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Today, the editor brings you the part of the VIKOR multi-attribute decision-making method in "Multi-attribute Decision-making Methods and Application Research Considering Decision-Makers' Behavior in Probabilistic Language Environments".
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Today, the editor brings the VIKOR method of the article "Research on multi-attribute decision making method and its application considering decision makers' behavior in probabilistic linguistic environment".
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1 内容摘要（Content summary）
Today, the editor will interpret and share the VIKOR multi-attribute decision-making method part of "Multi-attribute Decision-making Methods and Application Research Considering Decision-making Behavior in Probabilistic Language Environment" from the three sections of "Mind Map, Intensive Reading Content, and Knowledge Supplement".
Today, the editor will interpret and share the VIKOR method of the article "Research on multi-attribute decision making method and its application considering decision makers' behavior in probabilistic linguistic environment" from the three sections of "mind map, intensive reading content, and knowledge supplement".
2 思维导图（Mind mapping）
3 精读内容（Intensive reading content）
The third part of Chapter 6 is an improved VIKOR multi-attribute decision-making method based on the probabilistic uncertainty language terminology, in which the authors extend the classical VIKOR multi-attribute decision-making method to the probabilistic uncertainty language environment to solve more complex multi-attribute decision-making problems.
The third section of Chapter 6 introduces the improved VIKOR multi-criteria decision-making method based on probabilistic uncertain linguistic term sets. The author extends the classical VIKOR method to address more complex multi-criteria decision-making problems in a probabilistic uncertain linguistic environment.
First, the authors introduce what is the VIKOR method, which is a ranking method based on ideal points and compromise programming, which is developed for multi-criteria optimization of complex systems, and the focus of the method is to rank the advantages and disadvantages of a set of available alternatives, and to select a compromise solution in an environment where conditions and criteria conflict.
First, the author describes the VIKOR method. VIKOR is a ranking method based on ideal points and compromise programming. It is developed for multi-criteria optimization of complex systems. The focus of the method is to rank a set of available alternative solutions and select a compromise solution in an environment where there are conflicts between conditions and criteria.
The VIKOR method is one of the representative methods suitable for multi-attribute decision-making, which is developed for the optimization of complex multi-attribute decision-making methods, and the alternatives are compromised by comparing the proximity of the alternatives to the ideal schemes.
VIKOR is one of the representative methods for multi-criteria decision-making. It is developed to optimize complex multi-criteria decision-making methods. By comparing the proximity of alternative solutions to the ideal solution, VIKOR performs compromise ranking of the alternative solutions. It emphasizes the use of linguistic variables to express attribute characteristics and rank the solutions.
Since it is based on the compromise ranking of ideal points, it is necessary to know the positive and negative ideal solutions of each attribute in advance, and determine the advantages and disadvantages of the scheme by comparing the difference between the evaluation value of the alternative scheme and the ideal solution. Based on the probabilistic uncertainty of the overall perceived utility, the authors obtain the initial decision matrix and introduce the specific sorting steps.
Since VIKOR relies on compromise ranking based on ideal points, it is necessary to know the positive and negative ideal solutions for each attribute in advance. By comparing the evaluation values of alternative solutions with the ideal solutions, the superiority and inferiority of the solutions are determined. The author obtains the initial decision matrix based on the overall perceived utility under probabilistic uncertainty and describes the specific ranking steps.
The first is to calculate the score-value matrix and the exact value matrix of the matrix, and then to determine the positive and negative ideal solutions of the probabilistic indeterminate linguistic terminology set. Then, the maximum individual regret between the probabilistic uncertainty language utility and the attributes of each alternative is determined, the value of the compromise function is calculated, and finally the schemes are ranked based on the above data.
The first step is to calculate the score matrix and the precise value matrix of the decision matrix. Then, the positive and negative ideal solutions of the probabilistic uncertain linguistic term set are determined. Next, the linguistic utility and the maximum individual regret between attributes for each alternative solution are determined. The compromise function value is calculated, and finally, the solutions are ranked based on the above data.
Finally, the authors present a brief decision-making step, which is one more step to obtain the decision-maker's evaluation information than the above method.
Finally, the author presents a brief decision-making process, which includes an additional step of obtaining evaluation information from the decision-maker compared to the aforementioned method.
4 知识补充（Knowledge supplement）
What is Group Utility?
What is collective utility value?
The group utility value is the weighted distance from each evaluation scheme to the optimal scheme (Minkowski distance with norm 1). The smaller the value, the better, and the smaller the group effect.
The collective utility value is the weighted distance (Minkowski distance with a norm of 1) from each evaluated solution to the optimal solution. A smaller value is better, indicating a larger collective effect.
What is Individual Regret?
What is individual regret value?
The individual regret value is the weighted distance from each evaluation scheme to the optimal scheme (the norm is the Minkowski distance of infinity). The smaller the value, the better, and the smaller the individual regret.
The individual regret value is the weighted distance (Minkowski distance with an infinite norm) from each evaluated solution to the optimal solution. A smaller value is better, indicating less individual regret.
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Resources:
翻译：ChatGPT 3.5
Text: Multi-Criteria Compromise Solution Sorting Method (VIKOR) - SPSSPRO Help Center
Reference: Yang Yaxu. Research on multi-attribute decision-making methods considering decision-makers' behaviors in probabilistic language environment and their applications[D]. Baoding: Hebei University, 2023.
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