几类不确定型粗决策方法研究

【作者】 范敏；

【导师】 邹平；

【作者基本信息】 昆明理工大学 ， 管理科学与工程， 2016， 博士

【摘要】 不确定型多属性决策是现代决策科学的重要分支,其理论与方法在管理、经济、军事、医药等诸多领域都有着广泛的应用。而粗糙集是以数据驱动的方法处理不确定、不一致信息的有力工具。近年来粗糙集与不确定型多属性决策交叉融合,已经发展成为一种新兴的不确定型粗决策方法,在智能模式识别、危机预测、文本自动分类、群决策等等方面都得到了成功的应用。决策的基础是人们对研究对象的感知,由于现实中不确定型问题的普遍性和人们感知的有限性,人们的感知所表达的常见数据类型除了精确实数值,还有大量的语言值、模糊数、直觉模糊数等多种数据类型。同时,人们的感知常基于研究对象的两两对比,即基于一种二元关系,所以在不确定型决策中,在常见的等价关系、一般二元关系、直觉模糊关系下,结合不同的数据类型,利用粗决策方法去研究各种现实的决策问题,具有重要的理论意义和实际应用价值。本文针对备选方案属性值在满足等价关系、一般关系和直觉模糊关系下的几类决策方法进行了系统的研究,并将其理论研究成果应用于城市交通实际问题。本文主要取得了以下成果：1、基于等价关系的多属性粗决策方面,为了解决传统属性约简算法对数据分布信息利用不足的缺点,提出了一种离散化和属性约简相结合的方法,使得决策系统中的信息得到更加充分的利用。首先,通过可辨识矩阵,定义属性值的重要性,得到离散化算法；然后再通过对不可分辩类的定义、属性重要性的讨论以及属性约简的启发式算法,得到了一种离散化与属性约简相结合的启发式算法。在UCI数据集上与其它算法进行对比实验,结果表明,该方法可以充分利用数据集本身的分布特点,且能得到较好的属性约简效果,特别是实例数较多的数据库中表现得很突出。由于考虑到属性值的重要性,所以该方法不仅适用于条件属性取值分布比较分散的情形,还适用于条件属性取值比较集中的情形。2、基于一般关系的多属性粗决策方面,通过构造一般关系下的S-粗糙集,将S-粗糙集动态地运用于构造膨胀和腐蚀算子,将等价关系下的S-粗糙集推广到了般二元关系下。在实例中,对图像边缘先用比较大的邻域算子进行试探,若算子能完全覆盖图像元素,则选用较大的邻域算子进行膨胀和腐蚀运算；若算子不能完全覆盖图像元素,则选用较小的邻域算子进行膨胀和腐蚀运算,动态地实现了对研究对象近似空间的描述。并将其应用于后面的图像边缘的腐蚀和膨胀处理中,通过图像处理结果验证了该算法的灵活性和有效性。3、基于直觉模糊集的多属性粗决策方面,提出了一种面向领域知识的基于直觉模糊熵的群决策方法。解决了专家对满意度和不满意度都比较接近0.5时,基于距离的方法对方案无法进行排序的问题。该方法主要将专家的领域知识与数据的直觉模糊熵相结合,发现基于直觉模糊熵的方法进一步反映了专家在评价中对模糊信息进行刻画的能力。首先利用直觉模糊信息熵,求得属性的权重；然后用AHP法求专家权重；接着,运用集结算子进行排序；最后,用实例说明了该方法的有效性。该研究为其它满意度和不满意度都比较接近0.5的群决策问题提供了有益的借鉴。4、基于直觉模糊集的博弈方法研究方面,提出了支付值为直觉模糊值的双矩阵博弈模型(IFPBiG)的一种求解方法,得到一种更一般的非零和、双方理性可以分别假设的矩阵博弈问题的求解方法,推广了现有的简化理性假设的方法。首先建立了支付值为直觉模糊值的双矩阵博弈模型(IFPBiG),讨论了求解该模型的两种非线性规划算法,并利用不动点理论严格地证明了支付值为直觉模糊值的双矩阵模型Nash均衡点的存在性。最后提出了求解IFPBiG的一种快速线性规划算法。该方法将经典博弈中理性假设的特殊简化情形推广到更一般的情形,对博弈假设问题进行了有益的探讨。本文的研究成果丰富了不确定型粗决策的研究,为不同数据类型的不确定型决策问题提供了新的有效的方法。更多还原

【Abstract】 Decision-making under uncertainty (DMU) is an important branch of modern decision science. Its theory and method are widely applied to many areas, such as management, economics, military affairs, medicine and so forth. The rough set is a data driven method dealing with uncertain and inconsistent information, which had become a powerful tool. Rough set and the uncertain multiple attribute decision-making theory had been fusioned in recent years. It has developed into a high-profile field of uncertain decision methods as:uncertain multiple attribute rough decision-making theory (UMARDM), which has been wildely used in intelligent control, enterprise financial crisis prediction model, automatic text classification, and so on, it has been successfully used in group decision making too.Decision is based on people’s awareness to the object of study, due to the prevalence of uncertain problems in reality and perception of finiteness, the descriptions of the research object is often fuzzy and uncertain, so the corresponding description of data has a variety of data types, such as:real number, language accurately and intuitionistic fuzzy Numbers, etc. At the same time people’s perception is often based on the research object of two contrasts. That is, people always through some comparable relationship between two objects, combined with people’s mental decision system, eventually get choice and decision making. Which of the two relations between the two is a kind of binary relation, so in uncertain decision making, in the common binary relation:equivalence relation, general binary relation, intuitionistic fuzzy relations, in combination with proper uncertain decision making tool, to study various realistic decision problem has important theoretical significance and practical application value.In this paper, under the equivalence relation, general binary relation and intuitionistic fuzzy relations of decision-making theory, its theoretical research was applied to traffic problems.The main results got in this thesis are summarized as follows:1. In the aspects of Uncertain Multiple Attribute Rough Decision-making theory (UMARDM) based on equivalence relation, in order to overcome the shortcomings of traditional reduction algorithm which under-utilization for data distribution information, proposed a combination of discretization and attribute reduction method, making more full use of the information in the decision-making system.First of all, through the discernibility matrix, defined the importance of attribute values, got discretization algorithms. Then through the definition of class, attribute, discussed the importance of attributes, get the heuristic algorithm of attribute reduction. It realized a discretization and attribute reduction combining in the heuristic algorithm. Other algorithms on UCI data sets experiment was compared with, the results shew that this method can make full use of the distribution characteristics of the data set itself, and can get better effects of attribute reduction. Especially the more number of data in the database, the more it was outstanding. Due to considering the importance of attribute values, so this method is not only applicable to the condition attribute values distribution of scattered, also can apply to condition attribute values which are centered.2. In the aspects of UMARDM based on general binary relation, defined S-Rough set under the general binary relations, which could dynamically use the corrosion and expansion operator to process the edge of images.The larger neighborhood operator was used to test, if the operator can completely cover image elements, choosed the larger neighborhood operator for expansion and corrosion calculations. If the operator cannot completely cover image elements, used the expansion and corrosion with smaller neighborhood operator. Finally, it wsa applied to the corrosion and expansion process of image edge. Through the image processing results, verified the flexibility and effectiveness of the algorithm.3. In the aspects of UMARDM based on intuitionistic fuzzy relations, put forward a domain knowledge oriented group decision-making method, which combined domain knowledge of experts with the data of intuitionistic fuzzy entropy, especially for satisfaction and dissatisfaction are close to 0.5, in this case, the traditional method based on distance often cannot be solved.Intuitionistic fuzzy information entropy was used to get weights of attributes. Then the AHP method was used to get expert weight. Finally, the aggregation operator was proposed to sort and used example to illustrate the effectiveness of the method. It provided the beneficial reference for other group decision-making problems which satisfaction and dissatisfaction are close to 0.5.4. In the aspects of matrix games based on intuitionistic fuzzy relations, proposed a linear programming method in solving a double matrix game model based on intuitionistic fuzzy sets (IFPBiG), get a more general method of matrix game problem with nonzero-sum, the rationalities of both sides can assume differently, it generalized the existing method of simplified rational assumption.Firstly, the IFPBiG was established. Then two kinds of nonlinear programming algorithm to solve the model were discussed, by using the fixed point theory proved the existence of Nash equilibrium. Finally a fast linear programming algorithm for solving IFPBiG was put forward. It allowed expressing human rationality with different values, which could be used as a more general case compared with classic rational assumption of game.The results of this article enriched the theory of multi-attributes rough decision-making, provided a new effective method for different types of uncertainty decision-making problem.更多还原