In the present paper, an inventory model without shortages has been considered in a fuzzy environment. Our goal is to determine the optimal total cost and the optimal order quantity for the proposed inventory model. The Trapezoidal fuzzy numbers have been introduced in order to achieve this goal. The computation of economic order quantity (EOQ) is carried out through defuzzification process by using signed distance method. The signed distance method is more applicable than the other methods of defuzzification. To illustrate the results of the proposed model, we have given two model examples and presented the computational results. Sensitivity for this model is also studied, which shows a linear relation between demand, EOQ, and total cost. The advantage of the proposed approach is that it is simple, gives a better result in relatively less computational work.

In financial planning problems, the determination of the best investment is one of the interesting optimization models. In the proposed work, an investment problem (IP) is introduced in vague environment. The vagueness in return parameter is characterized by normalized heptagonal fuzzy number (HFN). One of the suitable interval approximations, namely, an inexact rough interval of a normalized HFN is utilized. Afterward, the inexact rough interval investment problem is considered. A dynamic programming (DP) approach is developed, which is applied for optimizing the fuzzy investment problem. The ideology of ''rough interval number'' is suggested in the mathematical modeling framework of the proposed problem to show the rough data as an inexact rough interval of piecewise quadratic fuzzy numbers. Afterward, the DP approach is applied to solve and compute a rough interval solution. Finally, a numerical example is yielded for the utility of the approach to apply on real-world problem for the decision-maker. The obtained results consist of the total optimal return with inexact rough intervals on a $ 10 million investments is as follows: $ [[1.69, 2.08]: [1.75, 1.91]] millions.

is research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. rough the use of the α-level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker's choice between intervals. .e maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.