系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
3期
738~745
,共null页
模糊结构元 模糊值函数 伴随函数 结构序极值 广义极值
模糊結構元 模糊值函數 伴隨函數 結構序極值 廣義極值
모호결구원 모호치함수 반수함수 결구서겁치 엄의겁치
fuzzy structured element; fuzzy-valued function; adjoint function; structurally sequentialextreme; generalized extreme
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．
在模糊值函數的解析錶達方法未解決之前，模糊值函數的極值問題一直沒有被透徹地研究．在模糊值函數結構元錶達的基礎上，通過定義模糊數的一種結構序，提齣瞭模糊值函數的伴隨函數概唸，併證明瞭在結構序下的模糊值函數極值問題可以轉化為其伴隨函數的普通極值問題．同時．提齣瞭模糊值函數的廣義極值問題，給齣瞭結構元錶述下的模糊值函數廣義極值與廣義極值點的求解方法．研究結果不僅豐富瞭模糊優化理論與方法的研究內容，也為研究模糊運籌學中的優化問題提供瞭閤理且有用的分析工具．
재모호치함수적해석표체방법미해결지전，모호치함수적겁치문제일직몰유피투철지연구．재모호치함수결구원표체적기출상，통과정의모호수적일충결구서，제출료모호치함수적반수함수개념，병증명료재결구서하적모호치함수겁치문제가이전화위기반수함수적보통겁치문제．동시．제출료모호치함수적엄의겁치문제，급출료결구원표술하적모호치함수엄의겁치여엄의겁치점적구해방법．연구결과불부봉부료모호우화이론여방법적연구내용，야위연구모호운주학중적우화문제제공료합리차유용적분석공구．
Extreme of hlzzy-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 hlzzy 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.
