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  本文關鍵詞： 模糊優(yōu)化 模糊關系系統(tǒng) Minimax規(guī)劃 字典序最小解 P2P網(wǎng)絡系統(tǒng)　出處：《廣州大學》2016年博士論文　論文類型：學位論文

【摘要】：現(xiàn)實世界中有很多優(yōu)化模型都處于不確定環(huán)境之中.模糊數(shù)學規(guī)劃是處理帶有不確定因素的優(yōu)化模型的有效工具.本論文主要研究對象為全模糊線性規(guī)劃、模糊關系系統(tǒng)以及模糊關系數(shù)學規(guī)劃.基于實際應用背景,在文中我們提出多種模糊優(yōu)化問題,給出有效的求解算法,并以具體的數(shù)值例子說明算法的可行性.第一章是緒論.在這一章中我們分別對全模糊線性規(guī)劃、模糊關系系統(tǒng)以及模糊關系數(shù)學規(guī)劃作了簡要的概述.另外,我們還介紹了本文的研究動機、主要內(nèi)容和創(chuàng)新之處.在第二章中,我們研究了兩類全模糊線性規(guī)劃問題.全部系數(shù)和變量均表示模糊數(shù)的線性規(guī)劃一般稱為全模糊線性規(guī)劃.對于參數(shù)為LR平坦模糊數(shù)的全模糊線性規(guī)劃,我們定義了LR平坦模糊數(shù)集上的一種序關系.基于該序關系,相應的全模糊線性規(guī)劃可以等價轉換成一個確定性的多目標線性規(guī)劃并求解.而對于參數(shù)為三角模糊數(shù)且含彈性約束的全模糊線性規(guī)劃,我們利用三角模糊數(shù)的期望值和期望區(qū)間,定義了一種基于可能性的序關系,然后將彈性約束化為具有可能性的約束并利用定義的序關系進行求解.在第三章中,在簡單介紹了max-product模糊關系系統(tǒng)的應用背景之后,我們給出了它的解集結構、性質(zhì)和求解方法.對于P2P無線通訊基站系統(tǒng),在考慮基站優(yōu)先等級的情況下,我們定義并研究了max-product模糊關系不等式和方程的字典序最小解,給出了具有可操作性的求解算法和相應的數(shù)值例子。而在不需要考慮基站優(yōu)先等級的情況下,我們建立了含max-product算子的模糊關系minimax(或min-max)規(guī)劃,并給出具體的求解算法.而對于P2P無線網(wǎng)絡系統(tǒng),為了盡量降低系統(tǒng)終端(用戶)的不滿意度,我們建立并研究了含max-product算子的模糊關系半格化幾何規(guī)劃.在第四章中,我們主要研究了addition-min模糊關系系統(tǒng)及其優(yōu)化問題.最新文獻表明,一個P2P文件共享系統(tǒng)恰好可以約化為一組addition-min模糊關系不等式.為了盡量減少系統(tǒng)中的網(wǎng)絡堵塞,提高系統(tǒng)運行效率,我們分別在考慮和不考慮各終端優(yōu)先等級的情況下研究相應的優(yōu)化問題.在考慮各終端優(yōu)先等級的情況下,我們討論了addition-min模糊關系不等式的字典序最小解.另一方面,在不需要考慮各終端優(yōu)先等級的情況下,為了刻畫系統(tǒng)中的優(yōu)化模型,我們引進了含addition-min算子的模糊關系minimax規(guī)劃問題.接著我們分別構建了單變量規(guī)劃法和最優(yōu)向量法,用于求解所提出的問題.在約束條件的極小解不唯一的時候,最優(yōu)向量法可以找出問題的一個極小最優(yōu)解,而單變量規(guī)劃法得到的是問題的最大最優(yōu)解.第五章是總結和展望.在這一章中我們總結了本學位論文的主要內(nèi)容,并展望了一些接下來擬研究的問題.
[Abstract]:In the real world, many optimization models are in the uncertain environment. Fuzzy mathematical programming is an effective tool to deal with the optimization model with uncertain factors. Fuzzy relation system and fuzzy relation mathematical programming. Based on the practical application background, we put forward a variety of fuzzy optimization problems, and give an effective algorithm. The first chapter is the introduction. In this chapter, we give a brief overview of the total fuzzy linear programming, fuzzy relation system and fuzzy relational mathematical programming. We also introduce the motivation, main content and innovation of this paper. In the second chapter. In this paper, we study two kinds of total fuzzy linear programming problems. Linear programming with all coefficients and variables representing fuzzy numbers is generally called total fuzzy linear programming. We define a kind of order relation on LR flat fuzzy number set based on this order relation. The corresponding fully fuzzy linear programming can be equivalent to a deterministic multiobjective linear programming and be solved. For a fully fuzzy linear programming with triangular fuzzy numbers and elastic constraints. We define an order relation based on possibility by using the expected value and expected interval of triangular fuzzy number. Then the elastic constraint is transformed into the constraint with possibility and solved by using the defined order relation. In chapter 3, the application background of max-product fuzzy relation system is introduced briefly. We give its solution structure, properties and solution method. For P2P wireless communication base station system, we consider the priority of base station. We define and study the dictionary order minimum solution of max-product fuzzy relation inequality and equation. An operable solution algorithm and corresponding numerical examples are given without considering the priority of base station. We establish fuzzy relational minimax (or min-max) programming with max-product operators, and give a specific algorithm for solving P2P wireless networks. In order to reduce the dissatisfaction of the system terminal (user) as far as possible, we establish and study the fuzzy relation semilattice geometric programming with max-product operator. In Chapter 4th. We mainly study the fuzzy relation system of addition-min and its optimization problem. A P2P file sharing system can be reduced to a set of addition-min fuzzy relation inequalities in order to reduce the network congestion and improve the efficiency of the system. We study the corresponding optimization problems in the case of considering and disregarding the priority level of each terminal, respectively, in the case of considering the priority level of each terminal. In this paper, we discuss the dictionary order minimum solution of addition-min fuzzy relation inequality. On the other hand, in order to depict the optimization model of the system, we do not need to consider each terminal priority level. We introduce the fuzzy relational minimax programming problem with addition-min operators, and then we construct the univariate programming method and the optimal vector method, respectively. When the minimal solution of the constraint condition is not unique, the optimal vector method can find a minimal optimal solution of the problem. In this chapter, the main contents of this dissertation are summarized and some problems to be studied are prospected.
【學位授予單位】：廣州大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O159;O221

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本文編號：1463048