Table of contents
1. Overview of Multiple Attribute Decision Making
A detailed introduction to multiple attribute decision making
1.1 Basic steps of multi-attribute decision making
1.2 Commonly used multi-attribute decision-making methods
2. Practical case: factory location problem
3. Other multi-attribute decision-making methods
3.1 Analytic Hierarchy Process (AHP)
3.2 Fuzzy comprehensive evaluation method
3.3 Gray relational analysis method
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In modern decision science, multi-attribute decision-making occupies an important position. The theory and method of multi-attribute decision-making are widely used in many fields such as engineering design, economy, management and military affairs. This article will introduce the basic concept of multi-attribute decision-making, and demonstrate how to use MATLAB to model and solve multi-attribute decision-making through a practical case.
1. Overview of Multiple Attribute Decision Making
The essence of multi-attribute decision-making is to sort or optimize a group of (limited) alternatives in a certain way on the basis of existing decision-making information. It mainly consists of the following two parts:
- Get decision information. Decision information generally includes two aspects: attribute weight and attribute value. Among them, the determination of attribute weight is an important research content in multi-attribute decision making.
- In a certain way, the decision-making information is gathered and the schemes are sorted and optimized.
Below, we will show how to use MATLAB to model and solve multi-attribute decision-making through a practical case.
A detailed introduction to multiple attribute decision making
Multi-Attribute Decision Making (MADM) is a method for decision-making problems with multiple attributes or indicators. In the actual decision-making process, decision-makers need to comprehensively consider various attributes to obtain the optimal solution. Multi-attribute decision-making methods are widely used in economics, management, engineering design, military and other fields.
1.1 Basic steps of multi-attribute decision making
In general, the solution of multiple attribute decision-making problems can be divided into the following basic steps:
- Determining the decision-making goal: clarify the goal of the decision-making problem, such as maximizing benefits, minimizing costs, etc.
- Determine decision-making attributes: According to the decision-making goal, determine the attributes or indicators needed to evaluate alternatives.
- Determine attribute weights: Assign weights to each attribute to reflect the relative importance of different attributes in the decision. There are many ways to determine the weight, such as expert scoring method, analytic hierarchy process and so on.
- Collect Attribute Values: Collect data on the performance of alternatives on individual attributes.
- Apply multi-attribute decision-making methods: According to attribute weights and attribute values, use appropriate multi-attribute decision-making methods to evaluate and rank alternatives.
- Result analysis and decision-making: According to the evaluation results, analyze the advantages and disadvantages of each alternative, and provide support for decision makers.
1.2 Commonly used multi-attribute decision-making methods
According to different decision-making needs and problem characteristics, decision-makers can choose the appropriate multi-attribute decision-making method for decision analysis. The following briefly introduces several commonly used multi-attribute decision-making methods:
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Weighted Sum Method: The weighted sum method is a simple and intuitive method, which multiplies the performance of the alternatives on each attribute by the corresponding weight, and then adds the products to obtain a comprehensive score. The evaluation results are sorted based on the comprehensive score.
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Analytic Hierarchy Process (AHP): AHP is a structured decision-making method that analyzes the relative importance of each attribute and the relative pros and cons of alternatives on each attribute by constructing a hierarchical structure model. AHP can process qualitative and quantitative information, and is suitable for decision-making problems involving multiple attributes and complex relationships.
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Fuzzy comprehensive evaluation method: Fuzzy comprehensive evaluation method uses the principle of fuzzy mathematics to deal with uncertain information. This method is suitable for processing decision-making process
2. Practical case: factory location problem
Suppose a company needs to locate a new factory among four candidate locations (A, B, C, and D). Each candidate site has the following five attributes: land price (P), transportation (T), labor cost (L), market potential (M) and environmental impact (E). Based on these attributes, we need to evaluate and rank the candidate sites to select the best site for the factory.
First, we need to determine the weight of each attribute. This can be determined through methods such as expert scoring and historical data analysis. In this example, we assume that the following attribute weights have been obtained:
- Land Price (P): 0.25
- Traffic (T): 0.20
- Labor cost (L): 0.15
- Market Potential (M): 0.25
- Environmental impact (E): 0.15
Next, we need to collect the performance of each candidate place on these attributes. The data is shown in the table below:
| Place | land price (P) | Traffic (T) | Labor cost (L) | Market Potential (M) | Environmental Impact (E) |
|---|---|---|---|---|---|
| A | 7 | 8 | 5 | 6 | 9 |
| B | 5 | 6 | 8 | 7 | 4 |
| C | 6 | 9 | 7 | 8 | 6 |
| D | 4 | 5 | 6 | 9 | 8 |
We can use MATLAB to write the following code to perform multi-attribute decision analysis:
% 属性权重
weights = [0.25, 0.20, 0.15, 0.25, 0.15];
% 候选地点的属性值
attribute_values = [
7, 8, 5, 6, 9;
5, 6, 8, 7, 4;
6, 9, 7, 8, 6;
4, 5, 6, 9, 8;
];
% 计算每个候选地点的综合得分
scores = attribute_values * weights';
% 输出排序结果
[sorted_scores, sorted_index] = sort(scores, 'descend');
disp('综合得分从高到低的排序结果：');
disp(sorted_index);
After running the above code, we can get the following sorted results:
综合得分从高到低的排序结果：
3
1
4
2
According to the results of multi-attribute decision-making analysis, we can conclude that site C is the best site to build a factory, followed by site A, site D and site B rank third and fourth respectively.
This practical case shows how to use MATLAB to model and solve multi-attribute decision making. Through this example, we can see the application value of multi-attribute decision-making in practical problems. In practical applications, according to different decision-making requirements, it may be necessary to introduce other decision-making methods or adjust parameters such as weights to achieve the best decision-making effect.
3. Other multi-attribute decision-making methods
In addition to the above weighted sum method, there are many other multi-attribute decision-making methods that can be applied to practical problems. The following briefly introduces several commonly used methods:
3.1 Analytic Hierarchy Process (AHP)
Analytic Hierarchy Process (AHP) is a structured decision-making method that can process qualitative and quantitative information. AHP analyzes the relative importance of each attribute and the relative pros and cons of alternatives on each attribute by constructing a hierarchical structure model.
3.2 Fuzzy comprehensive evaluation method
The fuzzy comprehensive evaluation method uses the principle of fuzzy mathematics to deal with uncertain information. This method is suitable for dealing with ambiguity or uncertainty in the decision-making process. By introducing fuzzy sets and fuzzy relations, imprecise or fuzzy decision-making information can be transformed into evaluation results with a certain order of magnitude.
3.3 Gray relational analysis method
Gray relational analysis is an evaluation method based on system theory and gray system theory. This method determines the pros and cons of a scheme by analyzing the correlation between each alternative scheme and the ideal scheme. It is suitable for decision-making problems with incomplete data and incomplete information.
4 Conclusion
This paper introduces the basic concept of multi-attribute decision making, and demonstrates how to use MATLAB to model and solve multi-attribute decision making through a practical case. Multi-attribute decision-making methods are widely used in many fields such as engineering design, economy, management and military affairs, and have high practical value. In practical applications, according to different decision-making needs and problem characteristics, an appropriate decision-making method can be selected for decision-making analysis to achieve the best decision-making effect.