摘要：This tweet will introduce the 5 multi-attribute large group decision-making methods based on multi-granularity hesitant fuzzy lang
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“越览（82）——精读博士论文
《基于多粒度犹豫模糊语言信息的
多属性群决策方法研究》的5基于多粒度
犹豫模糊语言信息的多属性大群体决策方法（1）”。
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"Yue Lan (82)：Multi-attribute large group
decision-making method based on
multi-granular hesitant fuzzy linguistic information (1)'
Research on multi-attribute group decision method
based on multi-granularity hesitant
fuzzy language information'".
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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博士论文《基于多粒度犹豫模糊语言信息的多属性群决策方法研究》的5基于多粒度犹豫模糊语言信息的多属性大群体决策方法（1）。
This tweet will introduce the 5 multi-attribute large group decision-making methods based on multi-granularity hesitant fuzzy language information of the doctoral dissertation "Research on multi-attribute group decision-making methods based on multi-granularity hesitant fuzzy language information" from three aspects: mind map, intensive reading content, and knowledge supplement (1).
二、思维导图（Mind mapping）
三、精读内容（Intensive reading content）
本次推文主要从非平衡语言信息和平衡语言分布之间的转化、多属性大群体决策问题描述和多属性大群体决策方法三部分进行介绍。
This tweet mainly introduces the transformation between non-balanced language information and balanced language distribution, the description of multi-attribute large-group decision-making problems, and the multi-attribute large-group decision-making method.
（一）非平衡语言信息和平衡语言分布之间的转化（Transformation between unbalanced linguistic information and balanced linguistic distributions）
本节提出了将多粒度非平衡犹豫模糊语言术语集转化为平衡语言分布的方法，实现专家评价信息的一致化与集成，并研究了如何将平衡语言分布反馈为初始术语集的非平衡语言分布，从而提供可解释的决策结果。
This section proposes a method to transform multi-granular non-balanced hesitant fuzzy language term sets into balanced language distributions, to achieve consistency and integration of expert evaluation information, and studies how to feed back the balanced language distributions into the non-balanced language distributions of the initial term sets to provide interpretable decision results.
1. 非平衡犹豫模糊语言术语集与平衡语言分布的转化（Transformation of unbalanced hesitant fuzzy linguistic term sets to balanced linguistic distributions）
本节提出一种方法，将非平衡犹豫模糊语言术语集转化为平衡语言分布。具体步骤如下所示：
In this section, a method is proposed to transform an unbalanced hesitant fuzzy linguistic term set into a balanced linguistic distribution. The specific steps are as follows:
2. 平衡语言分布与非平衡语言分布的转化（Transformation of balanced and non-balanced language distributions）
本节研究重点在于将非平衡犹豫模糊语言术语集转化为平衡语言分布，然后通过进一步的操作将结果转化回非平衡语言分布。
This section focuses on transforming the unbalanced hesitant fuzzy linguistic term sets into balanced linguistic distributions, and then converting the results back into unbalanced linguistic distributions through further operations.
非平衡语言术语集首先被映射为平衡语言分布。公式（5.5）定义了数值标度，并证明了其关于语言术语的单调递增特性。
The unbalanced linguistic term set is first mapped to the balanced linguistic distribution. Equation (5.5) defines the numerical scale and proves its monotonically increasing property with respect to linguistic terms.
通过公式（5.8），平衡语言分布中的术语被转化为非平衡分布，满足逆函数关系。
With Equation (5.8), the terms in the balanced linguistic distribution are transformed into non-equilibrium distributions, satisfying the inverse function relationship.
这种转换方法不仅保证了评价结果在数值上的一致性，还通过回归非平衡分布，使其更符合专家的语言术语习惯。具体步骤如下所示：
This conversion method not only guarantees the numerical consistency of the evaluation results, but also makes it more in line with the experts' language terminology habits by regression to the non-equilibrium distribution. The specific steps are as follows:
（二）多属性大群体决策问题描述（Description of multi-attribute large group decision-making problem）
本节中定义了决策问题中的关键元素，包括备选方案集合、属性集合、专家集合，以及多粒度犹豫模糊语言术语集的使用方式。同时，针对不同属性的重要性，设定了权重向量，并引入了用于评价的数值标度函数。基于此，问题的核心在于利用混合型多粒度犹豫模糊语言信息，构建辅助模型，实现专家间的共识达成，对备选方案进行排序并最终选择最优方案。
This section defines the key elements of decision problems, including the set of alternatives, the set of attributes, the set of experts, and the use of the term set of multi-granular hesitant fuzzy language. At the same time, according to the importance of different attributes, the weight vector is set, and the numerical scaling function for evaluation is introduced. Based on this, the core of the problem is to use the mixed multi-granular hesitant fuzzy language information to build an auxiliary model to achieve consensus among experts, rank the alternatives and finally select the best solution.
（三）多属性大群体决策方法（Multi-attribute large group decision-making method）
本节提出一种针对多粒度犹豫模糊语言信息的大群体多属性决策方法。方法包括以下步骤：首先，将不同类型的多粒度语言信息统一为基本平衡语言术语集的语言分布；其次，根据专家间观点相似性进行聚类，将专家分为若干簇，并将各簇的属性值表示为语言分布；然后，基于精确度约束构建最小调整共识模型改进群体共识，得到调整后的决策矩阵；最后，通过集成和选择过程，对备选方案进行综合评价和排序。
This section proposes a large-group multi-attribute decision-making method for multi-granular hesitant fuzzy linguistic information. The method includes the following steps: first, unify different types of multi-granular linguistic information into the language distribution of the basic balanced language term set; second, cluster according to the similarity of opinions among experts, divide the experts into several clusters, and represent the attribute values of each cluster as the language distribution; then, construct a minimum adjustment consensus model based on precision constraints to improve the group consensus and obtain the adjusted decision matrix; finally, comprehensively evaluate and rank the alternatives through the integration and selection process.
同时，利用优化模型将综合评价转化为比例犹豫模糊语言术语集，为专家提供可解释性结果。具体框架图如下所示：
At the same time, the optimization model is used to transform the comprehensive evaluation into a proportional hesitation fuzzy language term set to provide experts with interpretable results. The specific framework diagram is as follows:
四、知识补充——模糊ｃ均值算法（Knowledge supplement — fuzzy c-means algorithm）
模糊 c均值算法是一种基于聚类分析的算法，用于将数据划分为多个类别。它是经典 k均值算法的模糊版本，允许一个数据点属于多个簇的可能性。其核心思想是通过最小化目标函数，计算数据点到每个簇中心的隶属度，从而完成数据分组。
The fuzzy c-means algorithm is an algorithm based on cluster analysis to divide data into multiple categories. It is a fuzzy version of the classical k-means algorithm, allowing the possibility that a data point belongs to multiple clusters. The core idea is to calculate the degree of membership of data points to the center of each cluster by minimizing the objective function, thus completing the data grouping.
1. 模糊隶属度（Fuzzy membership）
与硬聚类（如 k-均值）不同，模糊 c-均值允许数据点属于多个簇，每个数据点对不同簇的隶属度 uij 满足：
Unlike hard clustering (e.g., k-means), fuzzy c-means allows data points to belong to multiple clusters, and each data point's membership to different clusters satisfies:
2. 目标函数（Objective function）
通过最小化以下目标函数，确定簇中心和隶属度：
Determine cluster centers and membership degrees by minimizing the following objective functions:
3. 簇中心更新（Cluster center update）
4. 隶属度更新（Membership update）
根据当前簇中心更新隶属度：
Update the membership according to the current cluster center:
（二）算法步骤（Algorithm steps）
1. 初始化簇的数量 c、模糊因子 m 和初始隶属度矩阵 U。
1. The number of initialized clusters c, the ambiguity factor m, and the initial membership matrix U.
2. 根据隶属度计算每个簇的中心 vj。
2. Calculate the center vj of each cluster according to the degree of membership.
3. 更新隶属度矩阵 U。
3. Update the membership matrix U.
4. 迭代步骤 2 和 3，直到满足终止条件（如目标函数变化小于设定阈值）。
4. Iterate steps 2 and 3 until the termination condition is met (e.g. the objective function change is less than the set threshold).
5. 输出簇中心和隶属度矩阵。
5. Output cluster center and membership matrix.
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翻译：火山翻译
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参考文献：于文玉. 基于多粒度犹豫模糊语言信息的多属性群决策方法研究[D]. 大连理工大学, 2021.
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