Mathematical Problems in Engineering

Research Article

Multiattribute Group Decision-Making Method Using a Genetic K-Means Clustering Algorithm

Table 1

Attributes evaluated by decision-makers.
<(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2><(0.1, 0.3, 0.5, 0.7), (0.3, 0.4, 0.5, 0.6); 0.7, 0.2>
<(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.5, 0.6, 0.7, 0.8), (0.5, 0.6, 0.7, 0.8); 0.4, 0.3><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4>
<(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2><(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2>
<(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3>
<(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2><(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.3, 0.5, 0.7, 0.9), (0.3, 0.5, 0.7, 0.9); 0.6, 0.3>
<(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.5, 0.6, 0.7, 0.8), (0.5, 0.6, 0.7, 0.8); 0.4, 0.3><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2>
<(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4><(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4>
<(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.3, 0.5, 0.7, 0.9), (0.3, 0.5, 0.7, 0.9); 0.6, 0.3><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3>
<(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.3, 0.4, 0.5, 0.6), (0.3, 0.4, 0.5, 0.6); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2>
<(0.4, 0.5, 0.6, 0.7), (0.4, 0.5, 0.6, 0.7); 0.5, 0.4><(0.2, 0.4, 07, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.2, 0.3, 0.6, 0.7), (0.2, 0.3, 0.6, 0.7); 0.5, 0.4>
<(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.5, 0.6, 0.7, 0.8), (0.5, 0.6, 0.7, 0.8); 0.4, 0.3><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4>
<(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.4, 0.5, 0.6, 0.7), (0.4, 0.5, 0.6, 0.7); 0.5, 0.4><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3>
<(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2><(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3>
<(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3>
<(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.3, 0.4, 0.5, 0.6), (0.3, 0.4, 0.5, 0.6); 0.7, 0.2><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.2, 0.4, 07, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3>
<(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3>
<(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.3, 0.5, 0.7, 0.9), (0.3, 0.5, 0.7, 0.9); 0.6, 0.3><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3>
<(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.4, 0.5, 0.6, 0.7), (0.4, 0.5, 0.6, 0.7); 0.5, 0.4>
<(0.2, 0.3, 0.6, 0.7), (0.2, 0.3, 0.6, 0.7); 0.5, 0.4><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.2, 0.3, 0.6, 0.7), (0.2, 0.3, 0.6, 0.7); 0.5, 0.4><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.1, 0.2, 0.4, 0.5), (0.1, 0.2, 0.4, 0.5); 0.7, 0.2>
<(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4>
<(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.1, 0.2, 0.4, 0.5), (0.1, 0.2, 0.4, 0.5); 0.7, 0.2><(0.1, 0.2, 0.5, 0.6), (0.1, 0.2, 0.5, 0.6); 0.7, 0.2><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2>
<(0.3, 0.5, 0.7, 0.9), (0.3, 0.5, 0.7, 0.9); 0.6, 0.3><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.2, 0.4, 07, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.3, 0.4, 0.5, 0.6), (0.3, 0.4, 0.5, 0.6); 0.7, 0.2>
<(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.4, 0.5, 0.6, 0.7), (0.4, 0.5, 0.6, 0.7); 0.5, 0.4><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4><(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2>
<(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.3, 0.4, 0.5, 0.6), (0.3, 0.4, 0.5, 0.6); 0.7, 0.2><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.2, 0.3, 0.6, 0.7), (0.2, 0.3, 0.6, 0.7); 0.5, 0.4><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4>
<(0.1, 0.2, 0.4, 0.5), (0.1, 0.2, 0.4, 0.5); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.1, 0.2, 0.5, 0.6), (0.1, 0.2, 0.5, 0.6); 0.7, 0.2><(0.6, 0.7, 0.8, 0.9), (0.6, 0.7, 0.8, 0.9); 0.4, 0.3><(0.3, 0.4, 0.7, 0.8), (0.3, 0.4, 0.7, 0.8); 0.7, 0.2>
<(0.2, 0.4, 0.6, 0.8), (0.2, 0.4, 0.6, 0.8); 0.4, 0.3><(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2><(0.3, 0.5, 0.7, 0.9), (0.3, 0.5, 0.7, 0.9); 0.6, 0.3><(0.1, 0.2, 0.4, 0.5), (0.1, 0.2, 0.4, 0.5); 0.7, 0.2><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4>
<(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.5, 0.6, 0.7, 0.8), (0.5, 0.6, 0.7, 0.8); 0.4, 0.3><(0.2, 0.3, 0.6, 0.7), (0.2, 0.3, 0.6, 0.7); 0.5, 0.4><(0.1, 0.2, 0.3, 0.4), (0.1, 0.2, 0.3, 0.4); 0.7, 0.2>
<(0.3, 0.4, 0.6, 0.7), (0.3, 0.4, 0.6, 0.7); 0.7, 0.2><(0.2, 0.3, 0.4, 0.5), (0.2, 0.3, 0.4, 0.5); 0.5, 0.4><(0.2, 0.4, 0.7, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3>
<(0.4, 0.5, 0.7, 0.8), (0.4, 0.5, 0.7, 0.8); 0.5, 0.4><(0.5, 0.6, 0.8, 0.9), (0.5, 0.6, 0.8, 0.9); 0.4, 0.3><(0.2, 0.4, 07, 0.9), (0.2, 0.4, 0.7, 0.9); 0.4, 0.3><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.4, 0.5, 0.7, 0.9), (0.4, 0.5, 0.7, 0.9); 0.5, 0.4>
<(0.4, 0.5, 0.6, 0.7), (0.4, 0.5, 0.6, 0.7); 0.5, 0.4><(0.2, 0.3, 0.5, 0.6), (0.2, 0.3, 0.5, 0.6); 0.5, 0.4><(0.1, 0.3, 0.5, 0.7), (0.1, 0.3, 0.5, 0.7); 0.6, 0.3><(0.1, 0.3, 0.6, 0.8), (0.1, 0.3, 0.6, 0.8); 0.6, 0.3><(0.1, 0.2, 0.4, 0.5), (0.1, 0.2, 0.4, 0.5); 0.7, 0.2>