Utility value situation and MATLAB application in multi-attribute decision-making
In real life, we often need to make various decisions, and decisions usually involve multiple attributes or factors. In order to make better multi-attribute decision-making, we need to consider the weight and relative importance of various factors. This article will delve into the utility value situation in multi-attribute decision-making and introduce how to use MATLAB to apply this decision-making method.
Directory
- introduction
- Utility value situation in multi-attribute decision-making
- Key concepts
- decision model
- Application of MATLAB in multi-attribute decision-making
- Prepare data
- Build a decision model
- Evaluation plan
- Result analysis
- Sample code demonstration
- in conclusion
Introduction
In many practical decision-making scenarios, decision makers need to face multiple attributes or factors, which often have different weights and relative importance. Multi-attribute decision-making aims to help decision-makers choose the optimal solution, but due to the complex relationship between multiple attributes, decision-making models are needed to assist decision-making. The utility value scenario is a multi-attribute decision-making method that makes decisions by mapping the values of individual attributes to utility values. MATLAB is a powerful mathematical calculation tool that can be used to implement utility value situation decision-making models.
Utility value situation in multi-attribute decision-making
Key concepts
In the case of utility values in multi-attribute decision-making, we have the following key concepts:
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Attributes: Individual factors or indicators in a decision problem, which can be qualitative or quantitative.
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Utility value function: The utility value function maps the value of each attribute to a utility value, reflecting the decision-maker’s preference for that attribute.
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Decision-making options: Alternative options, each option has a set of attribute values.
Decision Model
The utility value situation model in multi-attribute decision-making can be expressed as:
U
(
x
)
=
f
1
(
x
1
)
+
f
2
(
x
2
)
+
…
+
f
n
(
x
n
)
U(x) = f_1(x_1) + f_2(x_2) + \ldots + f_n(x_n)
U(x)=f1?(x1?) + f2?(x2?) + … + fn?(xn?)
in:
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U
(
x
)
U(x)
U(x) is the solution
x
x
The total utility value of x.
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f
i
(
x
i
)
f_i(x_i)
fi?(xi?) is an attribute
i
i
The utility value function of i.
The goal of the decision maker is to choose an alternative
x
x
x, so that
U
(
x
)
U(x)
U(x) is maximized.
Application of MATLAB in multi-attribute decision-making
Now, let us see how to apply the utility value scenario method in multi-attribute decision-making using MATLAB.
Prepare data
First, we need to prepare data for the decision problem. This includes the values of individual attributes and the utility value function for each attribute. In MATLAB, we can use matrices to store attribute values and functions to represent utility value functions.
Building a decision model
In MATLAB, we can build a function that accepts the attribute values of a scenario as input and calculates the total utility value based on the utility value function. The following is an example MATLAB function:
function totalUtility = calculateUtility(attributes)
% Define the utility value function, assuming there are three attributes
utilityFunction1 = @(x) x;
utilityFunction2 = @(x) 2*x;
utilityFunction3 = @(x) log(x);
% Calculate the utility value of each attribute
utility1 = utilityFunction1(attributes(1));
utility2 = utilityFunction2(attributes(2));
utility3 = utilityFunction3(attributes(3));
% Calculate the total utility value
totalUtility = utility1 + utility2 + utility3;
end
Evaluation plan
Next, we can use MATLAB to evaluate different scenarios. For each option, we call the decision model function constructed above to calculate the total utility value. We can then compare the overall effectiveness of different options
Use values to determine the optimal solution.
Result analysis
Finally, we can analyze the total utility values of different options and select the option with the highest total utility value as the optimal decision. In addition, we can also perform sensitivity analysis to observe the impact of changes in different attribute values on optimal decisions.
Sample code demonstration
The following is a simple MATLAB example code that demonstrates how to apply the utility value scenario method to select the best investment option. Suppose there are two properties: expected return and risk. Our goal is to choose an investment option that maximizes the total utility value.
% defines the attribute value of the investment solution
expectedReturn = [0.08, 0.1, 0.12, 0.09];
risk = [0.1, 0.15, 0.2, 0.12];
% Build decision model function
function totalUtility = calculateUtility(attributes)
utilityFunction1 = @(x) x; % Utility value function of expected rate of return
utilityFunction2 = @(x) exp(-x); % utility value function of risk
utility1 = utilityFunction1(attributes(1));
utility2 = utilityFunction2(attributes(2));
totalUtility = utility1 + utility2;
end
% Evaluate various investment options
numSchemes = length(expectedReturn);
utilities = zeros(numSchemes, 1);
for i = 1:numSchemes
attributes = [expectedReturn(i), risk(i)];
utilities(i) = calculateUtility(attributes);
end
% Choose the best investment solution
[bestUtility, bestIndex] = max(utilities);
bestScheme = [expectedReturn(bestIndex), risk(bestIndex)];
fprintf('Best investment plan: expected return %.2f, risk %.2f\
', bestScheme(1), bestScheme(2));
Conclusion
The utility value situation method in multi-attribute decision-making is a powerful tool that can be used to help decision makers choose the optimal alternative. MATLAB provides a convenient platform for implementing and applying this decision-making method. By building decision-making models, evaluating options and analyzing results, we can better understand and optimize various decision-making problems. I hope this article will be helpful to multi-attribute decision-making and MATLAB applications.