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AIMS Mathematics

2022, Volume 7, Issue 2: 1678-1706. doi: 10.3934/math.2022097
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Research article

A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson's disease

  • 1.
    Deanship of Combined First Year, Umm Al-Qura University, Makkah, Saudi Arabia
  • 2.
    Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
  • 3.
    Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Pakistan
  • 4.
    University College of Jammum, Umm Al-Qura University, Makkah, Saudi Arabia
  • Received: 09 August 2021 Accepted: 25 October 2021 Published: 01 November 2021

  • MSC : 03B52, 03E72

  • The concept of spherical hesitant fuzzy set is a mathematical tool that have the ability to easily handle imprecise and uncertain information. The method of aggregation plays a great role in decision-making problems, particularly when there are more conflicting criteria. The purpose of this article is to present novel operational laws based on the Yager t-norm and t-conorm under spherical hesitant fuzzy information. Furthermore, based on the Yager operational laws, we develop the list of Yager weighted averaging and Yager weighted geometric aggregation operators. The basic fundamental properties of the proposed operators are given in detail. We design an algorithm to address the uncertainty and ambiguity information in multi-criteria group decision making (MCGDM) problems. Finally, a numerical example related to Parkinson disease is presented for the proposed model. To show the supremacy of the proposed algorithms, a comparative analysis of the proposed techniques with some existing approaches and with validity test is presented.

    Citation: Muhammad Naeem, Aziz Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Ayaz, Nejib Ghanmi. A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson's disease[J]. AIMS Mathematics, 2022, 7(2): 1678-1706. doi: 10.3934/math.2022097

    Related Papers:

  • The concept of spherical hesitant fuzzy set is a mathematical tool that have the ability to easily handle imprecise and uncertain information. The method of aggregation plays a great role in decision-making problems, particularly when there are more conflicting criteria. The purpose of this article is to present novel operational laws based on the Yager t-norm and t-conorm under spherical hesitant fuzzy information. Furthermore, based on the Yager operational laws, we develop the list of Yager weighted averaging and Yager weighted geometric aggregation operators. The basic fundamental properties of the proposed operators are given in detail. We design an algorithm to address the uncertainty and ambiguity information in multi-criteria group decision making (MCGDM) problems. Finally, a numerical example related to Parkinson disease is presented for the proposed model. To show the supremacy of the proposed algorithms, a comparative analysis of the proposed techniques with some existing approaches and with validity test is presented.


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    [1] S. Ashraf, S. Abdullah, T. Mahmood, GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems, Math. Sci., 12 (2018), 263–275. doi: 10.1007/s40096-018-0266-0. doi: 10.1007/s40096-018-0266-0
    [2] S. Ashraf, S. Abdullah, Spherical aggregation operators and their application in multiattribute group decision-making, Int. J. Intell. Syst., 34 (2019), 493–523. doi: 10.1002/int.22062. doi: 10.1002/int.22062
    [3] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, J. Intell. Fuzzy Syst., 36 (2019), 2829–2844. doi: 10.3233/JIFS-172009. doi: 10.3233/JIFS-172009
    [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 Syst., 38 (2020), 5241–5255. doi: 10.3233/JIFS-191819. doi: 10.3233/JIFS-191819
    [5] S. Ashraf, S. Abdullah, Emergency decision support modeling for COVID-19 based on spherical fuzzy information, Int. J. Intell. Syst., 35 (2020), 1601–1645. doi: 10.1002/int.22262. doi: 10.1002/int.22262
    [6] S. Ashraf, T. Mahmood, S. Abdullah, Q. Khan, Different approaches to multi-criteria group decision making problems for picture fuzzy environment, Bull. Braz. Math. Soc. New Series, 50 (2019), 373–397. doi: 10.1007/s00574-018-0103-y. doi: 10.1007/s00574-018-0103-y
    [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, in press. doi: 10.1007/s00500-020-05287-8.
    [8] 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. doi: 10.1007/s12652-019-01333-y. doi: 10.1007/s12652-019-01333-y
    [9] S. Ashraf, S. Abdullah, L. Abdullah, Child development influence environmental factors determined using spherical fuzzy distance measures, Mathematics, 7 (2019), 661. doi: 10.3390/math7080661. doi: 10.3390/math7080661
    [10] S. Ashraf, S. Abdullah, S. 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. doi: 10.3233/JIFS-181941. doi: 10.3233/JIFS-181941
    [11] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96. doi: 10.1016/S0165-0114(86)80034-3. doi: 10.1016/S0165-0114(86)80034-3
    [12] D. Bega, C. Zadikoff, Complementary & alternative management of Parkinson's disease: an evidence-based review of eastern influenced practices, J. Mov. Disord., 7 (2014), 57–66. doi: 10.14802/jmd.14009. doi: 10.14802/jmd.14009
    [13] 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. doi: 10.3390/e21121231. doi: 10.3390/e21121231
    [14] T. Y. Chen, The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making, Appl. Soft Comput., 26 (2015), 57–73. doi: 10.1016/j.asoc.2014.09.015. doi: 10.1016/j.asoc.2014.09.015
    [15] N. Chen, Z. Xu, M. Xia, Interval-valued hesitant preference relations and their applications to group decision making, Knowl. Based Syst., 37 (2013), 528–540. doi: 10.1016/j.knosys.2012.09.009. doi: 10.1016/j.knosys.2012.09.009
    [16] N. Chen, Z. Xu, M. Xia, Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Appl. Math. Model., 37 (2013), 2197–2211. doi:10.1016/j.apm.2012.04.031. doi: 10.1016/j.apm.2012.04.031
    [17] G. Deschrijver, C. Cornelis, E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Trans. Fuzzy Syst., 12 (2004), 45–61. doi: 10.1109/TFUZZ.2003.822678. doi: 10.1109/TFUZZ.2003.822678
    [18] J. X. Deng, Y. Deng, Information volume of fuzzy membership function, Int. J. Comput. Commun. Control, 16 (2021), jan. 2021. doi: 10.15837/ijccc.2021.1.4106. doi: 10.15837/ijccc.2021.1.4106
    [19] B. Farhadinia, Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets, Inf. Sci., 240 (2013), 129–144. doi: 10.1016/j.ins.2013.03.034. doi: 10.1016/j.ins.2013.03.034
    [20] X. Guan, G. Sun, X. Yi, J. Zhao, Grey relational analysis for hesitant fuzzy sets and its applications to multi attribute decision-making, Math. Probl. Eng., 2018 (2018), 7436054. doi: 10.1155/2018/7436054. doi: 10.1155/2018/7436054
    [21] 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. doi: 10.3390/e21070628. doi: 10.3390/e21070628
    [22] Y. Jin, S. Ashraf, S. Abdullah, M. Qiyas, M. Bano, S. Zeng, Linguistic spherical fuzzy aggregation operators and their applications in multi-attribute decision making problems, Mathematics, 7 (2019), 413. doi: 10.3390/math7050413. doi: 10.3390/math7050413
    [23] A. Khan, S. S. Abosuliman, S. Abdullah, M. Ayaz, A decision support model for hotel recommendation based on the online consumer reviews using logarithmic spherical hesitant fuzzy information, Entropy, 23 (2021), 432. doi: 10.3390/e23040432. doi: 10.3390/e23040432
    [24] A. Khan, S. S. Abosuliman, S. Ashraf, S. Abdullah, Hospital admission and care of COVID-19 patients problem based on spherical hesitant fuzzy decision support system, Int. J. Intell. Syst., 36 (2021), 4167–4209. doi: 10.1002/int.22455. doi: 10.1002/int.22455
    [25] G. Kou, O. O. Akdeniz, H. Dinçer, S. Yüksel, Fintech investments in European banks: a hybrid IT2 fuzzy multidimensional decision-making approach, Financ. Innov., 7 (2021), 39. doi: 10.1186/s40854-021-00256-y. doi: 10.1186/s40854-021-00256-y
    [26] D. Liang, Z. Xu, The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets, Appl. Soft Comput., 60 (2017), 167–179. doi: 10.1016/j.asoc.2017.06.034. doi: 10.1016/j.asoc.2017.06.034
    [27] G. Li, G. Kou, Y. Peng, Heterogeneous large-scale group decision making using fuzzy cluster analysis and its application to emergency response plan selection, IEEE Trans. Syst. Man Cybern., 2021, 1–13. doi: 10.1109/TSMC.2021.3068759. doi: 10.1109/TSMC.2021.3068759
    [28] T. Mahmood, A novel approach towards bipolar soft sets and their applications, J. Math., 2020 (2020), 4690808. doi: 10.1155/2020/4690808. doi: 10.1155/2020/4690808
    [29] T. Mahmood, U. Ur Rehman, Z. Ali, R. Chinram, Jaccard and Dice similarity measures based on novel complex dual hesitant fuzzy sets and their applications, Math. Probl. Eng., 2020 (2020), 5920432. doi: 10.1155/2020/5920432. doi: 10.1155/2020/5920432
    [30] M. Naeem, A. Khan, S. Abdullah, S. Ashraf, A. A. A. Khammash, Solid waste collection system selection based on sine trigonometric spherical hesitant fuzzy aggregation information, Intell. Autom. Soft Comput., 28 (2021), 459–476. doi: 10.32604/iasc.2021.016822. doi: 10.32604/iasc.2021.016822
    [31] A. Naseer, M. Rani, S. Naz, M. I. Razzak, M. Imran, G. Xu, Refining Parkinson's neurological disorder identification through deep transfer learning, Neural Comput. Applic., 32 (2020), 839–854. doi: 10.1007/s00521-019-04069-0. doi: 10.1007/s00521-019-04069-0
    [32] X. Peng, Y. Yang, Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making, Int. J. Intell. Syst., 31 (2016), 989–1020. doi: 10.1002/int.21814. doi: 10.1002/int.21814
    [33] A. Pinar, F. E. Boran, A q-rung orthopair fuzzy multi-criteria group decision making method for supplier selection based on a novel distance measure, Int. J. Mach. Learn. Cyber., 11 (2020), 1749–1780. doi: 10.1007/s13042-020-01070-1. doi: 10.1007/s13042-020-01070-1
    [34] X. Peng, H. Yuan, Y. Yang, Pythagorean fuzzy information measures and their applications, Int. J. Intell. Syst., 32 (2017), 991–1029. doi: 10.1002/int.21880. doi: 10.1002/int.21880
    [35] G. Qian, H. Wang, X. Feng, Generalized hesitant fuzzy sets and their application in decision support system, Knowl. Based Syst., 37 (2013), 357–365. doi: 10.1016/j.knosys.2012.08.019. doi: 10.1016/j.knosys.2012.08.019
    [36] 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. doi: 10.3233/JIFS-181922. doi: 10.3233/JIFS-181922
    [37] M. Riaz, A. Razzaq, H. Kalsoom, D. Pamučar, H. M. Athar Farid, Y. M. Chu, q-Rung orthopair fuzzy geometric aggregation operators based on generalized and group-generalized parameters with application to water loss management, Symmetry, 12 (2020), 1236. doi: 10.3390/sym12081236. doi: 10.3390/sym12081236
    [38] P. Ren, Z. Xu, X. Gou, Pythagorean fuzzy TODIM approach to multi-criteria decision making, Appl. Soft Comput., 42 (2016), 246–259. doi: 10.1016/j.asoc.2015.12.020. doi: 10.1016/j.asoc.2015.12.020
    [39] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529–539. doi: 10.1002/int.20418. doi: 10.1002/int.20418
    [40] Z. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans Fuzzy Syst., 15 (2007), 1179–1187. doi: 10.1109/TFUZZ.2006.890678. doi: 10.1109/TFUZZ.2006.890678
    [41] Z. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35 (2006), 417–433. doi: 10.1080/03081070600574353. doi: 10.1080/03081070600574353
    [42] Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inf. Sci., 181 (2011), 2128–2138. doi: 10.1016/j.ins.2011.01.028. doi: 10.1016/j.ins.2011.01.028
    [43] L. Xu, Y. Liu, H. Liu, Some improved q-rung orthopair fuzzy aggregation operators and their applications to multiattribute group decision-making, Math. Probl. Eng. 2019 (2019), 2036728. doi: 10.1155/2019/2036728. doi: 10.1155/2019/2036728
    [44] L. Xu, Y. Liu, H. Liu, On the conjunction of possibility measures under intuitionistic evidence sets, J. Ambient Intell. Humaniz. Comput., 12 (2021), 7827–7836. doi: 10.1007/s12652-020-02508-8. doi: 10.1007/s12652-020-02508-8
    [45] Y. Xue, Y. Deng, Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets, App. Intell., 12 (2021), 1–10. doi: 10.1007/s10489-021-02216-6. doi: 10.1007/s10489-021-02216-6
    [46] G. Wei, X. Zhao, R. Lin, Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making, Int. J. Comput., 3 (2010), 84–95. doi: 10.1080/18756891.2010.9727679. doi: 10.1080/18756891.2010.9727679
    [47] R. R. Yager, Pythagorean fuzzy subsets, In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. doi: 10.1109/IFSA-NAFIPS.2013.6608375.
    [48] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans Fuzzy Syst., 22 (2014), 958–965. doi: 10.1109/TFUZZ.2013.2278989. doi: 10.1109/TFUZZ.2013.2278989
    [49] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans Fuzzy Syst., 25 (2017), 1222–1230. doi: 10.1109/TFUZZ.2016.2604005. doi: 10.1109/TFUZZ.2016.2604005
    [50] D. Yu, G. Kou, Z. Xu, S. Shi, Analysis of collaboration evolution in AHP research: 1982–2018, Int. J. Inf. Technol. Decis. Mak., 20 (2021), 7–36. doi: 10.1142/S0219622020500406. doi: 10.1142/S0219622020500406
    [51] L. A. Zadeh, Fuzzy sets, Inf. Cont., 8 (1965), 338–353. doi: 10.1016/S0019-9958(65)90241-X. doi: 10.1016/S0019-9958(65)90241-X
    [52] S. Zeng, A. Hussain, T. Mahmood, M. Irfan Ali, S. Ashraf, M. Munir, Covering-based spherical fuzzy rough set model hybrid with TOPSIS for multi-attribute decision-making, Symmetry, 11 (2019), 547. doi: 10.3390/sym11040547. doi: 10.3390/sym11040547
    [53] X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061–1078. doi: 10.1002/int.21676. doi: 10.1002/int.21676
    [54] X. Zhang, A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making, Int. J. Intell. Syst., 31 (2016), 593–611. doi: 10.1002/int.21796. doi: 10.1002/int.21796
    [55] X. Zhang, Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods, Inf. Sci., 330 (2016), 104–124. doi: 10.1016/j.ins.2015.10.012. doi: 10.1016/j.ins.2015.10.012
    [56] R. Zhang, J. Wang, X. Zhu, M. Xia, M. Yu, Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multiattribute group decision-making, Complexity, 2017 (2017), 5937376. doi: 10.1155/2017/5937376. doi: 10.1155/2017/5937376
    [57] J. Zhang, G. Kou, Y. Peng, Y. Zhang, Estimating priorities from relative deviations in pairwise comparison matrices, Inf. Sci., 552 (2021), 310–327. doi: 10.1016/j.ins.2020.12.008. doi: 10.1016/j.ins.2020.12.008
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