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今天小編給大家帶來期刊論文精讀，
歡迎您的用心訪問！
本期推文閱讀時長大約6分鐘，請您耐心閱讀。
Share interest, spread happiness, increase knowledge, and leave beautiful.
Dear you,
this is the LearningYard Academy!
Today, the editor brings you an interpretation of the doctoral thesis,
welcome your visit!
This tweet usually takes about 6 minutes to read. Please be patient and read.
今天小編將從思維導圖、精讀內容、知識補充三個板塊為大家帶來期刊論文《Entropy of bi-capacities》實際應用內容 ，接下來我們開始今天的學習吧！
Today's editor will bring you the practical application content of the journal paper "Entropy of bi-capacities" from the three parts of mind map, intensive reading content and knowledge supplement. Next, let's start today's study!
01
思維導圖
本節內容的思維導圖如下所示：
The mind map of this section is as follows:
02
精讀內容
本節內容主要是將雙極容度熵應用到實際中，為了說明上文定義的熵在實際應用中的潛在有用性，作者考慮了以下簡單示例：科學系主任的目標是從學生的數學（M）、統計學（S）和英語（E）成績來評估學生，採用以下推理規則：
This section is mainly about the application of bipolar capacity entropy in practice. In order to illustrate the potential usefulness of the entropy defined above in practical application, the author considers the following simple examples: The goal of the head of the science department is to evaluate students from their achievements in mathematics (M), statistics (S) and English (E), and the following reasoning rules are adopted:
院長的偏好是b>a>c>d，院長的偏好不能通過Choquet積分容量來建模，然而，它們可以通過{M，S，E}上的雙極容量v的Choquet積分來建模，其係數必須滿足：
Dean's preference is b>a>c>d. Dean's preference cannot be modeled by Choquet integral capacity. However, they can be modeled by Choquet integral of bipolar capacity v on {M, S, E}, and their coefficients must meet:
一般來說，熵Hs可用於最大熵類原理的框架中，以確定（如果存在）與決策者偏好兼容的雙極容度，相應的Choquet積分最接近於Hs意義上的簡單算術平均值。
In general, entropy Hs can be used in the framework of the maximum entropy class principle to determine (if any) the bipolar capacity compatible with the preferences of decision makers, and the corresponding Choquet integral is closest to the simple arithmetic mean in the sense of Hs.
03
知識補充
在上文內容中，我們提到了最大熵，接下來和小編一起來學習一下吧！
In the above content, we mentioned the maximum entropy. Next, let's learn it with Xiaobian!
什麼是最大熵原理？最大熵原理是統計學習的一般原理，將它應用到分類就得到了最大熵模型假設分類模型是一個條件概率分布P(Y|X)，X表示輸入，Y表示輸出。這個模型表示的是對於給定的輸入X，以條件概率P(Y|X)輸出Y。給定一個訓練數據集T，我們的目標就是利用最大熵原理選擇最好的分類模型。
What is the maximum entropy principle? The maximum entropy principle is the general principle of statistical learning. When it is applied to classification, the maximum entropy model is obtained assuming that the classification model is a conditional probability distribution P (Y | X), where X represents the input and Y represents the output. This model represents output Y with conditional probability P (Y | X) for a given input X. Given a training data set T, our goal is to use the maximum entropy principle to select the best classification model.
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如果您對今天的文章有獨特的想法，
歡迎給我們留言，
讓我們相約明天，
祝您今天過得開心快樂！
That's it for today's sharing.
If you have a unique idea about today’s article,
welcome to leave us a message,
let us meet tomorrow,
I wish you a nice day today!
參考資料：deepl翻譯、百度百科、嗶哩嗶哩
參考文獻：Kojadinovic I, Marichal J L. Entropy of bi-capacities[J]. European journal of operational research, 2007, 178(1): 168-184.
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