In this paper, we study the min–max programming problem with n addition-min fuzzy relational inequality constraints. We prove that when the problem is feasible, an optimal solution always exists with all variables being of the same value. Based on this result, the min–max programming problem can be simplified as a single-variable optimization problem with the same optimal objective value. To solve the corresponding single-variable optimization problem, we propose an analytical method and an iterative method by successively approximating the lower bound of the optimal value. Numerical examples are given to illustrate our methods.

中文翻译：

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具有加减-最小模糊关系不等式的最小-最大规划问题的单变量方法

在本文中，我们研究了具有n个加法－最小模糊关系不等式约束的最小－最大规划问题。我们证明，当问题可行时，始终存在一个最优解，且所有变量都具有相同的值。基于此结果，最小-最大规划问题可以简化为具有相同最佳目标值的单变量优化问题。为了解决相应的单变量优化问题，我们通过逐次逼近最优值的下界，提出了一种解析方法和一种迭代方法。数值例子说明了我们的方法。