越览（100）——精读硕士论文的1.3国内外研究现状

摘要：This issue of tweets will introduce current research status at home and abroad of the master's thesis "Research on Multi-Attribute

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“越览（100）——精读硕士论文

《基于不完备信息系统的多属性模糊决策方法研究》

的1.3国内外研究现状”。

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"Yuelan (100): Intensive reading of the master's thesis

"1.3 Current research status at home and abroad of

multi-attribute fuzzy decision-making

methods based on incomplete

information systems"".

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一、内容摘要（Summary of content）

本期推文将从思维导图、精读内容、知识补充三个方面介绍硕士论文《基于不完备信息系统的多属性模糊决策方法研究》的国内外研究现状。

This issue of tweets will introduce current research status at home and abroad of the master's thesis "Research on Multi-Attribute Fuzzy Decision-making Method Based on Incomplete Information System" from three aspects: mind map, intensive reading content, and knowledge supplement.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

（一）多属性决策（Multiple attribute decision making）

多属性决策方法中，属性权重的确定是决策的关键因素，直接影响决策结果。国内研究方面，徐泽水提出结合主观与客观赋权的线性目标规划方法，王建明等人通过群决策模型利用经验和偏好确定权重。国外学者如T.L. Saaty提出的模糊层次分析法（AHP）和Chen的多属性组合分配方法，提供了不同的权重分配思路。

In the multi-attribute decision-making method, the determination of attribute weights is a key factor in decision-making and directly affects the decision results. In terms of domestic research, Xu Zeshui proposed a linear goal programming method that combines subjective and objective weighting, and Wang Jianming and others used experience and preferences to determine weights through a group decision-making model. Foreign scholars such as T.L. Saaty's fuzzy hierarchical analysis method (AHP) and Chen's multi-attribute combination allocation method provide different weight allocation ideas.

随着决策中的不确定性和模糊性的增加，模糊多属性决策方法广泛应用于处理模糊信息，尤其在决策者认知限制和主观偏好的情况下。近年来，苏冰杰提出的模糊信息熵法、刘议聪等人的基于信任关系的TODIM方法，提升了决策准确性和可靠性。

With the increase of uncertainty and ambiguity in decision making, fuzzy multi-attribute decision-making methods are widely used to process fuzzy information, especially under the condition of cognitive limitations and subjective preferences of decision makers. In recent years, the fuzzy information entropy method proposed by Su Bingjie and the TODIM method based on trust relationship proposed by Liu Yicong and others have improved the accuracy and reliability of decision making.

延迟决策成为新兴研究领域，研究者引入直觉模糊集和区间直觉模糊集来表示模糊信息，增强决策处理能力。基于模糊数的群体决策模型和优化评分函数等方法，进一步简化了决策过程，提高了模型的适用性。

Delayed decision making has become an emerging research field. Researchers have introduced intuitionistic fuzzy sets and interval intuitionistic fuzzy sets to represent fuzzy information and enhance decision-making processing capabilities. Methods such as group decision-making models based on fuzzy numbers and optimized scoring functions have further simplified the decision-making process and improved the applicability of the model.

（二）模糊模式识别评价方法（Evaluation method of fuzzy pattern recognition）

模糊模式识别是在传统模式识别方法基础上引入模糊集的一种技术，旨在处理模糊和不确定性信息，特别适用于识别和分类模糊、不完全或模糊边界的数据。模糊理论成为决策过程中处理不精确信息的关键工具。尽管模式识别在机器学习和人工智能领域得到广泛应用，但目前尚未有统一的定义。1991年，陈守煜教授首次提出模糊模式识别理论模型，旨在为信息存在模糊性的复杂系统提供传统方法无法有效评估的评价方式。

Fuzzy pattern recognition is a technique that introduces fuzzy sets on the basis of traditional pattern recognition methods. It aims to process fuzzy and uncertain information and is particularly suitable for identifying and classifying fuzzy, incomplete or fuzzy-boundary data. Fuzzy theory has become a key tool for dealing with imprecise information in the decision-making process. Although pattern recognition has been widely used in the fields of machine learning and artificial intelligence, there is currently no unified definition. In 1991, Professor Chen Shouyu first proposed a theoretical model of fuzzy pattern recognition, which aims to provide an evaluation method for complex systems with fuzzy information that cannot be effectively evaluated by traditional methods.

模糊模式识别方法通过建立数学模型，为评估和预测提供科学基础。目前，模式识别主要通过搜索大规模训练数据并提取数据规则来进行对象识别。在模式选择中，常使用欧氏贴近度、海明贴近度等方法进行排名。模糊数的引入推动了模糊模式识别的进一步发展，扩大了其应用领域。模糊模式识别广泛应用于工业制造、林业、水质分析等领域，以及以用户为主体的决策研究，特别是在方案评价和预测分析中发挥了重要作用。

Fuzzy pattern recognition methods provide a scientific basis for evaluation and prediction by establishing mathematical models. At present, pattern recognition mainly performs object recognition by searching large-scale training data and extracting data rules. In pattern selection, methods such as Euclidean closeness and Hamming closeness are often used for ranking. The introduction of fuzzy numbers has promoted the further development of fuzzy pattern recognition and expanded its application areas. Fuzzy pattern recognition is widely used in industrial manufacturing, forestry, water quality analysis and other fields, as well as decision-making research with users as the main body, especially in program evaluation and predictive analysis.

尽管模糊模式识别方法具有较强的灵活性和实用性，能够根据决策需求选择现有方案，但仍存在一些局限性，如构建标准复杂、数据需求量大且难以处理不完整信息，因此基于不完整信息的决策方法应用较为有限。

Although the fuzzy pattern recognition method is highly flexible and practical and can select existing solutions according to decision-making needs, it still has some limitations, such as complex construction standards, large data requirements and difficulty in processing incomplete information. Therefore, the application of decision-making methods based on incomplete information is relatively limited.

（三）不完备信息系统决策方法（Decision-making methods for incomplete information systems）

不完备信息系统中的决策研究主要集中在粗糙集理论和模糊集理论的应用。Yao提出的基于粗糙集的三支决策方法通过颗粒化信息处理，帮助应对不确定性和不精确性。Liu等人提出了直觉模糊信息系统中的三支决策方法，而Qian等人提出了层次化多颗粒化决策模型，涉及乐观与悲观主义的多分支三向决策。

Research on decision making in incomplete information systems mainly focuses on the application of rough set theory and fuzzy set theory. The three-way decision method based on rough sets proposed by Yao helps to deal with uncertainty and imprecision through granular information processing. Liu et al. proposed a three-way decision method in intuitionistic fuzzy information systems, while Qian et al. proposed a hierarchical multi-granular decision model involving multi-branch three-way decision-making with optimism and pessimism.

随着大数据和技术进步，研究者将粗糙集和模糊集理论结合用于处理信息缺失问题。例如，Kryszkiewicz提出了粗糙集推理方法，Chen等人发展了适用于不完备信息的粗糙集模型。同时，Huang和Zhan基于前景-后悔理论提出了多尺度信息决策系统。

With the advancement of big data and technology, researchers have combined rough set and fuzzy set theory to deal with information loss problems. For example, Kryszkiewicz proposed a rough set reasoning method, and Chen et al. developed a rough set model suitable for incomplete information. At the same time, Huang and Zhan proposed a multi-scale information decision system based on prospect-regret theory.

此外，研究还探讨了相似性和支配关系在不完备信息系统中的应用，Greco等人通过梯度支配关系提出了偏好关系和决策规则。总体而言，当前研究主要集中在基于粗糙集的属性补足、结合概率与行为决策的风险方法，以及基于支配关系的优化方法。

In addition, the study also explored the application of similarity and dominance relations in incomplete information systems. Greco et al. proposed preference relations and decision rules through gradient dominance relations. In general, current research mainly focuses on attribute complementation based on rough sets, risk methods combining probability and behavioral decision-making, and optimization methods based on dominance relations.

四、知识补充（Knowledge supplement）

主观赋权法和客观赋权法是多属性决策方法中常用的两种赋权方法，用于确定各个决策属性的重要性或权重。这两种方法在理论和实际应用中有不同的特点：

Subjective weighting method and objective weighting method are two commonly used weighting methods in multi-attribute decision-making methods, which are used to determine the importance or weight of each decision attribute. These two methods have different characteristics in theory and practical application:

1.主观赋权法（Subjective weighting method）

主观赋权法基于决策者的知识、经验和偏好来为各个属性分配权重。这种方法强调决策者对问题的理解和主观判断。常见的主观赋权方法包括：

Subjective weighting methods assign weights to attributes based on the decision maker's knowledge, experience, and preferences. This method emphasizes the decision maker's understanding of the problem and subjective judgment. Common subjective weighting methods include:

专家评估法：由专家根据经验和知识对属性进行打分，赋予不同的权重。

Expert evaluation method: Experts score attributes based on their experience and knowledge and assign different weights.

层次分析法：通过对比不同属性的相对重要性，利用两两比较法确定权重。

Analytical Hierarchy Process: By comparing the relative importance of different attributes, the weights are determined using the pairwise comparison method.

德尔菲法：通过多轮专家咨询，逐步收敛到一致的权重分配。

Delphi method: Through multiple rounds of expert consultation, gradually converge to a consistent weight distribution.

主观赋权法的优点是能够利用决策者的专业知识和经验，但也存在较大的主观性，容易受到决策者个人偏好和判断误差的影响。

The advantage of the subjective weighting method is that it can utilize the professional knowledge and experience of decision makers, but it is also highly subjective and easily affected by the decision maker's personal preferences and judgment errors.

2. 客观赋权法（Objective empowerment method）

客观赋权法则依赖于数据和客观分析，通过统计方法或数学模型来确定各个属性的权重。常见的客观赋权方法包括：

Objective weighting rules rely on data and objective analysis, and use statistical methods or mathematical models to determine the weights of various attributes. Common objective weighting methods include:

熵值法：基于信息熵理论，衡量属性信息的不确定性，信息量越大的属性权重越高。

Entropy method: Based on information entropy theory, it measures the uncertainty of attribute information. The greater the amount of information, the higher the attribute weight.

方差分析法：通过分析各个属性的方差，方差较大的属性通常被认为更为重要。

ANOVA: By analyzing the variance of each attribute, attributes with larger variance are usually considered more important.

回归分析法：通过建立回归模型，分析各个属性对决策结果的贡献，进而确定权重。

Regression analysis method: By establishing a regression model, the contribution of each attribute to the decision-making result is analyzed, and then the weight is determined.

客观赋权法的优点是权重的确定更加科学和数据驱动，减少了主观偏差。然而，它也可能忽略决策者的经验或偏好，且在数据不充分或质量较差时，赋权结果可能不准确。

The advantage of objective weighting is that the determination of weights is more scientific and data-driven, reducing subjective bias. However, it may also ignore the experience or preferences of decision makers, and when the data is insufficient or of poor quality, the weighting results may be inaccurate.

3.主观赋权法与客观赋权法的结合（Combination of subjective weighting method and objective weighting method）

为了克服各自的不足，许多研究采用了混合赋权法，即结合主观赋权法和客观赋权法，以期达到更加合理和均衡的权重分配。混合赋权法能够兼顾决策者的主观经验和数据的客观性，使决策过程更加全面和准确。

In order to overcome their respective shortcomings, many studies have adopted a hybrid weighting method, that is, combining subjective weighting method and objective weighting method, in order to achieve a more reasonable and balanced weight distribution. The hybrid weighting method can take into account the subjective experience of decision makers and the objectivity of data, making the decision-making process more comprehensive and accurate.

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