Mathematical Problems in Engineering

Research Article

An Extended Prospect Theory for Robot Evaluation and Selection considering Risk Preferences and Interactive Criteria

Table 6

Interval type-2 fuzzy evaluation matrix from decision-maker .
 c1c2c3c4c5c6c7
a1[(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.5, 0.7, 0.7, 0.9; 1), (0.6, 0.7, 0.7, 0.8; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)]
a2[(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)]
a3[(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)]
a4[(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.5, 0.7, 0.7, 0.9; 1), (0.6, 0.7, 0.7, 0.8; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.5, 0.7, 0.7, 0.9; 1), (0.6, 0.7, 0.7, 0.8; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)]
a5[(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)]
a6[(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)][(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)]
a7[(0.9, 1, 1, 1; 1), (0.95, 1, 1, 1; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0.1, 0.3, 0.3, 0.5; 1), (0.2, 0.3, 0.3, 0.4; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)]
a8[(0.7, 0.9, 0.9, 1; 1), (0.8, 0.9, 0.9, 0.95; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0, 0.1, 0.1, 0.3; 1), (0.05, 0.1, 0.1, 0.2; 0.9)][(0, 0, 0, 0.1; 1), (0, 0, 0, 0.05; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)][(0.3, 0.5, 0.5, 0.7; 1), (0.4, 0.5, 0.5, 0.6; 0.9)]