模糊值函数的极值问题

在模糊值函数的解析表达方法未解决之前，模糊值函数的极值问题一直没有被透彻地研究. 在模糊值函数结构元表达的基础上，通过定义模糊数的一种结构序，提出了模糊值函数的伴随函数概念，并证明了在结构序下的模糊值函数极值问题可以转化为其伴随函数的普通极值问题. 同时，提出了模糊值函数的广义极值问题，给出了结构元表述下的模糊值函数广义极值与广义极值点的求解方法. 研究结果不仅丰富了模糊优化理论与方法的研究内容，也为研究模糊运筹学中的优化问题提供了合理且有用的分析工具.

Extremal problem of fuzzy-valued function

Extreme of fuzzy-valued function was not thoroughly researched until we resolved the analytical expression of fuzzy-valued functions, in this paper, based on that the fuzzy-valued function could be expressed by structured element, we present adjoint function of fuzzy-valued function by defining a type of structured sequence of fuzzy numbers, and also prove that the research of extreme of fuzzy-valued function can be transformed into general extreme of its adjoint function under structured sequence. Meanwhile, we not only present the generalized extreme of fuzzy-valued function, but also give the methods for solving the generalized extreme value and generalized extreme points which are formulated by structured element, the research results enrich the research content of fuzzy optimization theory and methods, as well as provide a reasonable and useful analysis tool for studying optimization problem of fuzzy operations research.