小源笔记37：《双极容度多属性决策 VIKOR方法》双极容度概念解读

2022年10月07日23:36:27 教育 1842

分享兴趣，传播快乐，增长见闻，留下美好。

亲爱的您，

这里是LearningYard学苑！

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》双极容度概念解读，

欢迎您的用心访问！

本期推文阅读时长大约6分钟，请您耐心阅读。

Share interest, spread happiness, increase knowledge, and leave beautiful.

Dear you,

This is the LearningYard Academy!

Today, the editor brings you the theoretical part of the journal paper "Bipolar Tolerance Multi-attribute Decision-Making VIKOR Method for Attribute Correlation"Bipolar Tolerance Concept Interpretation,

Welcome your visit!

This tweet usually takes about 6 minutes to read. Please be patient and read.

多属性评价作为多准则决策的分支之一，在现实生活中有着广泛的应用。然而现实问题中，评价属性间常存在着关联，如互补关联、冗余关联等，很难构建完全独立的属性体系。因此，忽略属性间的关联可能会造成错误评价。现有的评价方法运用的前提都是假设属性间是相互独立，不能直接用于属性间存在关联的情况。容度理论是解决属性间关联的有效理论，近年来研究者将容度理论拓展为双极容度理论。双极容度理论更具一般性，能够有效的处理评价值为负值的情况。

As one of the branches of multi-criteria decision-making, multi-attribute evaluation has a wide range of applications in real life. However, in real problems, there are often associations between evaluation attributes, such as complementary associations, redundant associations, etc., and it is difficult to build a completely independent attribute system. Therefore, ignoring associations between attributes can result in false evaluations. The premise of the existing evaluation method is to assume that the attributes are independent of each other and cannot be directly used in the case of correlation between the attributes. Tolerance theory is an effective theory to solve the correlation between attributes, and in recent years, researchers have expanded the tolerance theory to bipolar tolerance theory. Bipolar tolerance theory is more general and can effectively deal with cases where the evaluation value is negative.

双极容度可以对指标值处于双极区间的指标权重和指标间关联进行建模，最常用的是双极区间为[-1,1]。以下为双极容度的定义：

Bipolar tolerance can model the index weight and the association between indicators whose index values are in the bipolar range, and the most commonly used bipolar range is [-1,1]. The following is the definition of bipolar capacitance:

在这种有属性关联的多属性决策，需要综合考察单个属性对所有属性集的作用，因此，根据Shapley值的定义，定义双极容度的Shapley值如下所示：

For the multi-attribute decision problem of attribute association, the degree to which the attribute contributes to the decision result must be comprehensively examined by the role of all attribute sets, referring to the definition of Shapley values in game theory, and defining the Shapley value of the bipolar tolerance of the limited discrete attribute (set).

接着，作者利用Choquet积分算子来对多属性决策问题的信息进行集结，根据属性的不同重要程度，利用双极容度来建模和测量，给出了双极容度Choquet积分算子的定义如下所示：

When the criticality of the attribute set is to be modeled and measured using bipolar tolerance, the information of the multi-attribute decision problem can be aggregated by the Choquet integral operator, and the definition of the bipolar tolerance Choquet integration operator is given: