Spherical q-linear Diophantine fuzzy aggregation information: Application in decision support systems

Shahzaib Ashraf; Huzaira Razzaque; Muhammad Naeem; Thongchai Botmart; Shahzaib Ashraf; Huzaira Razzaque; Muhammad Naeem; Thongchai Botmart

doi:10.3934/math.2023337

AIMS Mathematics

2023, Volume 8, Issue 3: 6651-6681. doi: 10.3934/math.2023337

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Research article

Spherical q-linear Diophantine fuzzy aggregation information: Application in decision support systems

1.
Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan
2.
Department of Mathematics, Deanship of Applied sciences, Umm Al-Qura University, Makkah, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 17 August 2022 Revised: 19 October 2022 Accepted: 05 December 2022 Published: 06 January 2023

The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.
- spherical q-linear Diophantine fuzzy set,
- operational laws,
- aggregation operators,
- decision making
Citation: Shahzaib Ashraf, Huzaira Razzaque, Muhammad Naeem, Thongchai Botmart. Spherical q-linear Diophantine fuzzy aggregation information: Application in decision support systems[J]. AIMS Mathematics, 2023, 8(3): 6651-6681. doi: 10.3934/math.2023337

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Abstract

The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.

References

[1]	K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31 (1989), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4 doi: 10.1016/0165-0114(89)90205-4
[2]	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
[3]	A. O. Almagrabi, S. Abdullah, M. Shams, Y. D. 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. https://doi.org/10.1007/s12652-021-03130-y doi: 10.1007/s12652-021-03130-y
[4]	S. Ashraf, S. Abdullah, M. Aslam, Symmetric sum based aggregation operators for spherical fuzzy information: Application in multi-attribute group decision making problem, J. Intell. Fuzzy Systs., 38 (2020), 5241–5255. https://doi.org/10.3233/JIFS-191819 doi: 10.3233/JIFS-191819
[5]	S. Ashraf, S. Abdullah, L. Abdullah, Child development influence environmental factors determined using spherical fuzzy distance measures, Mathematics, 7 (2019), 661. https://doi.org/10.3390/math7080661 doi: 10.3390/math7080661
[6]	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 Systs., 36 (2019), 6089–6102. https://doi.org/10.3233/JIFS-181941 doi: 10.3233/JIFS-181941
[7]	S. Ashraf, S. Abdullah, A. O. Almagrabi, A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19, Soft Comput., 2020. https://doi.org/10.1007/s00500-020-05287-8
[8]	S. Ashraf, S. Abdullah, Emergency decision support modeling for COVID-19 based on spherical fuzzy information, Int. J. Intell. Syst., 35 (2020), 1601–1645. https://doi.org/10.1002/int.22262 doi: 10.1002/int.22262
[9]	S. Ashraf S. Abdullah, Spherical aggregation operators and their application in multiattribute group decision-making, Int. J. Intell. Syst., 34 (2019), 493–523. https://doi.org/10.1002/int.22062 doi: 10.1002/int.22062
[10]	S. Ashraf, S. Abdullah, T. Mahmood, Spherical fuzzy Dombi aggregation operators and their application in group decision making problems, J Ambient Intell. Human. Comput., 11 (2020), 2731–2749. https://doi.org/10.1007/s12652-019-01333-y
[11]	S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, Spherical fuzzy sets and their applications in multi-attribute decision making problem, J. Intell. Fuzzy Syst., 36 (2019), 2829–2844. https://doi.org/10.3233/JIFS-172009 doi: 10.3233/JIFS-172009
[12]	S. Ayub, M. Shabir, M. Riaz, M. Aslam, R. Chinram, Linear Diophantine fuzzy relations and their algebraic properties with decision making, Symmetry, 13 (2021), 945. https://doi.org/10.3390/sym13060945 doi: 10.3390/sym13060945
[13]	K. Y. Bai, X. M. Zhu, J. Wang, R. T. Zhang, Some partitioned Maclaurin symmetric mean based on q-rung orthopair fuzzy information for dealing with multi-attribute group decision making, Symmetry, 10 (2018), 383. https://doi.org/10.3390/sym10090383 doi: 10.3390/sym10090383
[14]	O. Barukab, S. Abdullah, S. Ashraf, M. Arif, S. A. Khan, A new approach to fuzzy TOPSIS method based on entropy measure under spherical fuzzy information, Entropy, 21 (2019), 1231. https://doi.org/10.3390/e21121231 doi: 10.3390/e21121231
[15]	E. Alsuwat, S. Alzahrani, H. Alsuwat, Detecting COVID-19 Utilizing Probabilistic Graphical Models, Int. J. Adv. Comput. Sci. Appl., 12 (2021), 786–793. https://doi.org/10.14569/IJACSA.2021.0120692 doi: 10.14569/IJACSA.2021.0120692
[16]	A. Iampan, G. S. Garc, M. Riaz, H. M. Athar Farid, R. Chinram, Linear Diophantine fuzzy Einstein aggregation operators for multi-criteria decision making problems, J. Math., 2021 (2021), 5548033. https://doi.org/10.1155/2021/5548033 doi: 10.1155/2021/5548033
[17]	B. Farhadinia, Similarity-based multi-criteria decision making technique of pythagorean fuzzy set, Artif. Intell. Rev., 55 (2022), 2103–2148. https://doi.org/10.1007/s10462-021-10054-8 doi: 10.1007/s10462-021-10054-8
[18]	H. M. A. Farid, M. Riaz, M. J. Khan, P. Kumam, K. Sitthithakerngkiet, Sustainable thermal power equipment supplier selection by Einstein prioritized linear Diophantine fuzzy aggregation operators, AIMS Mathematics, 7 (2022), 11201–11242. https://doi.org/10.3934/math.2022627 doi: 10.3934/math.2022627
[19]	M. A. Firozja, B. Agheli, E. B. Jamkhaneh, A new similarity measure for Pythagorean fuzzy sets, Complex Intell. Syst., 6 (2020), 67–74. https://doi.org/10.1007/s40747-019-0114-3 doi: 10.1007/s40747-019-0114-3
[20]	H. Garg, Some series of intuitionistic fuzzy interactive averaging aggregation operators, SpringerPlus, 5 (2016), 999. https://doi.org/10.1186/s40064-016-2591-9 doi: 10.1186/s40064-016-2591-9
[21]	H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, Int. J. Intell. Syst., 31 (2016), 886–920. https://doi.org/10.1002/int.21809 doi: 10.1002/int.21809
[22]	H. Garg, Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process, Int. J. Intell. Syst., 32 (2017), 597–630. https://doi.org/10.1002/int.21860 doi: 10.1002/int.21860
[23]	H. Garg, New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications, Int. J. Intell. Syst., 34 (2019), 82–106 https://doi.org/10.1002/int.22043 doi: 10.1002/int.22043
[24]	H. Garg, Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment, Int. J. Intell. Syst., 33 (2018), 687–712. https://doi.org/10.1002/int.21949 doi: 10.1002/int.21949
[25]	F. K. Gündoğdu, C. Kahraman, A novel spherical fuzzy analytic hierarchy process and its renewable energy application, Soft Comput., 24 (2020), 4607–4621. https://doi.org/10.1007/s00500-019-04222-w doi: 10.1007/s00500-019-04222-w
[26]	F. K. Gündoğdu, C. Kahraman, A novel spherical fuzzy QFD method and its application to the linear delta robot technology development, Eng. Appl. Artif. Intel., 87 (2020), 103348. https://doi.org/10.1016/j.engappai.2019.103348 doi: 10.1016/j.engappai.2019.103348
[27]	G. Q. Huang, L. M. Xiao, W. Pedrycz, D. Pamucar, G. B. Zhang, L. Martínez, Design alternative assessment and selection: A novel Z-cloud rough number-based BWM-MABAC model, Inf. Sci., 603 (2022), 149–189. https://doi.org/10.1016/j.ins.2022.04.040 doi: 10.1016/j.ins.2022.04.040
[28]	G. Q. Huang, L. M. Xiao, G. B. Zhang, Assessment and prioritization method of key engineering characteristics for complex products based on cloud rough numbers, Adv. Eng. Inform., 49 (2021), 101309. https://doi.org/10.1016/j.aei.2021.101309 doi: 10.1016/j.aei.2021.101309
[29]	G. Q. Huang, L. M. Xiao, W. Pedrycz, G. B. Zhang, L. Martinez, Failure mode and effect analysis using T-spherical fuzzy maximizing deviation and combined comparison solution methods, IEEE T. Reliab., 2022, 1–22. https://doi.org/10.1109/TR.2022.3194057
[30]	Y. Jin, S. Ashraf, S. Abdullah, Spherical fuzzy logarithmic aggregation operators based on entropy and their application in decision support systems, Entropy, 21 (2019), 628. https://doi.org/10.3390/e21070628 doi: 10.3390/e21070628
[31]	S. M. Khalil, M. A. H. Hasab, Decision making using new distances of intuitionistic fuzzy sets and study their application in the universities, In: Intelligent and fuzzy techniques: Smart and innovative solutions, Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-51156-2_46
[32]	M. A. Khan, S. Ashraf, S. Abdullah, F. Ghani, Applications of probabilistic hesitant fuzzy rough set in decision support system, Soft Comput., 24 (2020), 16759–16774. https://doi.org/10.1007/s00500-020-04971-z doi: 10.1007/s00500-020-04971-z
[33]	M. J. Khan, P. Kumam, P. D. Liu, W. Kumam, S. Ashraf, A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system, Mathematics, 7 (2019), 742. https://doi.org/10.3390/math7080742 doi: 10.3390/math7080742
[34]	M. J. Khan, P. Kumam, P. D. Liu, W. Kumam, S. Ashraf, A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system, Mathematics, 7 (2019), 742. https://doi.org/10.3390/math7080742 doi: 10.3390/math7080742
[35]	D. Q. Li, W. Y. Zeng, Distance measure of Pythagorean fuzzy sets, Int. J. Intell. Syst., 33 (2018), 348–361. https://doi.org/10.1002/int.21934 doi: 10.1002/int.21934
[36]	Z. M. Ma, Z. S. Xu, Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, Int. J. Intell. Syst., 31 (2016), 1198–1219. https://doi.org/10.1002/int.21823 doi: 10.1002/int.21823
[37]	T. Mahmood, Z. Ali, M. Aslam, R. Chinram, Generalized Hamacher aggregation operators based on linear Diophantine uncertain linguistic setting and their applications in decision-making problems, IEEE Access, 9 (2021), 126748–126764. https://doi.org/10.1109/ACCESS.2021.3110273 doi: 10.1109/ACCESS.2021.3110273
[38]	X. D. Peng, J. G. Dai, Research on the assessment of classroom teaching quality with q-rung orthopair fuzzy information based on multiparametric similarity measure and combinative distancebased assessment, Int. J. Intell. Syst., 34 (2019), 1588–1630. https://doi.org/10.1002/int.22109 doi: 10.1002/int.22109
[39]	M. Qiyas, M. Naeem, S. Abdullah, N. Khan, A. Ali, Similarity measures based on q-rung linear Diophantine fuzzy sets and their application in logistics and supply chain management, J. Math., 2022 (2022), 4912964. https://doi.org/10.1155/2022/4912964 doi: 10.1155/2022/4912964
[40]	M. Rafiq, S. Ashraf, S. Abdullah, T. Mahmood, S. Muhammad, The cosine similarity measures of spherical fuzzy sets and their applications in decision making, J. Intell. Fuzzy Syst., 36 (2019), 6059–6073. https://doi.org/10.3233/JIFS-181922 doi: 10.3233/JIFS-181922
[41]	M. Riaz, H. M. A. Farid, M. Aslam, D. Pamucar, D. Bozanić, Novel approach for third-party reverse logistic provider selection process under linear Diophantine fuzzy prioritized aggregation operators, Symmetry, 13 (2021), 1152. https://doi.org/10.3390/sym13071152 doi: 10.3390/sym13071152
[42]	M. Riaz, M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, J. Intell. Fuzzy Syst., 37 (2019), 5417–5439. https://doi.org/10.3233/JIFS-190550 doi: 10.3233/JIFS-190550
[43]	M. Riaz, M. R. Hashmi, D. Pamucar, Y. M. Chu, Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM, Comput. Model. Eng. Sci., 126 (2021), 1125–1164. https://doi.org/10.32604/cmes.2021.013699 doi: 10.32604/cmes.2021.013699
[44]	A. Sotoudeh-Anvari, A critical review on theoretical drawbacks and mathematical incorrect assumptions in fuzzy OR methods: Review from 2010 to 2020, Appl. Soft Comput., 93 (2020), 106354. https://doi.org/10.1016/j.asoc.2020.106354 doi: 10.1016/j.asoc.2020.106354
[45]	L. M. Xiao, G. Q. Huang, W. Pedrycz, D. Pamucar, L. Martínez, G. B. Zhang, A q-rung orthopair fuzzy decision-making model with new score function and best-worst method for manufacturer selection, Inf. Sci., 608 (2022), 153–177. https://doi.org/10.1016/j.ins.2022.06.061 doi: 10.1016/j.ins.2022.06.061
[46]	L. M. Xiao, G. Q. Huang, G. B. Zhang, An integrated risk assessment method using Z-fuzzy clouds and generalized TODIM, Qual. Reliab. Eng., 38 (2022), 1909–1943. https://doi.org/10.1002/qre.3062 doi: 10.1002/qre.3062
[47]	Z. S. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35 (2006), 417–433.
[48]	Y. G. Xue, Y. Deng, Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets, Appl. Intell., 51 (2021), 6224–6233. https://doi.org/10.1007/s10489-021-02216-6 doi: 10.1007/s10489-021-02216-6
[49]	R. R. Yager, Pythagorean fuzzy subsets, 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013, 57–61.
[50]	R. R. Yager, Pythagorean membership grades in multi-criteria decision making, IEEE T. Fuzzy Syst., 22 (2014), 958–965.
[51]	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
[52]	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
[53]	S. Z. Zeng, A. Hussain, T. Mahmood, M. I. Ali, S. Ashraf, M. Munir, Covering-based spherical fuzzy rough set model hybrid with TOPSIS for multi-attribute decision-making, Symmetry, 11 (2019), 547. https://doi.org/10.3390/sym11040547 doi: 10.3390/sym11040547
[54]	S. Z. Zeng, Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach, Int. J. Intell. Syst., 32 (2017), 1136–1150. https://doi.org/10.1002/int.21886 doi: 10.1002/int.21886

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