【摘要】 模糊优化作为模糊数学的重要分支，凭借对现实问题中不确定性的有效处理能力成为研究热点.截集理论可实现模糊优化问题向区间优化问题的转化，约束区间算法(CIA)则是求解区间优化问题的有效手段，引入参数后还能将区间优化问题进一步转化为参数化实值优化问题.以模糊无约束优化问题为研究对象，探究求解该类问题的约束区间方法，结合截函数与CIA构建了对应的区间优化问题及参数化非线性优化问题，并证明了问题的局部等价性，即向量x是模糊无约束优化问题的局部弱极小解，当且仅当向量x为对应区间优化问题的局部弱极小解，也当且仅当向量x是CIA处理后的参数化非线性优化问题的局部极小解.通过具体算例验证CIA求解模糊无约束优化问题的有效性.更多还原

【Abstract】 As an important branch of fuzzy mathematics, fuzzy optimization has become a research hotspot due to its effective capability to handle uncertainties in real-world problems. Cut set theory can transform fuzzy optimization problems into interval optimization problems, and constrained interval algorithm(CIA) is an effective tool for solving interval optimization problems. Interval optimization problems can be further converted into parameterized real-valued optimization problems by introducing parameters. Constrained interval algorithm is explored for solving fuzzy unconstrained optimization problems. Combined with the cut function and CIA, the corresponding interval optimization problem and parameterized nonlinear programming are constructed. The local equivalence of the problems is proved, that is, x is a local weak minimum solution of the fuzzy unconstrained optimization problem if and only if x is a local weak minimum solution of the corresponding interval optimization problem, and if and only if x is a local minimum solution of the parameterized nonlinear programming. The effectiveness of CIA in solving fuzzy unconstrained optimization problems was verified through a specific numerical example.更多还原