Study of Multi-Objective Nonlinear Programming in Optimization of the Rough Interval Constraints

This paper studies a multi-objective nonlinear programming problem with rough intervals in the constraints. the problem was investigated by taking maximum value range and minimum value range inequalities as constraints conditions; hence, it was converted into two classical multi-objective nonlinear programming problems, called lower and upper approximation problems. all of the lower and upper approximation problems were solved by using the weighting method, where an optimal rough interval solution was obtained. the stability set of the first kind corresponding to the optimal rough interval solution was determined. finally, a numerical example was given for the sake of illustration.