Table 14.

Fuzzy ideal point and fuzzy anti-ideal point.

Reference point	${\tilde{\Lambda }}_1^{\mathrm{\ast }}$ ($\alpha$: $\alpha$ cut)	${\tilde{\Lambda }}_2^{\mathrm{\ast }}$ ($\alpha$: $\alpha$ cut)	${\tilde{\Lambda }}_3^{\mathrm{\ast }}$ ($\alpha$: $\alpha$ cut)	${\tilde{\Lambda }}_4^{\mathrm{\ast }}$ ($\alpha$: $\alpha$ cut)	${\tilde{\Lambda }}_5^{\mathrm{\ast }}$ ($\alpha$: $\alpha$ cut)
Fuzzy ideal point	0.0: [0.05, 0.24] 0.1: [0.05, 0.23] 0.2: [0.06, 0.21] 0.3: [0.06, 0.20] 0.4: [0.07, 0.18] 0.5: [0.08, 0.17] 0.6: [0.08, 0.16] 0.7: [0.09, 0.15] 0.8: [0.10, 0.14] 0.9: [0.11, 0.13] 1.0: [0.12, 0.12]	0.0: [0.01, 0.12] 0.1: [0.02, 0.11] 0.2: [0.02, 0.10] 0.3: [0.02, 0.09] 0.4: [0.02, 0.07] 0.5: [0.02, 0.06] 0.6: [0.02, 0.06] 0.7: [0.03, 0.05] 0.8: [0.03, 0.04] 0.9: [0.03, 0.04] 1.0: [0.03, 0.03]	0.0: [0.06, 0.29] 0.1: [0.07, 0.27] 0.2: [0.08, 0.25] 0.3: [0.08, 0.24] 0.4: [0.09, 0.22] 0.5: [0.09, 0.20] 0.6: [0.10, 0.19] 0.7: [0.11, 0.18] 0.8: [0.12, 0.16] 0.9: [0.13, 0.15] 1.0: [0.14, 0.14]	0.0: [0.11, 0.60] 0.1: [0.12, 0.57] 0.2: [0.14, 0.54] 0.3: [0.16, 0.51] 0.4: [0.18, 0.48] 0.5: [0.20, 0.45] 0.6: [0.22, 0.42] 0.7: [0.24, 0.39] 0.8: [0.27, 0.37] 0.9: [0.29, 0.34] 1.0: [0.31, 0.31]	0.0: [0.03, 0.26] 0.1: [0.03, 0.23] 0.2: [0.04, 0.21] 0.3: [0.04, 0.19] 0.4: [0.04, 0.17] 0.5: [0.05, 0.14] 0.6: [0.05, 0.13] 0.7: [0.06, 0.12] 0.8: [0.07, 0.10] 0.9: [0.07, 0.09] 1.0: [0.08, 0.08]
Fuzzy anti-ideal point	0.0: [0.00, 0.05] 0.1: [0.00, 0.04] 0.2: [0.00, 0.03] 0.3: [0.00, 0.03] 0.4: [0.00, 0.02] 0.5: [0.00, 0.02] 0.6: [0.00, 0.01] 0.7: [0.00, 0.01] 0.8: [0.00, 0.01] 0.9: [0.00, 0.00] 1.0: [0.00, 0.00]	0.0: [0.00, 0.02] 0.1: [0.00, 0.02] 0.2: [0.00, 0.02] 0.3: [0.00, 0.01] 0.4: [0.00, 0.01] 0.5: [0.00, 0.01] 0.6: [0.00, 0.00] 0.7: [0.00, 0.00] 0.8: [0.00, 0.00] 0.9: [0.00, 0.00] 1.0: [0.00, 0.00]	0.0: [0.00, 0.06] 0.1: [0.00, 0.05] 0.2: [0.00, 0.04] 0.3: [0.00, 0.03] 0.4: [0.00, 0.03] 0.5: [0.00, 0.02] 0.6: [0.00, 0.02] 0.7: [0.00, 0.01] 0.8: [0.00, 0.01] 0.9: [0.00, 0.00] 1.0: [0.00, 0.00]	0.0: [0.00, 0.12] 0.1: [0.00, 0.10] 0.2: [0.00, 0.09] 0.3: [0.00, 0.08] 0.4: [0.00, 0.06] 0.5: [0.00, 0.05] 0.6: [0.00, 0.04] 0.7: [0.00, 0.03] 0.8: [0.00, 0.02] 0.9: [0.00, 0.01] 1.0: [0.00, 0.00]	0.0: [0.01, 0.14] 0.1: [0.01, 0.12] 0.2: [0.01, 0.11] 0.3: [0.01, 0.09] 0.4: [0.01, 0.08] 0.5: [0.01, 0.07] 0.6: [0.02, 0.06] 0.7: [0.02, 0.05] 0.8: [0.02, 0.04] 0.9: [0.02, 0.03] 1.0: [0.03, 0.03]