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<p>The choice of lens impacts the quality of vision, comfort, and overall eye health. By correcting vision problems such as astigmatism, nearsightedness, or farsightedness, the right lens can guarantee precise and clear vision. The multi-attribute decision-making (MADM) technique is a valuable method for data aggregation with accuracy. The central theme of this article is to develop novel aggregation operators (AOs) by giving a positive value called the priority degree under a strict priority level. We establish a novel MADM method based on an interval-valued t-spherical fuzzy set (IV-TSFS) framework and the Einstein AOs. First, we established Einstein t-norm (TNM) and t-conorm (TCNM) operations based on the IV-TSFS framework. Next, we proposed new prioritized AOs, such as IV-TSF Einstein prioritized weighted averaging (IV-TSFEPWA), IV-TSF Einstein prioritized ordered weighted averaging (IV-TSFEPOWA), IV-TSF Einstein prioritized hybrid weighted averaging (IV-TSFEPHWA), IV-TSF Einstein prioritized weighted geometric (IV-TSFEPWG), IV-TSF Einstein prioritized ordered weighted geometric (IV-TSFEPOWG), and IV-TSF Einstein prioritized hybrid weighted geometric (IV-TSFEPHWG). Some essential axioms, such as boundedness, idempotency, and monotonicity, were also discussed. Then, we developed the MADM algorithm based on the IV-TSFEPWA and IV-TSFEPWG operators, which was monitored through a real-life case study on the selection of optimal eye lens manufacturing companies based on prioritized evaluation criteria. Additionally, to validate the novelty of the established model, a comparative study with existing approach is also provided, highlighting the applicability of the established work. Ultimately, the practical implications of established AOs and solid conclusions will be discussed.</p>

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An MADM approach for the assessment of eye lenses with fuzziness of using prioritized weighted operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月30日

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  • Chengli Hu,
  • Faizan Pervaiz,
  • Jing Zhang,
  • Kifayat Ullah,
  • Muhammad Rizwan Khan,
  • Ali Raza,
  • Zeeshan Ali,
  • Shi Yin,
  • Hanen Karamti

摘要

The choice of lens impacts the quality of vision, comfort, and overall eye health. By correcting vision problems such as astigmatism, nearsightedness, or farsightedness, the right lens can guarantee precise and clear vision. The multi-attribute decision-making (MADM) technique is a valuable method for data aggregation with accuracy. The central theme of this article is to develop novel aggregation operators (AOs) by giving a positive value called the priority degree under a strict priority level. We establish a novel MADM method based on an interval-valued t-spherical fuzzy set (IV-TSFS) framework and the Einstein AOs. First, we established Einstein t-norm (TNM) and t-conorm (TCNM) operations based on the IV-TSFS framework. Next, we proposed new prioritized AOs, such as IV-TSF Einstein prioritized weighted averaging (IV-TSFEPWA), IV-TSF Einstein prioritized ordered weighted averaging (IV-TSFEPOWA), IV-TSF Einstein prioritized hybrid weighted averaging (IV-TSFEPHWA), IV-TSF Einstein prioritized weighted geometric (IV-TSFEPWG), IV-TSF Einstein prioritized ordered weighted geometric (IV-TSFEPOWG), and IV-TSF Einstein prioritized hybrid weighted geometric (IV-TSFEPHWG). Some essential axioms, such as boundedness, idempotency, and monotonicity, were also discussed. Then, we developed the MADM algorithm based on the IV-TSFEPWA and IV-TSFEPWG operators, which was monitored through a real-life case study on the selection of optimal eye lens manufacturing companies based on prioritized evaluation criteria. Additionally, to validate the novelty of the established model, a comparative study with existing approach is also provided, highlighting the applicability of the established work. Ultimately, the practical implications of established AOs and solid conclusions will be discussed.