Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 5: 9524-9548. doi: 10.3934/math.2022530
Previous Article Next Article
Research article

Improved VIKOR methodology based on $ q $-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making

  • 1.
    Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
  • 2.
    Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Pakistan
  • 3.
    Deanship of Combined First Year, Umm Al-Qura University, Makkah, Saudi Arabia
  • 4.
    Research Institute for Natural Sciences, Hanyang University, Seoul, Korea
  • Received: 22 December 2021 Revised: 31 January 2022 Accepted: 14 February 2022 Published: 14 March 2022

  • MSC : 03B52, 03E72

  • The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.

    Citation: Attaullah, Shahzaib Ashraf, Noor Rehman, Asghar Khan, Muhammad Naeem, Choonkil Park. Improved VIKOR methodology based on $ q $-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making[J]. AIMS Mathematics, 2022, 7(5): 9524-9548. doi: 10.3934/math.2022530

    Related Papers:

  • The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.


    加载中


    [1] M. I. Ali, Another view on q-rung orthopair fuzzy sets, Int. J. Intell. Syst., 33 (2018), 2139–2153. https://doi.org/10.1002/int.22007 doi: 10.1002/int.22007
    [2] 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. Humaniz. Comput., 12 (2021), 3101–3119. https://doi.org/10.1007/s12652-020-02471-4 doi: 10.1007/s12652-020-02471-4
    [3] Attaullah, S. Ashraf, N. Rehman, A Khan, C. Park, A decision making algorithm for wind power plant based on q-rung orthopair hesitant fuzzy rough aggregation information and TOPSIS, AIMS Mathematics, 7 (2022), 5241–5274. https://doi.org/10.3934/math.2022292 doi: 10.3934/math.2022292
    [4] Attaullah, S. Ashraf, N. Rehman, H. AlSalman, A. H. 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). https://doi.org/10.1155/2022/5556309 doi: 10.1155/2022/5556309
    [5] 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
    [6] 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. https://doi.org/10.3233/JIFS-172009 doi: 10.3233/JIFS-172009
    [7] S. Ashraf, N. Rehman, A. Hussain, H. AlSalman, A. H. Gumaei, q-Rung Orthopair Fuzzy Rough Einstein Aggregation Information-Based EDAS Method: Applications in Robotic Agrifarming, Comput. Intell. Neurosci., 2021 (2021), 5520264. https://doi.org/10.1155/2021/55202649 doi: 10.1155/2021/55202649
    [8] S. Ashraf, N. Rehman, H. AlSalman, A. H. 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. https://doi.org/10.1155/2022/5556309 doi: 10.1155/2022/5556309
    [9] K. T. Atanassov, Intuitionistic fuzzy sets, Springer-Verlag Berlin Heidelberg, 35 (1999), 1–137. https://doi.org/10.1007/978-3-7908-1870-3_1 doi: 10.1007/978-3-7908-1870-3_1
    [10] B. Batool, M. Ahmad, S. Abdullah, S. Ashraf, R. Chinram, Entropy based Pythagorean probabilistic hesitant fuzzy decision making technique and its application for fog-haze factor Assessment problem, Entropy, 22 (2020), 318. https://doi.org/10.3390/e22030318 doi: 10.3390/e22030318
    [11] B. Batool, S. S. Abosuliman, S. Abdullah, S. Ashraf, EDAS method for decision support modeling under the Pythagorean probabilistic hesitant fuzzy aggregation information, J. Ambient Intell. Humaniz. Comput., 2021 (2021), 1–14. https://doi.org/10.1007/s12652-021-03181-1 doi: 10.1007/s12652-021-03181-1
    [12] B. Batool, S. Abdullah, S. Ashraf, M. Ahmad, Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making, Kybernetes, 2021. https://doi.org/10.1108/K-11-2020-0747 doi: 10.1108/K-11-2020-0747
    [13] C. Cornelis, M. De Cock, E. E. Kerre, Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge, Expert syst., 20 (2003), 260–270. https://doi.org/10.1111/1468-0394.00250 doi: 10.1111/1468-0394.00250
    [14] R. Chinram, A. Hussain, T. Mahmood, M. I. Ali, EDAS Method for Multi-Criteria Group Decision Making Based on Intuitionistic Fuzzy Rough Aggregation Operators, IEEE Access, 9 (2021), 10199–10216. https://doi.org/10.1109/ACCESS.2021.3049605 doi: 10.1109/ACCESS.2021.3049605
    [15] D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst., 17 (1990), 191–209. https://doi.org/10.1080/03081079008935107 doi: 10.1080/03081079008935107
    [16] A. A. Khan, S. Ashraf, S. Abdullah, M. Qiyas, J. Luo, S. Khan, Pythagorean fuzzy Dombi aggregation operators and their application in decision support system, Symmetry, 11 (2019), 383. https://doi.org/10.3390/sym11030383 doi: 10.3390/sym11030383
    [17] M. J. Khan, P. Kumam, M. Shutaywi, Knowledge measure for the q-rung orthopair fuzzy sets, Int. J. Intell. Syst., 36 (2021), 628–655. https://doi.org/10.1002/int.22313 doi: 10.1002/int.22313
    [18] 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
    [19] R. Krishankumar, Y. Gowtham, I. Ahmed, K. S. Ravichandran, S. Kar, Solving green supplier selection problem using q-rung orthopair fuzzy-based decision framework with unknown weight information, Appl. Soft Comput., 94 (2020), 106431. https://doi.org/10.1016/j.asoc.2020.106431 doi: 10.1016/j.asoc.2020.106431
    [20] 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
    [21] D. Liu, A. Huang, Consensus reaching process for fuzzy behavioral TOPSIS method with probabilistic linguistic q-rung orthopair fuzzy set based on correlation measure, Int. J. Intell. Syst., 35 (2020), 494–528. https://doi.org/10.1002/int.22215 doi: 10.1002/int.22215
    [22] A. R. Mishra, P. Rani, R. Krishankumar, K. S. Ravichandran, S. Kar, An extended fuzzy decision-making framework using hesitant fuzzy sets for the drug selection to treat the mild symptoms of Coronavirus Disease 2019 (COVID-19), Appl. Soft Comput., 103 (2021), 107155. https://doi.org/10.1016/j.asoc.2021.107155 doi: 10.1016/j.asoc.2021.107155
    [23] T. Mahmood, A novel approach towards bipolar soft sets and their applications, J. Math., 2020 (2020), 4690808. https://doi.org/10.1155/2020/4690808 doi: 10.1155/2020/4690808
    [24] T. Mahmood, U. Ur Rehman, A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures, Int. J. Intell. Syst., 37(1) (2022), 535–567. https://doi.org/10.1002/int.22639 doi: 10.1002/int.22639
    [25] Z. Pawlak, Rough sets, In. j. comput. inf. sci., 11 (1982), 341–356. https://doi.org/10.1007/BF01001956 doi: 10.1007/BF01001956
    [26] X. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Int. J. Intell. Syst., 30 (2015), 1133–1160. https://doi.org/10.1002/int.21738 doi: 10.1002/int.21738
    [27] X. Peng, J. Dai, H. Garg, Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function, Int. J. Intell. Syst., 33 (2018), 2255-2282. https://doi.org/10.1002/int.22028 doi: 10.1002/int.22028
    [28] X. Peng, L. Liu, Information measures for q-rung orthopair fuzzy sets, Int. J. Inte. Syst., 34 (2019), 1795–1834. https://doi.org/10.1002/int.22115 doi: 10.1002/int.22115
    [29] V. Torra, Hesitant fuzzy sets, Int. J. Inte. Syst., 25 (2010), 529–539. https://doi.org/10.1002/int.20418 doi: 10.1002/int.20418
    [30] P. Wang, G. Wei, J. Wang, R. Lin, Y. Wei, Dual hesitant q-rung orthopair fuzzy hamacher aggregation operators and their applications in scheme selection of construction project, Symmetry, 11 (2019), 771. https://doi.org/10.3390/sym11060771 doi: 10.3390/sym11060771
    [31] J. Wang, G. Wei, C. Wei, Y. Wei, Dual hesitant q-Rung Orthopair fuzzy Muirhead mean operators in multiple attribute decision making, IEEE Access, 7 (2019), 67139–67166. https://doi.org/10.1109/ACCESS.2019.2917662 doi: 10.1109/ACCESS.2019.2917662
    [32] Y. Wang, Z. Shan, L. Huang, The extension of TOPSIS method for multi-attribute decision-making with q-Rung orthopair hesitant fuzzy sets, IEEE Access, 8 (2020), 165151–165167. https://doi.org/10.1109/ACCESS.2020.3018542 doi: 10.1109/ACCESS.2020.3018542
    [33] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [34] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 25 (2016), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
    [35] S. M. Yun, S. J. Lee, Intuitionistic fuzzy rough approximation operators, Int. J. Fuzzy Log. Intell., 15 (2015), 208–215. https://doi.org/10.1109/GrC.2010.182 doi: 10.1109/GrC.2010.182
    [36] 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
    [37] J. Zhan, H. M. Malik, M. Akram, Novel decision-making algorithms based on intuitionistic fuzzy rough environment, Int. J. Mach. Learn. Cybern., 10 (2019), 1459–1485. https://doi.org/10.1007/s13042-018-0827-4 doi: 10.1007/s13042-018-0827-4
    [38] X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J. Inte. Syst., 29 (2014), 1061–1078. https://doi.org/10.1002/int.21676 doi: 10.1002/int.21676
    [39] C. Zhang, Classification rule mining algorithm combining intuitionistic fuzzy rough sets and genetic algorithm, Int. J. Fuzzy Syst., 22 (2020), 1694–1715. https://doi.org/10.1007/s40815-020-00849-2 doi: 10.1007/s40815-020-00849-2
    [40] L. Zhou, W. Z. Wu, On generalized intuitionistic fuzzy rough approximation operators, Inf. Sci., 178 (2008), 2448–2465. https://doi.org/10.1016/j.ins.2008.01.012 doi: 10.1016/j.ins.2008.01.012
  • Reader Comments
  • © 2022 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1499) PDF downloads(80) Cited by(7)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(13)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog