求解模糊不等式约束下的非线性优化问题，给出精确最优解算法。
Exact alternative optima for nonlinear optimization problems defined with maximum component objective function constrained by the Sugeno-Weber fuzzy relational inequalities
- 基于最大-苏格诺-韦伯复合构造可行域，利用模糊交并运算建模
- 提出判别可行性条件并设计可得精确最优解的算法
- 适合研究模糊优化与决策系统的人参考
本文研究一类带有模糊关系不等式约束的格优化问题，其中可行域由两个不等式模糊系统交集构成，采用苏格诺-韦伯族t-范数作为模糊合成运算。该族t-范数与t-余范在多种模糊建模问题中广泛应用，由Weber提出用于模糊集合的交运算，Sugeno则将其用于α-模糊测度的加法规则。首先分析了以max-Sugeno-Weber复合定义的可行域，给出了判定可行性的充要条件；随后基于问题的理论性质，提出一种求解该非线性优化问题的算法，并证明其可获得精确最优解，最后通过实例说明算法有效性。
原文摘要 · Abstract (English)
In this paper, we study a latticized optimization problem with fuzzy relational inequality constraints where the feasible region is formed as the intersection of two inequality fuzzy systems and Sugeno-Weber family of t-norms is considered as fuzzy composition. Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called alpha-fuzzy measures. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Sugeno-Weber composition and a necessary and sufficient condition is presented for determining the feasibility. Then, based on some theoretical properties of the problem, an algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.
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