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A Novel Approached Based on T-Spherical Fuzzy Schweizer-Sklar Power Heronian Mean Operator for Evaluating Water Reuse Applications under Uncertainty

Author

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  • Qaisar Khan

    (Department of Pure and Applied Mathematics, University of Haripur, Haripur 22620, KPK, Pakistan)

  • Jeonghwan Gwak

    (Department of Software, Korea National University of Transportation, Chungju 27469, Korea
    Department of Biomedical Engineering, Korea National University of Transportation, Chungju 27469, Korea
    Department of AI Robotics Engineering, Korea National University of Transportation, Chungju 27469, Korea
    Department of IT & Energy Convergence (BK21 FOUR), Korea National University of Transportation, Chungju 27469, Korea)

  • Muhammad Shahzad

    (Department of Pure and Applied Mathematics, University of Haripur, Haripur 22620, KPK, Pakistan)

  • Muhammad Kamran Alam

    (Department of Pure and Applied Mathematics, University of Haripur, Haripur 22620, KPK, Pakistan)

Abstract

The T-Spherical Fuzzy set (T-SPHFS) is one of the core simplifications of quite a lot of fuzzy concepts such as fuzzy set (FS), intuitionistic fuzzy set (ITFS), picture fuzzy set (PIFS), Q-rung orthopair fuzzy set (Q-RUOFS), etc. T-SPHFS reveals fuzzy judgment by the degree of positive membership, degree of abstinence, degree of negative membership, and degree of refusal with relaxed conditions, and this is a more powerful mathematical tool to pair with inconsistent, indecisive, and indistinguishable information. In this article, several novel operational laws for T-SPFNs based on the Schweizer–Sklar t-norm (SSTN) and the Schweizer–Sklar t-conorm (SSTCN) are initiated, and some desirable characteristics of these operational laws are investigated. Further, maintaining the dominance of the power aggregation (POA) operators that confiscate the ramifications of the inappropriate data and Heronian mean (HEM) operators that consider the interrelationship among the input information being aggregated, we intend to focus on the T-Spherical fuzzy Schweizer–Sklar power Heronian mean (T-SPHFSSPHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power geometric Heronian mean (T-SPHFSSPGHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted Heronian mean (T-SPHFSSPWHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted geometric Heronian mean (T-SPHFSSPWGHEM) operator, and their core properties and exceptional cases in connection with the parameters. Additionally, deployed on these newly initiated aggregation operators (AOs), a novel multiple attribute decision making (MADM) model is proposed. Then, the initiated model is applied to the City of Penticton (British Columbia, Canada) to select the best choice among the accessible seven water reuse choices to manifest the practicality and potency of the preferred model and a comparison with the proffered models is also particularized.

Suggested Citation

  • Qaisar Khan & Jeonghwan Gwak & Muhammad Shahzad & Muhammad Kamran Alam, 2021. "A Novel Approached Based on T-Spherical Fuzzy Schweizer-Sklar Power Heronian Mean Operator for Evaluating Water Reuse Applications under Uncertainty," Sustainability, MDPI, vol. 13(13), pages 1-35, June.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:13:p:7108-:d:581664
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    References listed on IDEAS

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    Cited by:

    1. Wei Yang & Yongfeng Pang, 2022. "T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making," Mathematics, MDPI, vol. 10(6), pages 1-33, March.
    2. Zhiyuan Chen & Di Shen & Fuping Yu & Xinlei Tang & Zhe Zhang, 2023. "Multi-attribute decision-making method based on q-rung orthopair probabilistic hesitant fuzzy schweizer-sklar power weighted hamy mean operator," PLOS ONE, Public Library of Science, vol. 18(2), pages 1-26, February.
    3. Areeba Naseem & Kifayat Ullah & Maria Akram & Darko Božanić & Goran Ćirović, 2022. "Assessment of Smart Grid Systems for Electricity Using Power Maclaurin Symmetric Mean Operators Based on T-Spherical Fuzzy Information," Energies, MDPI, vol. 15(21), pages 1-25, October.

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