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Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications

Author

Listed:
  • Harish Garg

    (School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, India)

  • Jeonghwan Gwak

    (Department of Software, Korea National University of Transportation, Chungju 27469, Korea)

  • Tahir Mahmood

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Zeeshan Ali

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

Abstract

The aim of this paper is to present the novel concept of Complex q-rung orthopair fuzzy set (Cq-ROFS) which is a useful tool to cope with unresolved and complicated information. It is characterized by a complex-valued membership grade and a complex-valued non-membership grade, the distinction of which is that the sum of q-powers of the real parts (imaginary parts) of the membership and non-membership grades is less than or equal to one. To explore the study, we present some basic operational laws, score and accuracy functions and investigate their properties. Further, to aggregate the given information of Cq-ROFS, we present several weighted averaging and geometric power aggregation operators named as complex q-rung orthopair fuzzy (Cq-ROF) power averaging operator, Cq-ROF power geometric operator, Cq-ROF power weighted averaging operator, Cq-ROF power weighted geometric operator, Cq-ROF hybrid averaging operator and Cq-ROF power hybrid geometric operator. Properties and special cases of the proposed approaches are discussed in detail. Moreover, the VIKOR (“VIseKriterijumska Optimizacija I Kompromisno Resenje”) method for Cq-ROFSs is introduced and its aspects discussed. Furthermore, the above mentioned approaches apply to multi-attribute decision-making problems and VIKOR methods, in which experts state their preferences in the Cq-ROF environment to demonstrate the feasibility, reliability and effectiveness of the proposed approaches. Finally, the proposed approach is compared with existing methods through numerical examples.

Suggested Citation

  • Harish Garg & Jeonghwan Gwak & Tahir Mahmood & Zeeshan Ali, 2020. "Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications," Mathematics, MDPI, vol. 8(4), pages 1-34, April.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:538-:d:341726
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    References listed on IDEAS

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    1. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    2. Harish Garg & Dimple Rani, 2019. "Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment," Group Decision and Negotiation, Springer, vol. 28(5), pages 991-1050, October.
    3. Tanuj Kumar & Rakesh Kumar Bajaj, 2014. "On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies," Journal of Mathematics, Hindawi, vol. 2014, pages 1-12, December.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    7. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    8. Abd Ulazeez M. Alkouri & Abdul Razak Salleh, 2013. "Complex Atanassov's Intuitionistic Fuzzy Relation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-18, June.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    10. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    11. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    12. Shouzhen Zeng & Jianping Chen & Xingsen Li, 2016. "A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 403-422, March.
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