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Today, the editor brings you intensive reading of journal papers,
welcome your visit!
This tweet usually takes about 6 minutes to read. Please be patient and read.
今天小编将从思维导图、精读内容、知识补充三个板块为大家带来论文《属性关联的双极容度多属性决策 VIKOR方法》步骤四，接下来我们开始今天的学习吧！
Today, the editor will bring you the fourth step of the paper "VIKOR Method of Bipolar Tolerance Multi-attribute Decision Making of Attribute Association" from the three parts of mind map, intensive reading content and knowledge supplement. Next, let's start today's study!
思维导图
本节内容思维导图如下所示：
A mind map of the contents of this section is shown below.
精读内容
论文的步骤四中，作者首先考虑了属性关联关系，来计算权重，那么我们为什么需要考虑属性的关联关系，以及考虑属性关联关系过程中，我们使用了哪些方法。
In the fourth step of the paper, the author first considered the attribute association to calculate the weight, then why we need to consider the attribute association, and what methods we used in the process of considering the attribute association.
小编通过查询资料与分析，了解到关联型决策分析是决策科学领域近年来快速发展的重要研究分支，尤其是供应链整合和管理协同创新方面，相关研究并不是很全面，针对关联性决策分析的研究脉络来看，90年代以前主要是侧重实验和定性方法研究检验属性、指标、方案、目标、决策者等不同决策要素的关联存在性，而在2000年以后的研究更倾向于定量化的方法探索研究。而随着全球供应链的整合发展与现金ICT技术的广泛应用，跨组织、跨流程等方面的关联性决策分析问题与日俱增，涌现了许多离岸多来源外包关联性业务遴选等问题，需要进行对该领域是深入解析和方法对比。
Through data and analysis, the editor learned that relevance decision analysis is an important branch of research in the field of decision-making science that has developed rapidly in recent years, especially in the field of supply chain integration and management collaborative innovation. The relevant research is not very comprehensive. From the perspective of the research context of relevance decision analysis, before the 1990s, it mainly focused on experimental and qualitative methods to test attributes, indicators, plans, objectives The relevance and existence of different decision-making factors, such as decision-makers, and the research after 2000 is more inclined to explore the quantitative method. With the integration and development of the global supply chain and the wide application of the cash ICT technology, the problems of cross-organizational and cross-process related decision analysis are increasing day by day, and many problems such as the selection of offshore multi-source outsourcing related business have emerged, which requires in-depth analysis and method comparison in this field.
对于关联信息，其获取信息方式灵活化、工具化和智能化，可以通过一定时间积累形成的历史数据，还可以源自专家智慧的主管判定信息，也可以借助工具获取仿真模拟信息和实时动态信息。问卷调查法、网络层次分析、灰关联分析等一些成熟的方法也能作为工具获取关联信息。
For the associated information, its access to information is flexible, instrumental and intelligent. It can be formed through historical data accumulated over a certain period of time, can also be derived from expert intelligence of the supervisor's judgment information, and can also obtain simulation information and real-time dynamic information with the help of tools. Some mature methods such as questionnaire survey, network analytic hierarchy process and grey relational analysis can also be used as tools to obtain relevant information.
关联属性决策涉及到属性/指标关联、方案关联、目标关联和决策者关联，本篇复刻论文主要是针对属性/指标关联情境的决策分析方法进行研究和探索，针对此类型问题，可以利用多准则妥协优化解、ANP、Choquet积分等方法。
Related attribute decision involves attribute/indicator association, scheme association, target association and decision maker association. This replica paper mainly studies and explores the decision analysis methods of attribute/indicator association situation. For this type of problem, multi-criteria compromise optimization, ANP, Choquet integral and other methods can be used.
接下来，步骤四中还叙述到“由于fij属于R，落在双极区间”，这里我们该如何理解呢？
Next, in Step 4, it is also described that "because fij belongs to R, it falls in the bipolar region". How do we understand it here?
首先，我们需要了解容度理论的内涵，容度又被称为模糊测度、非可加测度，最早由日本学者Sugeno提出，用于对属性间的关联度进行测量，在考虑属性关联的多属性决策中，一般将容度值作为属性集的权重。
First of all, we need to understand the connotation of tolerance theory, which is also called fuzzy measure and non-additive measure. It was first proposed by Japanese scholar Sugeno to measure the correlation degree between attributes. In multi-attribute decision making considering attribute correlation, the tolerance value is generally taken as the weight of attribute set.
其次，当容度值处于 0 到 1 之间，可视为单极容度。Grabisch指出以前考虑属性关联都是使用的单极容度的概念，决策者对于属性参数的确定基本局限在[0，1]之间。然而一个人对于事物的偏好通常是两极的，我们可以认为它好，也可以认为它不好，这是单极的区间无法体现出来的，因此针对现实生活中人们心理上对事物的偏好有喜爱、中立、厌恶的表现，双极区间可以更加清楚地表现出来。
Secondly, when the capacitance value is between 0 and 1, it can be regarded as unipolar capacitance. Grabisch pointed out that the concept of unipolar tolerance was used to consider attribute association before, and the decision makers' determination of attribute parameters was basically limited to [0, 1]. However, a person's preference for things is usually bipolar. We can think of it as good or bad, which is not reflected in the unipolar interval. Therefore, in view of people's psychological preference for things in real life, there are likes, neutrality and aversion, and the bipolar interval can be more clearly displayed.
最后，典型的双极区间有[-1，1]（有界），R（无界），{非常差，差，一般，好，非常好}（有序）等。最常用的是[-1，1]，用0表示中立态度，（0，1]表示赞成偏好，[-1，0）表示反对偏好，可以起到奖优罚劣的作用。
Finally, typical bipolar intervals are [- 1,1] (bounded), R (unbounded), {very poor, poor, average, good, very good} (ordered), etc. The most commonly used is [- 1, 1]. Use 0 to indicate a neutral attitude, (0, 1] to indicate a favorable preference, and [- 1, 0) to indicate a negative preference, which can play the role of rewarding the good and punishing the bad.
知识补充
在上文中，我们提到了考虑属性关联时可以利用容度理论，这时学者们常常结合模糊积分建模，例如与 Choquet 积分相结合，虽然容度理论可以定量处理属性间的关联，但所需确定的参数较多。
In the above, we mentioned that the tolerance theory can be used when considering attribute association. At this time, scholars often combine fuzzy integral modeling, for example, with Choquet integral. Although the tolerance theory can quantitatively deal with the association between attributes, it requires more parameters to be determined.
假设有 n 个属性，则就有 2的n次方个属性（集），相应的也就需要确定 （2的n次方-2 ）个容度值；当 n 值较大时，需确定的容度值个数会按指数级增长，下图为各类容度的所需确定的参数数目以及精准度等方面的对比：
If there are n attributes, then there are 2 nth power attributes (sets), and accordingly, it is necessary to determine (2 nth power - 2) capacity values; When the value of n is large, the number of capacity values to be determined will increase exponentially. The following figure shows the comparison of the number of parameters to be determined and the accuracy of various capacities:
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参考资料：DeepL翻译、百度百科
参考文献：
[1]林萍萍,李登峰,江彬倩,余高锋,韦安鹏.属性关联的双极容度多属性决策VIKOR方法[J].系统工程理论与实践,2021,41(08):2147-2156.
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