interval type-2 fuzzy linear programming problem with vagueness in the resources vector

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.