本文選題：模糊二次規(guī)劃 + 二次隸屬函數(shù)�。� 參考：《廣州大學(xué)》2017年碩士論文

【摘要】：帶軟約束的模糊二次規(guī)劃問題,由一個二次目標(biāo)函數(shù)和若干線性約束條件在模糊環(huán)境中組合而成。求解方法需要先將模糊約束轉(zhuǎn)化為隸屬度形式,此處通常采用線性隸屬函數(shù)描述�？紤]到線性函數(shù)形式單一,無法充分保證決策者的意愿。若改用非線性函數(shù)描述其滿意度,又會增加處理的難度�？梢�,尋找一類既能最大限度地保留決策者意愿,又能輕松求解的隸屬函數(shù)具有相當(dāng)?shù)默F(xiàn)實(shí)意義。采用可調(diào)節(jié)二次隸屬函數(shù)可以做到這一點(diǎn)。為此,論文主要針對帶軟約束的模糊二次規(guī)劃問題,改用二次隸屬函數(shù)或者正態(tài)隸屬函數(shù)刻畫模糊約束的滿意度,分別建立了兩種含不同隸屬函數(shù)的模糊二次規(guī)劃模型。由于正態(tài)函數(shù)在表達(dá)形式上的復(fù)雜性,進(jìn)一步提出用二次函數(shù)在關(guān)鍵點(diǎn)處近似替代正態(tài)函數(shù),從而簡化了含正態(tài)隸屬函數(shù)模型的求解。論文的主要內(nèi)容包括:1、針對帶軟約束的模糊二次規(guī)劃問題,以總結(jié)幾種基于線性隸屬函數(shù)的求解方法為依托,分析和探討模型的其它解法。2、提出了一類可調(diào)節(jié)二次隸屬函數(shù)供決策者選擇,建立了含二次隸屬函數(shù)的模糊二次規(guī)劃模型,比較了擴(kuò)展線性方法和參數(shù)規(guī)劃法兩類求解方法,從中找出一些規(guī)律性的東西。3、基于正態(tài)函數(shù)建構(gòu)含正態(tài)隸屬函數(shù)的模糊二次規(guī)劃模型,研究用二次函數(shù)在關(guān)鍵點(diǎn)處近似替代正態(tài)函數(shù)來簡化模型的求解問題,討論替換前后最優(yōu)解的變化情況。4、通過簡單實(shí)例,給出了目標(biāo)函數(shù)的等值線為圓形和拋物形兩類簡單的模糊二次規(guī)劃的圖解法,獲得了較滿意的結(jié)果。論文所用的方法優(yōu)勢在于,二次隸屬函數(shù)與該模型的目標(biāo)函數(shù)在表達(dá)形式上相一致。函數(shù)的形態(tài)可以隨意調(diào)節(jié),避免了采用其它非線性隸屬函數(shù)對求解的影響。該方法續(xù)寫了模糊二次規(guī)劃的內(nèi)容,也為決策者解決模糊環(huán)境下的規(guī)劃問題,提供了更豐富的途徑。
[Abstract]:The fuzzy quadratic programming problem with soft constraints is composed of a quadratic objective function and some linear constraints in a fuzzy environment. It is necessary to transform fuzzy constraint into membership form, which is usually described by linear membership function. Considering the single form of linear function, the will of decision maker can not be fully guaranteed. If the nonlinear function is used to describe its satisfaction, it will increase the difficulty of processing. Therefore, it is of practical significance to find a kind of membership function which can not only retain the will of the decision maker to the maximum extent, but also solve the membership function easily. This can be achieved by using adjustable quadratic membership function. To solve the problem of fuzzy quadratic programming with soft constraints, this paper uses quadratic membership function or normal membership function to describe the satisfaction of fuzzy constraints, and establishes two fuzzy quadratic programming models with different membership functions. Due to the complexity of normal function in expression form, it is further proposed that the quadratic function be used to approximate the normal function at the key point, thus simplifying the solution of the model of membership function containing normal state. The main contents of this paper include: 1. Aiming at the fuzzy quadratic programming problem with soft constraints, we summarize several solving methods based on linear membership function. Based on the analysis and discussion of other solutions of the model, a class of adjustable quadratic membership function is proposed for decision makers to choose. A fuzzy quadratic programming model with quadratic membership function is established. The extended linear method and parametric programming method are compared. Based on the normal function, the fuzzy quadratic programming model with normal membership function is constructed, and the problem of solving the model is simplified by using quadratic function to approximate replace normal function at the key point. The variation of the optimal solution before and after substitution is discussed. By a simple example, the graphic method of two simple fuzzy quadratic programming, which the objective function is circular and parabolic, is given, and the satisfactory results are obtained. The advantage of the method is that the quadratic membership function is consistent with the objective function of the model. The shape of the function can be adjusted at will to avoid the influence of other nonlinear membership functions on the solution. The method extends the content of fuzzy quadratic programming and provides a more abundant way for decision makers to solve the planning problem in fuzzy environment.
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O221

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