Neutrosophic Optimization in Transportation Networks: Navigating Transportation Challenges with and Without Warehouses - Kaspar, Kalaivani; Kaliyaperumal, Palanivel (International Journal of Industrial Engineering: Theory, Applications and Practice, 2024)
Neutrosophic set theory is an extension of classical set theory that deals with uncertainty, imprecision, and indeterminacy by introducing three degrees of membership, and further it offers the researchers a wide range of applications in numerous disciplines. In general, neutrosophic sets (NS) focus on the hesitant, ambiguous, and uncertain data present in real-world mathematical challenges. They are an enhanced form of crisp, fuzzy, and intuitionistic fuzzy sets. The simplest form of the neutrosophic set is a single-valued set, and it provides better outcomes than a regular NS. Recent research enhances the applications of single-valued neutrosophic sets (SVNS) through approaches like MCDM, MADM, MCGDM, and many other extensively deployed fields. This study has proposed two different ranking methods, namely the Removal Area Method (RAM) and the Mean Interval Method (MIM), to de-neutrosify the single-valued trapezoidal neutrosophic numbers (SVTNNS). These methods offer significantly greater accuracy compared to conventional transportation problem (TP) approaches, particularly when evaluated using various ranking functions through (SVTNNS). Further, the TP has been addressed with or without warehouses to determine the optimum cost for the proposed problems, where all the source, demand, and cost representations are treated as SVTNNS. The quantitative analysis of the transportation problem, both with and without the inclusion of warehouses, yielded optimal results of 3,684.83 and 263,703.64 using the MIM and RAM ranking methods, respectively. Thus, the proposed ranking methods demonstrate their innovation and effectiveness by outperforming traditional approaches in transportation problems, as validated through comprehensive numerical examples. Additionally, a thorough comparison with conventional methods highlights the impact of the new techniques in achieving optimal solutions. The detailed results, further supported by sensitivity analysis, provide strong evidence that the optimal solutions are robust and justified, confirming the reliability and accuracy of the proposed methods.