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今天小编为大家带来“越览（30）：精读期刊论文
《基于模糊马氏距离的行为三方决策:在供应链管理问题中的应用》
的5.一种结合Fermatean 模糊集的
新型三向多属性决策方法（2）”。
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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）
本期推文将从思维导图、精读内容、知识补充三个方面介绍期刊论文《基于模糊马氏距离的行为三方决策:在供应链管理问题中的应用》的基于pt的价值函数。
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、思维导图（Mind mapping）
三、精读内容（Intensive reading content）
（一）研究内容（Research content）
本章主要研究了基于前景理论的三向多属性决策模型（3WMADM），旨在通过量化决策者的风险态度来优化决策过程。为了开发基于pt的三向决策规则，本部分提出了一个计算值函数的新程序，能够有效处理不确定性环境下的决策问题。
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的价值函数分析（Value function analysis based on pt）
1.接近系数（Proximity coefficient）
在这个决策模型中，我们首先要定义一个衡量决策选项与理想状态之间差距的标准。这个差距可以用一个叫做“接近系数”的指标来表示，它告诉我们每个选项离理想状态有多近。本部分首先定义了对象相对于正理想解（PIO）和负理想解（NIO）的接近系数。
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.相对损失函数（Relative loss function）
接下来，讨论的是如何通过数学函数来量化决策过程中的潜在损失，并且这些函数考虑到了决策者的风险偏好。根据之前学者的研究，本部分定义了“相对损失函数”，这个函数能够帮助决策者了解在做出某个决策时可能产生的损失。这种量化可以帮助决策者更好地理解他们面临的风险，并据此做出更加明智的选择。
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.效用函数（Utility function）
其次，描述了如何在决策过程中定义和使用效用函数。效用函数是用来衡量决策者从接受或拒绝一个决策选项中获得的好处或满足感的工具。当决策者接受一个看起来不错的选项时，或者拒绝一个看起来不好的选项时，能获得更大的价值。高价值意味着高效用，离理想状态越近的选项带来的效用越高。
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.利润函数（Profit function）
利润函数是结合了相对损失函数和效用函数的信息，用来衡量一个决策选项的实际经济价值或效益。利润函数的定义使得决策者可以比较不同选项之间的经济效益，从而做出更好的决策。
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.价值函数（Value function）
价值函数是用来衡量决策选项的价值，它考虑了决策者的风险偏好。根据定义的价值函数不等式，可以得出当利润为正时，接受、不确定、拒绝行为的价值依次递增，当利润为负时，接受、不确定、拒绝行为的价值依次递增。
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）三向多属性决策模型（3WMADM）
本节提出了一种基于前景理论的决策模型，该模型通过定义概率权重函数来反映决策者在面对不确定性时的行为特征，并通过计算每个决策选项的前景值来帮助决策者做出最优选择。决策者应选择前景值最高的选项作为最终决策。
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）研究结论（Research conclusion）
本部分发展了一套完整的三向决策规则，该规则基于前景理论，能够有效处理不确定性环境下的决策问题。通过算法决策者可以根据给定的数据和偏好信息对方案进行分类和排序，从而选出最优解。最后，通过示例验证了该模型的有效性和实用性，展示了如何利用所提出的框架来指导决策过程。
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、知识补充——概率权重函数（Knowledge supplement — Probability weight function）
概率权重函数是前景理论中的一个重要组成部分，它用于描述人们在面对概率信息时的心理偏差。在标准的概率论中，事件发生的概率是客观的，但在现实生活中，人们往往会对这些概率有主观上的扭曲。概率权重函数就是用来捕捉这种扭曲的函数。
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.
在前景理论中，人们对事件发生概率的感知并不总是与实际概率相匹配。例如，人们往往会高估小概率事件的发生可能性，而低估大概率事件的发生可能性。
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.
概率权重函数在决策理论中有着广泛的应用，尤其是在风险管理、金融决策和行为经济学等领域。例如，在风险管理中，决策者需要评估各种风险情景的可能性，而概率权重函数可以帮助他们更准确地理解和量化人们对风险的感知偏差。
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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翻译：ChatGPT
参考资料：百度百科、Chat GPT
参考文献：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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