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<p>In this study, we propose a 4-dimensional multi-item, multi-objective fractional transportation problem where the parameters operate within a Neutrosophic environment. A corresponding deterministic model for the problem is developed, where each objective’s marginal evaluation is assessed using 3 unique membership functions—truth; indeterminacy; and falsity—within the Neutrosophic framework. These evaluations are further distinguished by different types of membership functions, including linear and nonlinear, providing decision-makers with the flexibility to select the function that best meets their requirements. The proposed Neutrosophic optimization technique is tested on existing numerical problems, demonstrating its validity and practicality. The model’s effectiveness is illustrated through a numerical example, with results analyzed and discussed. In conclusion, findings are summarized, accompanied by recommendations for future research directions.</p>

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A neutrosophic multi-objective multi-item 4-dimensional fractional transportation problem

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • A. N. Revathi,
  • Nachiappan Angappan,
  • Salahuddin

摘要

In this study, we propose a 4-dimensional multi-item, multi-objective fractional transportation problem where the parameters operate within a Neutrosophic environment. A corresponding deterministic model for the problem is developed, where each objective’s marginal evaluation is assessed using 3 unique membership functions—truth; indeterminacy; and falsity—within the Neutrosophic framework. These evaluations are further distinguished by different types of membership functions, including linear and nonlinear, providing decision-makers with the flexibility to select the function that best meets their requirements. The proposed Neutrosophic optimization technique is tested on existing numerical problems, demonstrating its validity and practicality. The model’s effectiveness is illustrated through a numerical example, with results analyzed and discussed. In conclusion, findings are summarized, accompanied by recommendations for future research directions.