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<p>Generally, in case of transportation problem, mathematical frameworks predominantly focus on positive beliefs to manage uncertain and vague information, often overlooking the negative perspectives in decision-making. To address this gap, we introduce a four-dimensional transportation problem (4D-TP) model within a bipolar neutrosophic environment, which incorporates both positive and negative aspects of human cognition. The proposed model is formulated as a multi-item 4D-TP with breakability, aimed at maximizing profit by considering key parameters such as costs, accessibility, demands, and transportation capacities, all represented using single-valued triangular bipolar neutrosophic numbers. Unlike traditional approaches that assume uniformity in the number of routes for each origin-destination pair, our model accommodates varying numbers of routes, reflecting more realistic transportation scenarios. Furthermore, this is the first attempt to solve the 4D-TP using possibility measure associated with single-valued triangular bipolar neutrosophic number, which includes truth, indeterminacy, and falsity membership functions to capture both positive and negative dimensions. To validate the model, we provide a numerical example and solve it using the Generalized Reduced Gradient method, implemented in the LINGO-14.0 solver. Some managerial implications are also included at the end.</p>

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Bipolar neutrosophic multi-item four-dimensional transportation problem with variable routes for breakable items

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Sarbari Samanta,
  • Dipankar Chakraborty,
  • Dipak Kumar Jana

摘要

Generally, in case of transportation problem, mathematical frameworks predominantly focus on positive beliefs to manage uncertain and vague information, often overlooking the negative perspectives in decision-making. To address this gap, we introduce a four-dimensional transportation problem (4D-TP) model within a bipolar neutrosophic environment, which incorporates both positive and negative aspects of human cognition. The proposed model is formulated as a multi-item 4D-TP with breakability, aimed at maximizing profit by considering key parameters such as costs, accessibility, demands, and transportation capacities, all represented using single-valued triangular bipolar neutrosophic numbers. Unlike traditional approaches that assume uniformity in the number of routes for each origin-destination pair, our model accommodates varying numbers of routes, reflecting more realistic transportation scenarios. Furthermore, this is the first attempt to solve the 4D-TP using possibility measure associated with single-valued triangular bipolar neutrosophic number, which includes truth, indeterminacy, and falsity membership functions to capture both positive and negative dimensions. To validate the model, we provide a numerical example and solve it using the Generalized Reduced Gradient method, implemented in the LINGO-14.0 solver. Some managerial implications are also included at the end.