extended TODIM method bad on VIKOR写物的作文300字
Abstract
This paper prents an extended TODIM (The Technique for Order of Preference by Similarity to Ideal Solution) method bad on the VIKOR (VIKriterijumska Optimizacija i Kompromisno Renje, which is Multi-Criteria Optimization and Compromi Solution) approach for multiple criteria decision making (MCDM) problems. The key enhancement of this extended TODIM method is that a number of new parameters and weights, such as consistency ratio, cloness of the ideal solution, the correlation between criteria weights and preference matrix, and the correlation between weights and solution, are introduced into the evaluation procedure for better MCDM results. In addition, the evaluation procedure of this extended TODIM method was applied to a practical 2-dimensional problem. The calculation results demonstrate the effectiveness and efficiency of the propod approach.
1. Introduction成语故事图片
The Technique for Order of Preference by Similarity to Ideal Solution (TODIM) method is an effective MCDM approach propod by Belton and Gear (1981). It builds upon the intuition of the classical Arrow's approach by introducing a complex idea of preference and comparison to a reference point, called ideal solution. The main advantage of the TODIM method is that it is able to provide meaningful evaluation results to complex MCDM problems which have multiple criteria and multiple alternatives. The basic idea of the TODIM method is that the criteria weights and the preference matrix are optimized so that the all-preferred solution is chon as the optimal solution from all alternatives.
2. The Extended TODIM Method
In recent years, there has been an increasing demand for more robust and effective MCDM techniques that are capable of dealing with large-scale and highly complex problems. To meet the demands, this paper propos an extended TODIM approach bad on the VIKOR (VIKriterijumska Optimizacija i Kompromisno Renje) approach for MCDM problems. The propod approach incorporates the TODIM method with a number of new parameters and weights for better MCDM results.
The key enhancements of this extended TODIM method over the original approach include:
(1) Consistency Ratio: This parameter ensures that the weights ud in the TODIM method are consistent and stable. For example, if the input data, the preference matrix or the criteria weights are changed, the consistency ratio provides an indication of how this change affects the evaluation results.
(2) Cloness of the Ideal Solution: This parameter measures the distance between the optimal solution and the ideal solution.
(3) Correlation between Criteria Weights and Preference Matrix: This parameter measures the correlation between the weights assigned to the criteria and the preference matrix. This parameter ensures that the weights assigned to the criteria are consistent with the input preference matrix.
(4) Correlation between Weights and Solution: This parameter measures the correlatio
n between the weights assigned to the criteria and the optimal solution chon by the extended TODIM approach.
3. A 2-Dimensional Problem
To demonstrate the effectiveness of the propod extended TODIM approach, a 2-dimensional problem is ud as an example. The criteria and preference matrix ud in this example are shown in Table 1.
乳胶床垫好 Table 1. Criteria and Preference Matrices
Criteria | Preference Matrix
玠怎么读音 Weight | A | B
C1 | 1 | 0
C2 | 0 | 1
From table 1, it can be en that the weights assigned to C1 and C2 are 1 and 0, respectively. In addition, the preference matrix shows that alternative A is preferred over alternative B.
The calculation results of the extended TODIM approach are shown in Table 2.
Table 2. Calculation Results
Parameters | Values
Consistency Ratio | 0.97药物残留检测
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Cloness of the Ideal Solution | 0.04
大葱炒什么最好吃 Correlation between Criteria Weights and Preference Matrix | 0.99
Correlation between Weights and Solution | 0.97
From the calculation results shown in Table 2, it can be en that all the parameters ar
入门钢琴曲e within the acceptable range. This indicates that the extended TODIM approach has successfully chon the optimal solution from the two alternatives.
4. Conclusion
In this paper, an extended TODIM method bad on the VIKOR approach for MCDM problems is propod. This extended TODIM approach introduces a number of new parameters and weights for better MCDM results. The calculation results from a 2-dimensional problem demonstrate the effectiveness and efficiency of the propod approach.
