Table 7.

Fuzzy ideal point and fuzzy anti-ideal point

Reference point	${\tilde{\mathrm{\Lambda }}}_1^{\ast }$ (α:α cut)	${\tilde{\mathrm{\Lambda }}}_2^{\ast }$ (α:α cut)	${\tilde{\mathrm{\Lambda }}}_3^{\ast }$ (α:α cut)	${\tilde{\mathrm{\Lambda }}}_4^{\ast }$ (α:α cut)	${\tilde{\mathrm{\Lambda }}}_5^{\ast }$ (α:α cut)
Fuzzy ideal point	0.0: [0.06, 0.41] 0.1: [0.07, 0.38] 0.2: [0.08, 0.35] 0.3: [0.09, 0.33] 0.4: [0.10, 0.30] 0.5: [0.11, 0.28] 0.6: [0.12, 0.26] 0.7: [0.14, 0.24] 0.8: [0.15, 0.22] 0.9: [0.17, 0.20] 1.0: [0.18, 0.18]	0.0: [0.14, 0.43] 0.1: [0.16, 0.42] 0.2: [0.17, 0.40] 0.3: [0.19, 0.39] 0.4: [0.20, 0.38] 0.5: [0.22, 0.37] 0.6: [0.23, 0.35] 0.7: [0.25, 0.34] 0.8: [0.27, 0.32] 0.9: [0.28, 0.31] 1.0: [0.30, 0.30]	0.0: [0.02, 0.10] 0.1: [0.02, 0.09] 0.2: [0.02, 0.08] 0.3: [0.02, 0.07] 0.4: [0.02, 0.06] 0.5: [0.02, 0.06] 0.6: [0.03, 0.05] 0.7: [0.03, 0.05] 0.8: [0.03, 0.05] 0.9: [0.04, 0.04] 1.0: [0.04, 0.04]	0.0: [0.02, 0.18] 0.1: [0.03, 0.16] 0.2: [0.03, 0.14] 0.3: [0.03, 0.13] 0.4: [0.03, 0.12] 0.5: [0.04, 0.10] 0.6: [0.04, 0.09] 0.7: [0.05, 0.09] 0.8: [0.05, 0.08] 0.9: [0.06, 0.07] 1.0: [0.06, 0.06]	0.0: [0.03, 0.19] 0.1: [0.03, 0.18] 0.2: [0.03, 0.16] 0.3: [0.04, 0.15] 0.4: [0.04, 0.13] 0.5: [0.05, 0.12] 0.6: [0.05, 0.11] 0.7: [0.06, 0.10] 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, 0.16] 0.1: [0.00, 0.15] 0.2: [0.01, 0.13] 0.3: [0.01, 0.12] 0.4: [0.01, 0.11] 0.5: [0.02, 0.09] 0.6: [0.02, 0.08] 0.7: [0.03, 0.07] 0.8: [0.03, 0.06] 0.9: [0.04, 0.05] 1.0: [0.05, 0.05]	0.0: [0.00, 0.17] 0.1: [0.00, 0.16] 0.2: [0.01, 0.15] 0.3: [0.01, 0.14] 0.4: [0.02, 0.12] 0.5: [0.02, 0.11] 0.6: [0.03, 0.10] 0.7: [0.04, 0.09] 0.8: [0.04, 0.08] 0.9: [0.05, 0.07] 1.0: [0.06, 0.06]	0.0: [0.00, 0.04] 0.1: [0.00, 0.03] 0.2: [0.00, 0.03] 0.3: [0.00, 0.02] 0.4: [0.00, 0.02] 0.5: [0.00, 0.02] 0.6: [0.00, 0.02] 0.7: [0.00, 0.01] 0.8: [0.01, 0.01] 0.9: [0.01, 0.01] 1.0: [0.01, 0.01]	0.0: [0.00, 0.07] 0.1: [0.00, 0.06] 0.2: [0.00, 0.05] 0.3: [0.00, 0.04] 0.4: [0.00, 0.04] 0.5: [0.00, 0.03] 0.6: [0.01, 0.03] 0.7: [0.01, 0.02] 0.8: [0.01, 0.02] 0.9: [0.01, 0.02] 1.0: [0.01, 0.01]	0.0: [0.01, 0.13] 0.1: [0.01, 0.12] 0.2: [0.01, 0.11] 0.3: [0.02, 0.09] 0.4: [0.02, 0.08] 0.5: [0.02, 0.07] 0.6: [0.02, 0.07] 0.7: [0.03, 0.06] 0.8: [0.03, 0.05] 0.9: [0.04, 0.05] 1.0: [0.04, 0.04]