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Centroid and Graded Mean Ranking Methods for Intuitionistic Trapezoidal Dense Fuzzy Set to Solve MCDM Problems of Robot Selection

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Abstract

Fuzzy ranking plays a vital role in decision-making problems and various fuzzy applications. There are plenty of ranking methods that are used to rank fuzzy numbers. However, they fail to give satisfactory results in certain situations due to the complexity of the problem. In this present study, an attempt has been made to introduce four types of ranking methods in the field of intuitionistic dense fuzzy (IDF) depending on centroid and graded mean ranking. Also, arithmetic operations based on \(\lambda _1, \lambda _2\)-cuts, fuzzy numbers, and extension principles are defined for IDF environment. A model is framed to rank MCDM problems, which are aggregated using a weighted aggregation operator and ordered using the proposed and extended ranking methods. To illustrate the proposed MCDM model under the field of IDF, the problem of robot selection is taken for war fighter robots and exoskeleton robots to help and replace humans in war and help assistive walking patients with spinal cord injuries. The result reveals that the Ripsaw and Rewalk emerge as preferable options for substituting humans in the contexts of war fighters and exoskeleton robots, respectively. To analyze the effectiveness of the ranking results, comparative and sensitivity analyses are examined. Thus, the results provide a satisfactory output.

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Acknowledgements

This work was supported by National Research Foundation(NRF) of Korea Grant funded by the Korean Government(MSIT) Grant NRF-2022R1C1C1006671.

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This work was not received any external funding source.

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Authors and Affiliations

  1. Mathematics Division, School of Advanced Sciences, Vellore Institute of Technology (Chennai Campus), Chennai, India

    Swethaa Sampathkumar & Felix Augustin

  2. Department of Mathematics, Bharathiar University, Coimbatore, 600046, India

    Samayan Narayanamoorthy

  3. Decisions Lab, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    Ali Ahmadian

  4. Department of computer science and Mathematics, Lebanese American University, Beirut, Lebanon

    Ali Ahmadian

  5. Department of Law, Economics and Human Sciences, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    Massimiliano Ferrara

  6. Department of Industrial and Management Engineering, Institute of Digital Anti-Aging Health Care, Inje University, 197 Inje-ro, Gimhae-si, Gyeongsangnam-do, 50834, Republic of Korea

    Daekook Kang

  7. Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey

    Ali Ahmadian

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  1. Swethaa Sampathkumar
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Sampathkumar, S., Augustin, F., Narayanamoorthy, S. et al. Centroid and Graded Mean Ranking Methods for Intuitionistic Trapezoidal Dense Fuzzy Set to Solve MCDM Problems of Robot Selection. Int. J. Fuzzy Syst. 26, 1958–1981 (2024). https://doi.org/10.1007/s40815-023-01647-2

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  • DOI: https://doi.org/10.1007/s40815-023-01647-2

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