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今天小編為大家帶來“越覽（30）：精讀期刊論文
《基于模糊馬氏距離的行為三方決策:在供應鍊管理問題中的應用》
的5.一種結合Fermatean 模糊集的
新型三向多屬性決策方法（2）”。
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Dear, this is LearningYard Academy!
Today, the editor brings you the
＂Yue Lan (30)：5. A novel three-way multi-attribute decision-making method combining Fermatean fuzzy sets (2)
＇Behavioural three-way decision making
with Fermatean fuzzy Mahalanobis distance:
Application to the supply chain management problems＇＂.
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一、内容摘要（Summary of content）
本期推文将從思維導圖、精讀内容、知識補充三個方面介紹期刊論文《基于模糊馬氏距離的行為三方決策:在供應鍊管理問題中的應用》的基于pt的價值函數。
This tweet will introduce PT-based value functions of the journal paper " Behavioural three-way decision making with Fermatean fuzzy Mahalanobis distance: Application to the supply chain management problems " from three aspects: mind mapping, intensive reading content, and knowledge supplementation.
二、思維導圖（Mind mapping）
三、精讀内容（Intensive reading content）
（一）研究内容（Research content）
本章主要研究了基于前景理論的三向多屬性決策模型（3WMADM），旨在通過量化決策者的風險态度來優化決策過程。為了開發基于pt的三向決策規則，本部分提出了一個計算值函數的新程式，能夠有效處理不确定性環境下的決策問題。
This chapter mainly studies the three-way multi-attribute decision model based on prospect theory (3WMADM), which aims to optimize the decision-making process by quantifying the decision-maker's risk attitude. In order to develop the three-way decision-making rule based on pt, this part proposes a new program for calculating value functions, which can effectively deal with decision-making problems in uncertain environments.
（二）基于pt的價值函數分析（Value function analysis based on pt）
1.接近系數（Proximity coefficient）
在這個決策模型中，我們首先要定義一個衡量決策選項與理想狀态之間差距的标準。這個差距可以用一個叫做“接近系數”的名額來表示，它告訴我們每個選項離理想狀态有多近。本部分首先定義了對象相對于正理想解（PIO）和負理想解（NIO）的接近系數。
In this decision model, we first define a criterion for measuring the gap between the decision options and the ideal state. This gap can be expressed by a metric called the "proximity coefficient", which tells us how close each option is to the ideal state. This section first defines the proximity coefficient of the object with respect to the positive ideal solution (PIO) and the negative ideal solution (NIO).
2.相對損失函數（Relative loss function）
接下來，讨論的是如何通過數學函數來量化決策過程中的潛在損失，并且這些函數考慮到了決策者的風險偏好。根據之前學者的研究，本部分定義了“相對損失函數”，這個函數能夠幫助決策者了解在做出某個決策時可能産生的損失。這種量化可以幫助決策者更好地了解他們面臨的風險，并據此做出更加明智的選擇。
Next, we discuss how to quantify the potential losses in the decision-making process through mathematical functions, and these functions take into account the decision maker's risk appetite. According to previous research by scholars, this section defines a "relative loss function", which can help decision makers understand the possible losses when making a decision. This quantification can help decision makers better understand the risks they face and make more informed choices based on it.
3.效用函數（Utility function）
其次，描述了如何在決策過程中定義和使用效用函數。效用函數是用來衡量決策者從接受或拒絕一個決策選項中獲得的好處或滿足感的工具。當決策者接受一個看起來不錯的選項時，或者拒絕一個看起來不好的選項時，能獲得更大的價值。高價值意味着高效用，離理想狀态越近的選項帶來的效用越高。
Second, it describes how to define and use utility functions in the decision-making process. Utility functions are tools used to measure the benefits or satisfaction a decision maker gets from accepting or rejecting a decision option. Greater value is gained when a decision maker accepts an option that looks good, or rejects an option that doesn't look good. High value means efficient use, and the closer an option is to the ideal state, the higher the utility.
4.利潤函數（Profit function）
利潤函數是結合了相對損失函數和效用函數的資訊，用來衡量一個決策選項的實際經濟價值或效益。利潤函數的定義使得決策者可以比較不同選項之間的經濟效益，進而做出更好的決策。
The profit function is a combination of relative loss function and utility function information to measure the actual economic value or benefit of a decision option. The definition of the profit function allows decision makers to compare the economic benefits of different options and make better decisions.
5.價值函數（Value function）
價值函數是用來衡量決策選項的價值，它考慮了決策者的風險偏好。根據定義的價值函數不等式，可以得出當利潤為正時，接受、不确定、拒絕行為的價值依次遞增，當利潤為負時，接受、不确定、拒絕行為的價值依次遞增。
The value function is used to measure the value of decision options, which takes into account the decision maker's risk appetite. According to the defined value function inequality, it can be concluded that when the profit is positive, the value of the actions of acceptance, uncertainty, and rejection increases in sequence, and when the profit is negative, the value of the actions of acceptance, uncertainty, and rejection increases in sequence.
（三）三向多屬性決策模型（3WMADM）
本節提出了一種基于前景理論的決策模型，該模型通過定義機率權重函數來反映決策者在面對不确定性時的行為特征，并通過計算每個決策選項的前景值來幫助決策者做出最優選擇。決策者應選擇前景值最高的選項作為最終決策。
This section proposes a decision model based on prospect theory, which defines a probability weight function to reflect the behavior characteristics of decision makers in the face of uncertainty, and calculates the prospect value of each decision option to help decision makers make the best choice. The decision maker should choose the option with the highest prospect value as the final decision.
（四）研究結論（Research conclusion）
本部分發展了一套完整的三向決策規則，該規則基于前景理論，能夠有效處理不确定性環境下的決策問題。通過算法決策者可以根據給定的資料和偏好資訊對方案進行分類和排序，進而選出最優解。最後，通過示例驗證了該模型的有效性和實用性，展示了如何利用所提出的架構來指導決策過程。
This part develops a complete set of three-way decision rules, which are based on prospect theory and can effectively handle decision-making problems in uncertain environments. Through algorithms, decision makers can classify and rank schemes based on given data and preference information, thus selecting the optimal solution. Finally, an example verifies the validity and practicality of the model, and shows how to use the proposed framework to guide the decision-making process.
四、知識補充——機率權重函數（Knowledge supplement — Probability weight function）
機率權重函數是前景理論中的一個重要組成部分，它用于描述人們在面對機率資訊時的心理偏差。在标準的機率論中，事件發生的機率是客觀的，但在現實生活中，人們往往會對這些機率有主觀上的扭曲。機率權重函數就是用來捕捉這種扭曲的函數。
The probability weighting function is an important part of prospect theory. It is used to describe people's psychological biases in the face of probabilistic information. In standard probability theory, the probability of an event happening is objective, but in real life, people often have subjective distortions to these probabilities. The probability weighting function is used to capture this distortion.
在前景理論中，人們對事件發生機率的感覺并不總是與實際機率相比對。例如，人們往往會高估小機率事件的發生可能性，而低估大機率事件的發生可能性。
In prospect theory, people's perception of the probability of an event occurring does not always match the actual probability. For example, people tend to overestimate the probability of a small probability event and underestimate the probability of a high probability event.
機率權重函數在決策理論中有着廣泛的應用，尤其是在風險管理、金融決策和行為經濟學等領域。例如，在風險管理中，決策者需要評估各種風險情景的可能性，而機率權重函數可以幫助他們更準确地了解和量化人們對風險的感覺偏差。
Probability weighting functions are widely used in decision theory, especially in risk management, financial decision-making, and behavioral economics. For example, in risk management, decision makers need to evaluate the likelihood of various risk scenarios, and probability weighting functions can help them more accurately understand and quantify people's perceived biases towards risk.
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翻譯：ChatGPT
參考資料：百度百科、Chat GPT
參考文獻：Mondal A, Roy S K. Behavioural three-way decision making with Fermatean fuzzy Mahalanobis distance: Application to the supply chain management problems[J]. Applied Soft Computing, 2024, 1(151): 1-20.
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