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Table 3. The weighted normalized decision matrix and the negative-ideal solution of Example 1

Table 3 The weighted normalized decision matrix and the negative-ideal solution of Example 1

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To describe the proposed method, we use a simple situation with seven alternatives and two criteria. Suppose that weighted normalized performance values (7;;) have been calculated. These values are dimensionless and between 0 and 1. Figure 1 shows the position of all alternatives according to these values. Figure 1. A simple graphical example with two criteria As can be seen in this figure, ns = [0.10.1] is the negative-ideal point (solution).The Euclidean distances of alternatives from this point are:
To describe the proposed method, we use a simple situation with seven alternatives and two criteria. Suppose that weighted normalized performance values (7;;) have been calculated. These values are dimensionless and between 0 and 1. Figure 1 shows the position of all alternatives according to these values. Figure 1. A simple graphical example with two criteria As can be seen in this figure, ns = [0.10.1] is the negative-ideal point (solution).The Euclidean distances of alternatives from this point are:
This example is adapted from Chakraborty and Zavadskas (2014) which is related to the selection of the most appropriate industrial robot. Five different criteria which are considered in this robot selection problem are: load kg), maximum tip speed (in mm/s), repeatability (in mm), memory capacity (in capacity (in points or steps) and manipulator reach (in mm). Among these criteria, the load capacity, maximum tip speed, memory capacity, and manipulator reac as benefit criteria, and the repeatability is defined as a cost criterion. 1 h are defined This problem consists of seven alternatives, and the corresponding data are given in Table 1.
This example is adapted from Chakraborty and Zavadskas (2014) which is related to the selection of the most appropriate industrial robot. Five different criteria which are considered in this robot selection problem are: load kg), maximum tip speed (in mm/s), repeatability (in mm), memory capacity (in capacity (in points or steps) and manipulator reach (in mm). Among these criteria, the load capacity, maximum tip speed, memory capacity, and manipulator reac as benefit criteria, and the repeatability is defined as a cost criterion. 1 h are defined This problem consists of seven alternatives, and the corresponding data are given in Table 1.
Table 2. The normalized decision matrix of Example 1 Using weights of criteria that are given in Table 1, the weighted normalized performance values can be calculated, and then the negative-ideal solution is determined. According to the obtained values, the Euclidean and Taxicab distances of alternatives from the negative-ideal solution are also computed. The results are presented in Table 3.
Table 2. The normalized decision matrix of Example 1 Using weights of criteria that are given in Table 1, the weighted normalized performance values can be calculated, and then the negative-ideal solution is determined. According to the obtained values, the Euclidean and Taxicab distances of alternatives from the negative-ideal solution are also computed. The results are presented in Table 3.
Mehdi Keshavarz Ghorabaee, Edmundas Kazimieras Zavadskas, Zenonas T urskis, Jurgita A ntucheviciene
Mehdi Keshavarz Ghorabaee, Edmundas Kazimieras Zavadskas, Zenonas T urskis, Jurgita A ntucheviciene
Table 5. Data of Example 2 This example is adapted from Zavadskas and Turskis (2010) and considers the evaluation of microclimate in an office. Six criteria determined for this evaluation process are: the amount of air per head (in m*/h), relative air humidity (in percent), air temperature (in °C), illumination during work hours (in 1x), rate of air flow (in m/s), and dew point (in ‘C). All of these criteria are defined as benefit criteria except the rate of air flow and the dew point. Fourteen alternatives should be evaluated according to these criteria. The data of this problem are shown in Table 5,
Table 5. Data of Example 2 This example is adapted from Zavadskas and Turskis (2010) and considers the evaluation of microclimate in an office. Six criteria determined for this evaluation process are: the amount of air per head (in m*/h), relative air humidity (in percent), air temperature (in °C), illumination during work hours (in 1x), rate of air flow (in m/s), and dew point (in ‘C). All of these criteria are defined as benefit criteria except the rate of air flow and the dew point. Fourteen alternatives should be evaluated according to these criteria. The data of this problem are shown in Table 5,
Table 6. The normalized decision matrix of Example 2 To calculate the negative-ideal solution, we should obtain the weighted normalized performance values first. Table 7 shows the weighted normalized decision-matrix and corresponding negative-ideal solutions. Also, in the last two columns of this table, the Euclidean and Taxicab distances of alternatives from the negative-ideal solution are represented.
Table 6. The normalized decision matrix of Example 2 To calculate the negative-ideal solution, we should obtain the weighted normalized performance values first. Table 7 shows the weighted normalized decision-matrix and corresponding negative-ideal solutions. Also, in the last two columns of this table, the Euclidean and Taxicab distances of alternatives from the negative-ideal solution are represented.
Table 9. Data of the MCDM problem for comparative sensitivity analysis Table 10. Simulated weights of criteria in different sets
Table 9. Data of the MCDM problem for comparative sensitivity analysis Table 10. Simulated weights of criteria in different sets
Table 12. Correlation coefficients between the ranking results of the CODAS and the other methods As previously mentioned, a threshold parameter (z) is used in the process of the CODAS method. We suggest a value between 0.01 and 0.05 for this parameter. However, we want to evaluate the effect of changing this parameter on the ranking result of the CODAS methods. According to Table 12, the minimum value of the Spearman's rank correlation coefficient is in the set 1 of criteria weights (7, = 0.83). So this set of criteria weights, which is more sensitive than the other sets, is selected for analysis of changing the threshold parameter. We use fifteen values for this parameter in the range of 0.01 to 1. The ranking results obtained by the CODAS method in different values of 7 are presented in Table 13. The graphical changes in the ranking of alternatives are also depicted in Figure 2.
Table 12. Correlation coefficients between the ranking results of the CODAS and the other methods As previously mentioned, a threshold parameter (z) is used in the process of the CODAS method. We suggest a value between 0.01 and 0.05 for this parameter. However, we want to evaluate the effect of changing this parameter on the ranking result of the CODAS methods. According to Table 12, the minimum value of the Spearman's rank correlation coefficient is in the set 1 of criteria weights (7, = 0.83). So this set of criteria weights, which is more sensitive than the other sets, is selected for analysis of changing the threshold parameter. We use fifteen values for this parameter in the range of 0.01 to 1. The ranking results obtained by the CODAS method in different values of 7 are presented in Table 13. The graphical changes in the ranking of alternatives are also depicted in Figure 2.
Table 13. Ranking results with different values of t
Table 13. Ranking results with different values of t
Figure 2. Effect of changing the ct parameter on ranking of alternatives A New Combinative Distance-based Assessment (CODAS) Method for Mullti- Criteria Decision-making
Figure 2. Effect of changing the ct parameter on ranking of alternatives A New Combinative Distance-based Assessment (CODAS) Method for Mullti- Criteria Decision-making
Related topics:
Decision MakingJudgment and Decision Making (Judgment And Decision Making)Decision And Game TheoryDecision Making Under UncertaintyMulti Criteria Decision MakingDecision TheoryMulticriteria Decision AnalysisMultiple attributes decision makingMultiple criteria decision making (MCDM)Decision Science
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