【作者】 施丽娟；

【导师】 黄天民；

【作者基本信息】 西南交通大学 ， 应用数学， 2010， 硕士

【摘要】 本文用理论与实验的方法研究基于直觉模糊集和区间直觉模糊集的多属性决策,建立了几种不同决策环境下的多属性决策模型,对直觉模糊多属性决策方法进行了探讨。针对属性权重已知的区间直觉模糊多属性决策,基于直觉模糊集思想与集对分析思想兼容性的考虑,将区间直觉模糊决策矩阵转化为联系度矩阵,算出各方案的综合联系度,由模糊集对势给出方案排序式,再结合区间数排序方法最终实现方案排序,最后利用算例说明该方法的可行性。多属性决策问题的许多求解方法,一般都与属性权重有着密切的关系,因为权重的合理性直接影响着多属性决策排序的准确性,所以在多属性决策中,权重问题的研究占据有重要地位。针对属性权重完全未知的直觉模糊多属性决策,先从局部考虑,建立一个目标规划模型来获得单个方案的最优权重,再从全局考虑,基于投影法提出了一种非线性的二次规划模型,获得系统最优权重；对于属性权重完全未知且属性值为区间直觉模糊数的多属性决策问题,提出了区间直觉模糊熵权的确定方法；针对决策者的偏好信息和决策矩阵元素均为区间直觉模糊数的多属性决策问题,通过求解主观偏好与客观偏好的总绝对偏差最小,同时各方案综合属性值差距最大的双目标规划模型,得到属性的最优权重向量。求得属性权重后可算出方案综合属性值,通过比较得分函数值和精确函数值实现方案排序或择优。更多还原

【Abstract】 This paper studies multil-attribute decision-making problems based on intuitionist fuzzy sets and interval-valued intuitionist fuzzy sets. Several multi-attribute decision models were established under the different decision-making environment. This paper mainly discussed the methods of intuitionist fuzzy multil-attribute decision-making problems.Studies a kind of multi-attribute decision-making problem in which the attributes weights are given as real numbers and the attribute values are described by interval-valued intuitionist fuzzy numbers. First based on the compatibility between the set pair analysis theory and intuitionist fuzzy set theory, the interval-valued intuitionist fuzzy decision matrix is transformed into the relation degree matrix. Second obtained the synthesize relation degree. Get an interval numbers form raking by a raking formula, and then raking alternatives by interval numbers raking. Finally, an example is used to illustrate the feasibiling and practicability of the proposed approach.Many multi-attributes decision-making problems solving methods were associated to attribute weights. Because reasonable weight direct influence the accuracy of multi-attribute decision making. Therefore, in multi-attribute decision making, weight studies occupy an important position.When the multi-attribute decision-making problems in which the information about the attribute weights are unknown completely and the attribute values are described by intuitionist fuzzy numbers. Firstly, a linear objective programming model for determine the ideal attribute weights of single program is proposed by considering in local. Secondly, a quadratic programming model is set up based on the projection method. Then the optimal weights were gated. When the multi-attribute decision-making problem in which the information about the attribute weights are unknown completely and the attribute values are described by interval-valued intuitionist fuzzy numbers, a new method is proposed to determine entropy weights of interval-valued intuitionist fuzzy number. When the multi-attribute decision-making problem in which the preference information on alternatives and the attribute values are described by interval-valued intuitionist fuzzy numbers. After solving the two objects programming of minimizing the total absolute deviation between the subjective and objective preference and maximizing the ranges of the comprehensive attribute values of alternative, the weights of the attributes were obtained objectively. According to the comprehensive attribute values, the alternatives were ranked by using score function.更多还原