小源筆記37：《雙極容度多屬性決策 VIKOR方法》雙極容度概念解讀

2022年10月07日23:36:27 教育 1842

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今天小編給大家帶來期刊論文《屬性關聯的雙極容度多屬性決策 VIKOR方法》雙極容度概念解讀，

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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,

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多屬性評價作為多準則決策的分支之一，在現實生活中有著廣泛的應用。然而現實問題中，評價屬性間常存在著關聯，如互補關聯、冗餘關聯等，很難構建完全獨立的屬性體系。因此，忽略屬性間的關聯可能會造成錯誤評價。現有的評價方法運用的前提都是假設屬性間是相互獨立，不能直接用於屬性間存在關聯的情況。容度理論是解決屬性間關聯的有效理論，近年來研究者將容度理論拓展為雙極容度理論。雙極容度理論更具一般性，能夠有效的處理評價值為負值的情況。

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.

雙極容度可以對指標值處於雙極區間的指標權重和指標間關聯進行建模，最常用的是雙極區間為[-1,1]。以下為雙極容度的定義：

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:

在這種有屬性關聯的多屬性決策，需要綜合考察單個屬性對所有屬性集的作用，因此，根據Shapley值的定義，定義雙極容度的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).

接著，作者利用Choquet積分運算元來對多屬性決策問題的信息進行集結，根據屬性的不同重要程度，利用雙極容度來建模和測量，給出了雙極容度Choquet積分運算元的定義如下所示：

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: