越览（91）——精读硕士论文的研究对象和关键词定义

摘要：This post will introduce the research object and keyword definition of the master's thesis "Research on multi-Attribute fuzzy deci

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“越览（91）——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》

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"Yuelan (91): Intensive reading of the master's thesis

"Research objects and keyword definitions 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》的研究对象和关键词定义。

This post will introduce the research object and keyword definition 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）研究对象——不完备信息系统（Research object—incomplete information system）

不完备信息系统是指在实际应用中，由于信息的缺失、错误或不完整，导致系统中的某些信息无法完全或准确获得的情形。在一个完备的信息系统中，每个属性的值都是可用且已知的，然而在不完备信息系统中，由于某些数据缺失或不确定，导致部分信息不可得，这种不完全或不精确的信息会影响决策过程。

An incomplete information system refers to a situation in which some information in the system cannot be fully or accurately obtained due to missing, wrong or incomplete information in practical applications. In a complete information system, the value of each attribute is available and known, but in an incomplete information system, some information is unavailable due to missing or uncertain data. This incomplete or inaccurate information will affect the decision-making process.

（二）关键词定义（Keyword definition）

1.模糊模式识别（Fuzzy pattern recognition）

模糊模式识别是在模式识别方法的基础上引入模糊集，模糊模式识别是一种处理模糊和不确定性信息的技术。它的目标是识别和分类模糊和不明确的数据或信息，通常涉及到不完全的、模糊的、或模糊边界的模式和特征。

Fuzzy pattern recognition is a technique that introduces fuzzy sets on the basis of pattern recognition methods. Fuzzy pattern recognition is a technique for processing fuzzy and uncertain information. Its goal is to identify and classify fuzzy and ambiguous data or information, usually involving incomplete, fuzzy, or fuzzy-boundary patterns and features.

2.贴近度（Closeness）

在模糊模式识别中，“贴近度”通常指的是样本或模式在某些特定属性上的值与目标模式或标准之间的相似度。这种相似度或“贴近度”可以通过模糊集合的成员度来度量，即某一事物在特定属性上的隶属度越高，说明它与目标模式的贴近度越高。

In fuzzy pattern recognition, "closeness" usually refers to the similarity between the value of a sample or pattern on certain specific attributes and the target pattern or standard. This similarity or "closeness" can be measured by the membership degree of the fuzzy set, that is, the higher the membership degree of a thing on a specific attribute, the closer it is to the target pattern.

3.多属性决策（Multiple attribute decision making）

多属性决策指的是在决策过程中，考虑多个不同的评价标准或属性，对备选方案进行综合评估，从而选择最优或最适合的决策方案。多属性决策方法广泛应用于各种实际问题中，尤其在面对复杂且具有多个决策因素的情境下，能够帮助决策者做出合理的选择。

Multi-attribute decision-making refers to the process of considering multiple different evaluation criteria or attributes in the decision-making process, comprehensively evaluating alternative options, and selecting the best or most suitable decision-making solution. Multi-attribute decision-making methods are widely used in various practical problems, especially in complex situations with multiple decision factors, which can help decision makers make reasonable choices.

4.属性权重（Attribute weight）

属性权重在多属性决策中指的是每个属性在决策过程中的相对重要性。它反映了决策者在综合评估各个备选方案时，不同属性对最终决策结果的影响程度。每个属性的权重值通常是根据其对决策目标的贡献或影响来确定的，权重值越高的属性，其在最终决策中的作用越大。

Attribute weight in multi-attribute decision-making refers to the relative importance of each attribute in the decision-making process. It reflects the degree of influence of different attributes on the final decision result when the decision maker comprehensively evaluates various alternatives. The weight value of each attribute is usually determined based on its contribution or influence on the decision goal. The higher the weight value of the attribute, the greater its role in the final decision.

四、知识补充——粗糙集理论（Knowledge supplement——Rough set theory）

粗糙集理论是一种处理不完备、不精确、不确定信息的数学理论，最早由波兰学者Zdzisław Pawlak于1982年提出。粗糙集理论的核心思想是，通过对不完备或模糊数据的分析，从中提取出重要的决策规则，而不依赖于外部知识或预定义的假设。

Rough set theory is a mathematical theory for dealing with incomplete, imprecise and uncertain information, first proposed by Polish scholar Zdzisław Pawlak in 1982. The core idea of rough set theory is to extract important decision rules from incomplete or fuzzy data without relying on external knowledge or predefined assumptions.

粗糙集理论的基本概念和要素包括以下几个方面：

The basic concepts and elements of rough set theory include the following aspects:

1.信息系统（Information systems）

粗糙集理论应用于信息系统，一个信息系统通常由对象、属性及其属性值组成。例如，决策系统中的数据可以被表示为一个表格，其中每一行代表一个决策对象（如客户、产品、实验等），每一列代表一个属性（如年龄、收入、产品特征等），表格中的每个元素则是属性的取值。

Rough set theory is applied to information systems. An information system usually consists of objects, attributes and their attribute values. For example, the data in a decision system can be represented as a table, where each row represents a decision object (such as customer, product, experiment, etc.), each column represents an attribute (such as age, income, product features, etc.), and each element in the table is the value of the attribute.

2.等价关系（Equivalence relation）

粗糙集理论的基础是等价关系。在信息系统中，等价关系用于将对象分成若干个等价类。对于给定的属性集，等价关系将数据对象划分为若干个集合（等价类），其中每个类内的对象在该属性上具有相同的取值。通过这种划分，可以帮助我们识别出数据对象之间的相似性。

The basis of rough set theory is equivalence relation. In information systems, equivalence relation is used to divide objects into several equivalence classes. For a given set of attributes, equivalence relation divides data objects into several sets (equivalence classes), where objects in each class have the same value for the attribute. This division can help us identify the similarities between data objects.

3.上近似集和下近似集（Upper and lower approximation sets）

粗糙集通过上近似集和下近似集来表示不完备信息的处理方法。

Rough sets use upper approximation sets and lower approximation sets to represent the method of dealing with incomplete information.

上近似集：一个对象的上近似集是指所有可能属于该集合的对象的集合，表示在信息不完全或不确定的情况下，我们认为该对象属于目标集合的所有对象。

Upper approximate set: The upper approximate set of an object refers to the set of all objects that may belong to the set, indicating that when the information is incomplete or uncertain, we believe that the object belongs to all objects in the target set.

下近似集：一个对象的下近似集是指所有确实属于该集合的对象的集合，表示在信息不完全时，至少可以确定该对象属于目标集合的那些对象。

Lower approximate set: The lower approximate set of an object refers to the set of all objects that do belong to the set, indicating those objects that can at least be determined to belong to the target set when the information is incomplete.

这两个近似集帮助在处理不完全信息时，明确哪些对象是可以确定属于某一类别的（下近似集），哪些对象是可能属于该类别的（上近似集）。

These two approximate sets help to clarify which objects can be determined to belong to a certain category (lower approximate set) and which objects may belong to the category (upper approximate set) when dealing with incomplete information.

4.属性约简（Attribute reduction）

粗糙集的一个重要应用是属性约简。在信息系统中，可能有许多属性，但并不是所有的属性都对分类或决策具有重要影响。通过粗糙集理论，能够分析哪些属性是冗余的，哪些属性对于分类是必须的。通过属性约简，可以去除冗余属性，保留关键属性，从而减少决策问题的复杂度。

An important application of rough sets is attribute reduction. In information systems, there may be many attributes, but not all attributes have an important impact on classification or decision-making. Through rough set theory, it is possible to analyze which attributes are redundant and which attributes are necessary for classification. Through attribute reduction, redundant attributes can be removed and key attributes can be retained, thereby reducing the complexity of decision-making problems.

5.决策规则提取（Decision rule extraction）

粗糙集理论还可以用于从数据中提取决策规则。决策规则是通过分析数据中的关系和模式，找出描述对象和决策结果之间关联的规则。比如，通过粗糙集理论可以得出类似“如果年龄>30且收入>5000，那么推荐投资A项目”的规则。

Rough set theory can also be used to extract decision rules from data. Decision rules are rules that describe the relationship between objects and decision results by analyzing the relationships and patterns in the data. For example, through rough set theory, we can derive a rule like "if age > 30 and income > 5000, then recommend investment in project A".

这些规则是通过对信息系统中的数据进行分析而自动生成的，不需要事先定义，因此特别适合处理不完备或不确定的信息。

These rules are automatically generated by analyzing the data in the information system and do not need to be defined in advance, so they are particularly suitable for processing incomplete or uncertain information.

6.处理不完备信息（Dealing with incomplete information）

粗糙集理论的一个重要优势是其能够在没有外部信息的情况下处理不完备和不精确信息。例如，当某些属性值缺失时，粗糙集能够通过近似集的概念来分析和处理这些缺失的数据，而不需要补充缺失的具体信息。

An important advantage of rough set theory is that it can handle incomplete and imprecise information without external information. For example, when some attribute valuesare missing, rough sets can analyze and handle these missing data through the concept of approximate sets without supplementing the missing specific information.

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