关于直觉模糊数和模糊二次规划的研究

发布时间：2018-03-21 22:29

本文选题：直觉模糊集(IFN)　切入点：直觉模糊数(IFS)　出处：《广州大学》2016年硕士论文　论文类型：学位论文

【摘要】：针对模糊二次规划问题(FQP),本文提出了将容差法与罚函数法结合起来求解的一种新型解法。首先用容差法将模糊问题清晰化,接着运用罚函数法进行求解,最后用数值例子,验证了这种方法是可行、有效的。同时,在学习了直觉模糊集(IFS)的理论基础上,用IFS描述FQP问题的约束条件,其中重点研究了含直觉梯形模糊数与直觉三角模糊数的模糊规划问题。因此,模糊集理论的内容得到了进一步的补充说明,也当决策者在解决不确定问题时,能得到更精确的结果。本文共四章,第一章是绪论,分两个小节简要说明,第一小节介绍了模糊二次规划(FQP)的选题背景、意义及发展动向;第二小节主要介绍了研究内容及论文的结构安排。第二章是预备知识,首先详细介绍了直觉模糊集(IFS)的基本概念和基本性质,然后过渡到直觉模糊数(IFN)的概念,从中给出了直觉梯形模糊数和直觉三角模糊数的基本概念、性质及运算规律,为后文的内容提供了理论依据。第三章主要介绍了几种IFN的排序方法:加权期望法、相关模糊数的值和模糊度法、Hamming距离法,并对这些方法进行了简要的说明,为第四章对含有直觉模糊系数的FQP问题的求解提供了方法依据。第四章是关于模糊二次规划(FQP)的内容,是本文的主体内容,首先介绍了FQP的分类问题,然后介绍了求解FQP的基本方法容差法与罚函数法结合法和λ-截集法,其中容差法与罚函数法结合法是一种新型解法,同时用数值例子,验证了这种方法是可行的、有效的,最后运用加权期望排序法研究了系数为直觉模糊数(IFN)的FQP问题。
[Abstract]:For the problem of fuzzy quadratic programming, a new method, which combines tolerance method with penalty function method, is proposed in this paper. Firstly, tolerance method is used to clear the fuzzy problem, then penalty function method is used to solve the problem. Finally, numerical examples are used. It is proved that this method is feasible and effective. At the same time, on the basis of studying the theory of intuitionistic fuzzy set (IFS), the constraint conditions of FQP problem are described by IFS. The fuzzy programming problem with intuitionistic trapezoid fuzzy number and intuitionistic triangular fuzzy number is studied emphatically. Therefore, the content of fuzzy set theory is further supplemented, and when the decision maker is solving the uncertain problem, There are four chapters in this paper. The first chapter is introduction, which is divided into two sections. The first section introduces the background, significance and development trend of fuzzy quadratic programming. The second section mainly introduces the research content and the structure arrangement of the thesis. The second chapter is the preparatory knowledge. Firstly, it introduces the basic concepts and properties of intuitionistic fuzzy sets (IFS), and then transitions to the concept of intuitionistic fuzzy numbers (IFNs). The basic concepts, properties and operation rules of intuitionistic trapezoid fuzzy number and intuitionistic triangular fuzzy number are given. The value of correlation fuzzy number and the method of ambiguity degree and hamming distance method are briefly explained, which provides the method basis for the solution of FQP problem with intuitionistic fuzzy coefficient in chapter 4. Chapter 4 is about the content of fuzzy quadratic programming. It is the main content of this paper. Firstly, the classification problem of FQP is introduced, then the basic method of solving FQP is introduced, which combines tolerance method with penalty function method and 位 -section set method, among which the combination of tolerance method and penalty function method is a new method. At the same time, numerical examples show that this method is feasible and effective. Finally, the weighted expectation ranking method is used to study the FQP problem with the coefficient of intuitionistic fuzzy number (IFN).
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O159;O221

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