模糊关系系统及其优化问题研究

发布时间：2018-01-25 14:25

本文关键词： 模糊优化模糊关系系统 Minimax规划字典序最小解 P2P网络系统　出处：《广州大学》2016年博士论文　论文类型：学位论文

【摘要】：现实世界中有很多优化模型都处于不确定环境之中.模糊数学规划是处理带有不确定因素的优化模型的有效工具.本论文主要研究对象为全模糊线性规划、模糊关系系统以及模糊关系数学规划.基于实际应用背景,在文中我们提出多种模糊优化问题,给出有效的求解算法,并以具体的数值例子说明算法的可行性.第一章是绪论.在这一章中我们分别对全模糊线性规划、模糊关系系统以及模糊关系数学规划作了简要的概述.另外,我们还介绍了本文的研究动机、主要内容和创新之处.在第二章中,我们研究了两类全模糊线性规划问题.全部系数和变量均表示模糊数的线性规划一般称为全模糊线性规划.对于参数为LR平坦模糊数的全模糊线性规划,我们定义了LR平坦模糊数集上的一种序关系.基于该序关系,相应的全模糊线性规划可以等价转换成一个确定性的多目标线性规划并求解.而对于参数为三角模糊数且含弹性约束的全模糊线性规划,我们利用三角模糊数的期望值和期望区间,定义了一种基于可能性的序关系,然后将弹性约束化为具有可能性的约束并利用定义的序关系进行求解.在第三章中,在简单介绍了max-product模糊关系系统的应用背景之后,我们给出了它的解集结构、性质和求解方法.对于P2P无线通讯基站系统,在考虑基站优先等级的情况下,我们定义并研究了max-product模糊关系不等式和方程的字典序最小解,给出了具有可操作性的求解算法和相应的数值例子。而在不需要考虑基站优先等级的情况下,我们建立了含max-product算子的模糊关系minimax(或min-max)规划,并给出具体的求解算法.而对于P2P无线网络系统,为了尽量降低系统终端(用户)的不满意度,我们建立并研究了含max-product算子的模糊关系半格化几何规划.在第四章中,我们主要研究了addition-min模糊关系系统及其优化问题.最新文献表明,一个P2P文件共享系统恰好可以约化为一组addition-min模糊关系不等式.为了尽量减少系统中的网络堵塞,提高系统运行效率,我们分别在考虑和不考虑各终端优先等级的情况下研究相应的优化问题.在考虑各终端优先等级的情况下,我们讨论了addition-min模糊关系不等式的字典序最小解.另一方面,在不需要考虑各终端优先等级的情况下,为了刻画系统中的优化模型,我们引进了含addition-min算子的模糊关系minimax规划问题.接着我们分别构建了单变量规划法和最优向量法,用于求解所提出的问题.在约束条件的极小解不唯一的时候,最优向量法可以找出问题的一个极小最优解,而单变量规划法得到的是问题的最大最优解.第五章是总结和展望.在这一章中我们总结了本学位论文的主要内容,并展望了一些接下来拟研究的问题.
[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.
【学位授予单位】：广州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O159;O221

【参考文献】