基于四参数区间直觉模糊集的多准则决策方法研究

发布时间：2018-01-27 04:46

本文关键词： 四参数区间直觉模糊数集结算子心态指标函数多准则决策　出处：《中南大学》2012年硕士论文　论文类型：学位论文

【摘要】：模糊多准则决策是不确定性多准则决策中一个十分重要的研究领域。在经济生活中,由于人类认识客观世界的模糊性以及认识对象的不确定性,人们在做决策时常常会遇到决策信息不全的情形,此时决策者给出的准则值通常采用经典的模糊数,而人们对事物认识和判断往往采用依靠自己的直觉,表示对事物支持和反对的程度,从而产生了直觉模糊数。然而,直觉模糊数并不能准确描述物质的模糊本质,从而利用区间数来描述直觉中的隶属度和非隶属度,更能体现事物的本质,因而区间直觉以及模糊数直觉模糊数应运而生,并将其应用在信息不确定或不完全确定的模糊多准则决策中。但是,在现实生活中,隶属度和非隶属度区间中的取值机会函数往往不是均匀分布,而是非线性的,因而在此基础上提出四参数区间直觉模糊数,具有实际意义。目前,有关四参数区间直觉模糊数在多准则决策中的研究不多,因此对准则值为四参数区间直觉模糊数的多准则决策问题进行研究具有重要意义。本文在现有前人的研究成果基础上,分析了直觉和区间直觉模糊数的不足和缺点,针对信息完全和不完全,准则值为四参数区间直觉模糊多准则决策问题进行了深入的研究,建立了相应的决策模型,并求解。本文工作成果如下： (1)提出了四参数区间数及四参数区间直觉模糊数的概念,扩展了参数区间以及参数区间直觉模糊数的基本性质以及运算规则,丰富了直觉模糊数的理论。 (2)给出了FPIIFN-WAA算子及其性质,FPIIFN-WGA算子性质,FPIIFN-OWA算子及其性质,I-FPIIFN-OWA算子及其性质,并给出了他们的运算性质。针对各种相关的决策情况,提出了基于集结算子的四参数区间直觉模糊多准则决策方法。 (3)提出了四参数区间直觉模糊数的记分函数以及精确函数,给出了一种权重为四参数区间数准则值为四参数区间直觉模糊数的多准则决策方法。基于欧式距离,以及风险偏好指标,建立线性规划模型求解最优组合权重,给出了一种基于F-TOPSIS的四参数区间直觉模糊多准则决策方法。 (4)提出了四参数区间直觉模糊数的心态指标记分函数并运用心态指标记分函数进行四参数区间直觉模糊数的大小排序。同时提出了一种心态指标函数的四参数区间直觉多准则决策方法,并将此方法应用到实际的房地产评估决策中。在网络优化SEO中,运用前文提出的三种排序方法进行对比,验证了结果的一致性和合理性。本文通过相应的实例进行分析,说明了以上所提出的方法合理性和科学性,从而为人们认识模糊世界提供了一个有效的方法和途径。
[Abstract]:Fuzzy multi-criteria decision making is a very important research field in uncertain multi-criteria decision-making. In economic life, due to the fuzziness of human understanding of the objective world and the uncertainty of the object of understanding. When people make a decision, they often encounter the situation of incomplete decision information. At this time, the criteria given by the decision maker usually use the classical fuzzy number, and people often rely on their own intuition to know and judge things. The degree of support and opposition to things, which results in intuitionistic fuzzy numbers. However, intuitionistic fuzzy numbers cannot accurately describe the fuzzy nature of matter. Thus using interval numbers to describe the degree of membership and non-membership in intuition can reflect the essence of things more. Therefore interval intuition and fuzzy number intuitionistic fuzzy numbers emerge as the times require. It is applied to fuzzy multi-criteria decision making with uncertain or incomplete information. However, in real life, the opportunity function of membership and non-membership is not uniform distribution, but nonlinear, so on the basis of this, a four-parameter interval intuitionistic fuzzy number is proposed. At present, there are few researches on the interval intuitionistic fuzzy number of four parameters in multi-criteria decision making. Therefore, it is of great significance to study the multi-criteria decision making problem in which the criterion value is an interval intuitionistic fuzzy number with four parameters. Based on the existing research results, this paper analyzes the shortcomings and shortcomings of intuitionistic and interval intuitionistic fuzzy numbers, aiming at the complete and incomplete information. The criterion value is the four-parameter interval intuitionistic fuzzy multi-criteria decision making problem. The corresponding decision model is established and solved. The results of this paper are as follows: 1) the concepts of four-parameter interval number and four-parameter interval intuitionistic fuzzy number are proposed, and the basic properties and operation rules of parameter interval and parameter interval intuitionistic fuzzy number are extended. It enriches the theory of intuitionistic fuzzy numbers. The properties of FPIIFN-WGA operator and FPIIFN-OWA operator are given. I-FPIIFN-OWA operators and their properties are given. Based on aggregation operator, a four parameter interval intuitionistic fuzzy multiple criteria decision making method is proposed. A scoring function and an exact function for interval intuitionistic fuzzy numbers with four parameters are proposed. In this paper, a multi-criteria decision method with the weight of four-parameter interval number criterion and four-parameter interval intuitionistic fuzzy number is presented. Based on Euclidean distance and risk preference index, a linear programming model is established to solve the optimal combination weight. A four parameter interval intuitionistic fuzzy multiple criteria decision making method based on F-TOPSIS is presented. 4). In this paper, the mental index scoring function of the four parameter interval intuitionistic fuzzy number is put forward, and the size order of the four parameter interval intuitionistic fuzzy number is carried out by using the mental index score function. At the same time, a four parameter interval of the mental state index function is proposed. Intuitionistic multi-criteria decision making method. And this method is applied to the real estate evaluation decision. In the network optimization SEO, the three sort methods proposed above are compared. The consistency and rationality of the results are verified. Through the analysis of the corresponding examples, the rationality and scientificity of the methods proposed above are explained. Thus, it provides an effective way for people to understand the fuzzy world.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：C934;F224

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