interval linear programming

One of the special cases of type-2 fuzzy sets are the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that have imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods.

Many real-world problems occur under uncertainty. In this paper, we consider interval linear programming (ILP) which can be used to tackle un certainties. Several methods have been proposed by researchers, such as the best and worst cases, Two-step method (TSM), improved TSM, ILP, improved ILP, three-step method, and robust two-step method. First, we define feasibility and optimality conditions in ILP models and review some solving methods shortly, and then show that some solutions of the TSM method are not feasible. Therefore, we propose an updated TSM method (namely, UTSM) by considering the feasibility and optimality conditions. In this paper, the UTSM method was applied to identify the reduction of aerosols by using two controllers with a minimized cost to demonstrate its application under uncertainty. Compared with other methods, the solutions obtained through ILP were presented as interval, which can provide intervals for the decision variables, objective function, and decision-makers. Therefore, the decision-makers can make the best decision based on the obtained solutionsthrough ILP, and then identify desired plans for aerosol-emission control under uncertainty.