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.

Decision-making is an essential task in Science and Engineering. Since most of the real-world problems have uncertainty in nature, making the decision is challengeable one for the decision makers. Soft set has the advantage of free from the deficiency of the parameterization tools of existing theories, namely probability, fuzzy theory and the theory of rough sets. Linguistic terms mean different things to different people, so variability in expert's acceptance degree is possible. Here usage of type-1 fuzzy leads to noisy and uncertain, and the parameters also may be noisy and hence type-2 fuzzy sets may be used to address the mentioned issues. Therefore, a triangular interval type-2 fuzzy soft set has been considered in the present work by combining triangular interval type-2 fuzzy set and soft set. In this paper, a triangular interval type-2 fuzzy soft weighted arithmetic operator (TIT2FSWA) has been proposed with its desired mathematical properties; also applied the proposed methodology in a decision-making problem for profit analysis. Further comparative analysis has been made with the existing methods to show the effectiveness of the proposed method.

The objective of design optimization of pressure vessels is cost reduction by reducing weight with adequate strength and stiffness. Optimization is the act of obtaining the best result under given circumstances. Conventional design aims at finding acceptability design which merely satisfies the functional and other requirements of the problem. In general, there will be more than one acceptable designs and the purpose of design optimization is to choose the best. In the present work parameters such as thickness of the shell, and dish end, length and radius of the pressure vessel are optimized by making use of ACO has been shown for a Pressure vessel problem with four variables and four design constraints. It is found that the results obtained from ACO are better as its search is for global optimum as against the local optimum in traditional search methods. The results of the ACO have been checked using ANSYS, and it is found to perform satisfactorily.