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今天小编给大家带来期刊论文《属性关联的双极容度多属性决策 VIKOR方法》决策步骤理论基础3，
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Today, the editor brings you the theoretical basis of decision steps in the journal paper "Attribute Association Bipolar Capacity Multi-attribute Decision VIKOR Method" ,
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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
本节内容主要针对步骤四的内容进行具体分析，作者首先利用双极容度对交互的属性集权重进行建模策略，如下所示：
The content of this section focuses on the specific analysis of Step 4, where the authors first use the bipolar tolerance to model the interaction's attribute set weights as follows.
然后，作者优化了模型，并在求解权重之前，确定双击容度的shapley值，如下所示：
The authors then optimized the model and determined the shapley value of the double hit tolerance before solving for the weights, as follows.
知识补充
在论文决策步骤四中，作者计算属性权重时，需要考虑属性关联的关系，为避免计算出现Grabisch悖论，文章采用双极容度对交互的属性的权重进行建模测量，这里我们需要了解容度理论、模糊测度的含义。
In the decision step four of the paper, when the authors calculate the attribute weights, they need to consider the relationship of attribute associations, and to avoid the Grabisch paradox in the calculation, the article uses bipolar tolerance to model the measurement of the weights of the interacting attributes, and here we need to understand the meaning of tolerance theory, fuzzy measure.
1
Part.1
容度理论
用容度理论考虑属性关联时，用的都是单极区间，表现在容度值属于[0,1]且决策者对方案评价值的确定都是局限在[0,1]之间。但是人们对一个事物的偏好，通常有喜爱、中立、厌恶的表现，这是单极区间所无法表示的。双极区间可以弥补此不足之处，双极区间是从负值（厌恶）到正值（喜爱），包括一个中间值（中立）。典型的双极区间是[-1,1]，可以起到“奖优罚劣”的作用。故 Grabisch 将容度理论拓展为双极容度理论，双极容度是容度的更一般表现形式。双极容度值属于 [-1,1]，这就有效解决了属性的评价值为负值时的权重确定问题。
When considering attribute associations using tolerance theory, unipolar intervals are used, as shown by the fact that the tolerance value belongs to [0,1] and the decision maker's determination of the evaluation value of the solution is limited to the range [0,1]. However, people's preference for a thing usually has a favorite, a neutral, or an averse expression, which cannot be represented by unipolar intervals. Bipolar intervals can compensate for this deficiency by ranging from negative (dislike) to positive (like) values, including an intermediate value (neutral). A typical bipolar interval is [-1,1], which serves as a "reward for the good and punishment for the bad". Therefore, Grabisch extended the tolerance theory to bipolar tolerance theory, which is a more general expression of tolerance. The bipolar tolerance value belongs to [-1,1], which effectively solves the problem of determining the weight when the evaluation value of an attribute is negative.
2
Part.2
模糊测度
1974年，日本学者Sugeno为解决属性之间存在关联而又不具备可加性的多属性决策问题，提出了模糊测度，它可以表示一个或多个属性的综合重要程度，可以更加准确地描述个属性之间的相互关系。因此，基于模糊测度属性重要模型可以更准确地表示各属性的重要程度。
In 1974, Sugeno, a Japanese scholar, proposed a fuzzy measure to solve the multi-attribute decision problem where attributes are related but not additive, which can represent the combined importance of one or more attributes and can more accurately describe the interrelationship between attributes. Therefore, the fuzzy measure-based attribute importance model can represent the importance of each attribute more accurately.
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参考资料：DeepL翻译、百度百科、知乎
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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