IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p538-d341726.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/538/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/538/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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 4.
    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 3.
    7. 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.
    8. 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.
    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 3.
    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 2.
    11. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ping Wang & Jie Wang & Guiwu Wei & Cun Wei, 2019. "Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications," Mathematics, MDPI, vol. 7(4), pages 1-23, April.
    2. Chao Song & Jian-Qiang Wang & Jun-Bo Li, 2020. "New Framework for Quality Function Deployment Using Linguistic Z-Numbers," Mathematics, MDPI, vol. 8(2), pages 1-20, February.
    3. Máximo Méndez & Mariano Frutos & Fabio Miguel & Ricardo Aguasca-Colomo, 2020. "TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    4. Mei Tang & Jie Wang & Jianping Lu & Guiwu Wei & Cun Wei & Yu Wei, 2019. "Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making," Mathematics, MDPI, vol. 7(4), pages 1-27, April.
    5. Kritana Prueksakorn & Cheng-Xu Piao & Hyunchul Ha & Taehyeung Kim, 2015. "Computational and Experimental Investigation for an Optimal Design of Industrial Windows to Allow Natural Ventilation during Wind-Driven Rain," Sustainability, MDPI, vol. 7(8), pages 1-22, August.
    6. Hualin Xie & Jinlang Zou & Hailing Jiang & Ning Zhang & Yongrok Choi, 2014. "Spatiotemporal Pattern and Driving Forces of Arable Land-Use Intensity in China: Toward Sustainable Land Management Using Emergy Analysis," Sustainability, MDPI, vol. 6(6), pages 1-17, May.
    7. Stephan E. Maurer & Andrei V. Potlogea, 2021. "Male‐biased Demand Shocks and Women's Labour Force Participation: Evidence from Large Oil Field Discoveries," Economica, London School of Economics and Political Science, vol. 88(349), pages 167-188, January.
    8. Tie Hua Zhou & Ling Wang & Keun Ho Ryu, 2015. "Supporting Keyword Search for Image Retrieval with Integration of Probabilistic Annotation," Sustainability, MDPI, vol. 7(5), pages 1-18, May.
    9. T. Karski, 2019. "Opinions and Controversies in Problem of The So-Called Idiopathic Scoliosis. Information About Etiology, New Classification and New Therapy," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 12(5), pages 9612-9616, January.
    10. Sung-Won Park & Sung-Yong Son, 2017. "Cost Analysis for a Hybrid Advanced Metering Infrastructure in Korea," Energies, MDPI, vol. 10(9), pages 1-18, September.
    11. Wesley Mendes-da-Silva, 2020. "What Makes an Article be More Cited?," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 24(6), pages 507-513.
    12. Martin Valtierra-Rodriguez & Juan Pablo Amezquita-Sanchez & Arturo Garcia-Perez & David Camarena-Martinez, 2019. "Complete Ensemble Empirical Mode Decomposition on FPGA for Condition Monitoring of Broken Bars in Induction Motors," Mathematics, MDPI, vol. 7(9), pages 1-19, August.
    13. Akca Yasar & Gokhan Ozer, 2016. "Determination the Factors that Affect the Use of Enterprise Resource Planning Information System through Technology Acceptance Model," International Journal of Business and Management, Canadian Center of Science and Education, vol. 11(10), pages 1-91, September.
    14. Julián Miranda & Angélica Flórez & Gustavo Ospina & Ciro Gamboa & Carlos Flórez & Miguel Altuve, 2020. "Proposal for a System Model for Offline Seismic Event Detection in Colombia," Future Internet, MDPI, vol. 12(12), pages 1-17, December.
    15. Wisdom Akpalu & Mintewab Bezabih, 2015. "Tenure Insecurity, Climate Variability and Renting out Decisions among Female Small-Holder Farmers in Ethiopia," Sustainability, MDPI, vol. 7(6), pages 1-16, June.
    16. Wei Chen & Shu-Yu Liu & Chih-Han Chen & Yi-Shan Lee, 2011. "Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games," Games, MDPI, vol. 2(1), pages 1-13, March.
    17. David Harborth & Sebastian Pape, 2020. "Empirically Investigating Extraneous Influences on the “APCO” Model—Childhood Brand Nostalgia and the Positivity Bias," Future Internet, MDPI, vol. 12(12), pages 1-16, December.
    18. Peterson, Willis L., 1973. "Publication Productivities Of U.S. Economics Department Graduates," Staff Papers 14105, University of Minnesota, Department of Applied Economics.
    19. Taeyeoun Roh & Yujin Jeong & Byungun Yoon, 2017. "Developing a Methodology of Structuring and Layering Technological Information in Patent Documents through Natural Language Processing," Sustainability, MDPI, vol. 9(11), pages 1-19, November.
    20. He-Yau Kang & Amy H. I. Lee & Tzu-Ting Huang, 2016. "Project Management for a Wind Turbine Construction by Applying Fuzzy Multiple Objective Linear Programming Models," Energies, MDPI, vol. 9(12), pages 1-15, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:538-:d:341726. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.