In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment.

Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm.

An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections. In this contribution, we consider SPP through Bellman’s algorithm for a network using interval-valued neutrosophic numbers (IVNNs). We proposed a novel algorithm to obtain the neutrosophic shortest path between each pair of nodes. Length of all the edges is accredited an IVNN. Moreover, for the validation of the proposed algorithm, a numerical example has been offered. Also, a comparative analysis has been done with the existing methods which exhibit the advantages of the new algorithm.

The present paper considers the fuzzy economic manufacturing model (FEMM) for an inventory model with an imperfect production process that has been studied along with rework. During the pandemic, it is evident that the products accumulated without a sale, which has increased the maintenance cost of the products. This research paper compares a special sale of products with discount and without discount prices both in the fuzzy environment and in the crisp case. New computing methods based on fuzzy logic are being utilized to enhance identification, decision making, and optimization. A triangular fuzzy number is applied in the economic production quantity to emphasize the importance of optimal manufacturing. The EPQ model’s optimal total cost is obtained in the crisp version. It is to be noted that this model is developed in the fuzzy sense by using the deterioration as a triangular fuzzy number. The applications of this model in the fields are constructing customized industrial machinery or heavy‐duty construction equipment, specific chemicals, and processed food. By using MATLAB R2021, a numerical example of the optimal solution is provided. Finally, the present research discusses how changing several parameters affects the optimum total cost.