500-017-2838-6 doi: 10.1007/s00500-017-2838-6
[47]	B. Yao, J. Liu, R. Yan, Fuzzy soft set and soft fuzzy set, Proceedings of Fourth International Conference on Natural Computation, 2008,252–255. http://dx.doi.org/10.1109/ICNC.2008.137
[48]	S. Ashraf, H. Garg, M. Kousar, An industrial disaster emergency decision-making based on China Tianjin city port explosion under complex probabilistic hesitant fuzzy soft environment, Eng. Appl. Artif. Intell., 123 (2023), 106400. https://doi.org/10.1016/j.engappai.2023.106400 doi: 10.1016/j.engappai.2023.106400
[49]	G. Arioli, F. Gazzola, A new mathematical explanation of what triggered the catastrophic torsional mode of the Tacoma Narrows Bridge, Appl. Math. Model., 39 (2015), 901–912. http://dx.doi.org/10.1016/j.apm.2014.06.022 doi: 10.1016/j.apm.2014.06.022
[50]	Plus, Complex numbers: strength, Marianne, 2017. Available from: https://plus.maths.org/content/complex-numbers-strength.
[51]	K. Babitha, S. John, Hesitant fuzzy soft sets, Journal of New Results in Science, 3 (2013), 98–107.
[52]	H. Garg, T. Mahmood, U. Rehman, Z. Ali, CHFS: complex hesitant fuzzy sets-their applications to decision making with different and innovative distance measures, CAAI T. Intell. Techno., 6 (2021), 93–122. http://dx.doi.org/10.1049/cit2.12016 doi: 10.1049/cit2.12016
[53]	X. Li, Y. Sun, Stock intelligent investment strategy based on support vector machine parameter optimization algorithm, Neural Comput. Appl., 32 (2020), 1765–1775. http://dx.doi.org/10.1007/s00521-019-04566-2 doi: 10.1007/s00521-019-04566-2
[54]	S. Lu, Y. Ding, M. Liu, Z. Yin, L. Yin, W. Zheng, Multiscale feature extraction and fusion of image and text in VQA, Int. J. Comput. Intell. Syst., 16 (2023), 54. http://dx.doi.org/10.1007/s44196-023-00233-6 doi: 10.1007/s44196-023-00233-6
[55]	Z. Peng, J. Hu, K. Shi, R. Luo, R. Huang, B. Ghosh, et al., A novel optimal bipartite consensus control scheme for unknown multi-agent systems via model-free reinforcement learning, Appl. Math. Comput., 369 (2020), 124821. http://dx.doi.org/10.1016/j.amc.2019.124821 doi: 10.1016/j.amc.2019.124821

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