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AIMS Mathematics

2022, Volume 7, Issue 5: 9524-9548. doi: 10.3934/math.2022530
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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.


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