越览（105）——精读复刻论文的对比分析（4）

摘要：This issue will introduce the comparative analysis of the intensively read replica paper "Emergency decision-making method based o

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“越览（105）——精读复刻论文

《基于多粒度概率语言和双参照点的

应急决策方法》对比分析（4）。”

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Today, the editor brings the

"Yue Lan(105)—intensive reading replica paper

'Emergency decision-making method based on

multi-granularity probability language

and dual reference points

'comparative analysis (4)".

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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精读复刻论文《基于多粒度概率语言和双参照点的应急决策方法》的对比分析（4）。

This issue will introduce the comparative analysis of the intensively read replica paper "Emergency decision-making method based on multi-granularity probability language and dual reference points" in terms of mind maps, intensively read content, and knowledge supplementation.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

为了验证本文所提方法的有效性和优越性，本文将从关键风险因素的权重确定方法和可行方案的选择方法两个方面与现有的方法进行了对比分析。在关键风险因素权重确定方法的比较分析中，选用了四个不同文献中的方法来计算各项关键因素风险的权重。另外还采用了Pearson相关系数研究本文方法与现有方法的相关关系。

In order to verify the effectiveness and superiority of the proposed method, this paper will compare and analyze the existing methods from two aspects: the method of determining the weight of key risk factors and the method of selecting feasible solutions. In the comparative analysis of the method of determining the weight of key risk factors, four methods from different literatures were selected to calculate the weight of each key factor risk. In addition, the Pearson correlation coefficient was used to study the correlation between the proposed method and the existing methods.

本周基于WAA算子来计算本文案例中的各项关键因素风险的权重。基于所定义的广义区间二元语言WAA 算子，决策成员从给定的二元语言评估标度中选择偏好的语言短语，用二元语言区间值表征信息的不确定性。代码如下图所示：

This week, we calculated the risk weights of each key factor in this case based on the WAA operator. Based on the defined generalized interval bi-gram WAA operator, decision-makers select preferred language phrases from the given bi-gram evaluation scale and use the bi-gram interval value to represent the uncertainty of information. The code is shown in the figure below:

The operation results are shown in the figure below:

四、知识补充（Knowledge supplement）

模糊数是模糊集合理论中的一个概念，用于表示数值的不确定性或模糊性。在传统的集合论中，一个元素要么属于某个集合，要么不属于；但在模糊集合论中，元素可以有某种程度的成员资格，这个程度通常用介于0到1之间的实数来表示。模糊数是一种特殊的模糊集合，它定义在实数集上，并且具有以下特性：

Fuzzy numbers are a concept in fuzzy set theory used to represent the uncertainty or fuzziness of numerical values. In traditional set theory, an element either belongs to a certain set or does not; but in fuzzy set theory, elements can have some degree of membership, which is usually represented by real numbers between 0 and 1. Fuzzy numbers are a special kind of fuzzy set that are defined on the set of real numbers and have the following properties:

1.正则性：存在至少一个元素x，使得其隶属度函数μ(x) = 1，意味着有一个或多个点是完全属于该模糊集合的。

1. Regularity: The existence of at least one element x such that its membership function μ (x) = 1 implies that one or more points belong entirely to the fuzzy set.

2.凸性：对于所有隶属度函数值不小于某个α（0

2. Convexity: For all elements whose membership function value is not less than a certain α (0

3.有限支撑：隶属度大于0的元素所组成的集合是有界的，即模糊数不是无限延伸的。

3. Finite support: The set of elements with membership greater than 0 is bounded, that is, the fuzzy number does not extend infinitely.

4.上半连续性：隶属度函数是上半连续的，这意味着隶属度函数不会突然增加。

4. Upper Semi-Continuity: The membership function is upper semi-continuous, which means that the membership function does not increase suddenly.

最常见的模糊数类型是三角形模糊数和梯形模糊数，它们可以用三个或四个参数来描述，分别对应着模糊数的左肩、核心（最可能的值）、右肩以及可选的底部宽度。例如，一个三角形模糊数可以用 (a, b, c) 表示，其中 a 是左端点，b 是顶点（也是最大隶属度的位置），c 是右端点。

The most common types of fuzzy numbers are triangular fuzzy numbers and trapezoidal fuzzy numbers, which can be described by three or four parameters, corresponding to the left shoulder, core (most likely), right shoulder, and optional bottom width of the fuzzy number. For example, a triangular fuzzy number can be represented by (a, b, c), where a is the left endpoint, b is the vertex (also the location of maximum membership), and c is the right endpoint.

模糊数在许多领域都有应用，如模糊逻辑控制、决策分析、风险评估等，特别是在处理不确定信息时非常有用。

Fuzzy numbers are used in many fields, such as fuzzy logic control, decision analysis, threat and risk assessment, especially in dealing with uncertain information.

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