| | Name of the membership function | Linguistic terms | Description and range of the linguistic terms |
| | L1F1, L1F2, L1F3, L1F4 | fnf1 to 4 | Low ranges of relative natural frequency for first mode of vibration in ascending order, respectively | | M1F1, M1F2 | fnf5 to 6 | Medium ranges of relative natural frequency for first mode of vibration in ascending order, respectively | | H1F1, H1F2, H1F3, H1F4 | fnf7 to 10 | Higher ranges of relative natural frequency for first mode of vibration in ascending order, respectively | |
L2F1, L2F2, L2F3, L2F4 | snf1 to 4 | Low ranges of relative natural frequency for second mode of vibration in ascending order, respectively | | M2F1, M2F2 | snf5 to 6 | Medium ranges of relative natural frequency for second mode of vibration in ascending order, respectively | | H2F1, H2F2, H2F3, H2F4 | snf7 to 10 | Higher ranges of relative natural frequency for second mode of vibration in ascending order, respectively | | L3F1, L3F2, L3F3, L3F4 | tnf1 to 4 | Low ranges of relative natural frequency for third mode of vibration in ascending order, respectively | | M3F1, M3F2 | tnf5 to 6 | Medium ranges of relative natural frequency for third mode of vibration in ascending order, respectively | | H3F1, H3F2, H3F3, H3F4 | tnf7 to 10 | Higher ranges of relative natural frequency for third mode of vibration in ascending order, respectively | | L1M1, L1M2, L1M3, L1M4 | fms1 to 4 | Low ranges of mode shape deflection for first mode of vibration in ascending order, respectively | | M1M1, M1M2 | fms5 to 6 | Medium ranges of mode shape deflection for first mode of vibration in ascending order, respectively | | H1M1, H1M2, H1M3, H1M4 | fms7 to 10 | Higher ranges of mode shape deflection for first mode of vibration in ascending order, respectively | | L2M1, L2M2, L2M3, L2M4 | sms1 to 4 | Low ranges of mode shape deflection for second mode of vibration in ascending order, respectively | | M2M1, M2M2 | sms5 to 6 | Medium ranges of mode shape deflection for second mode of vibration in ascending order, respectively | | H2M1, H2M2, H2M3, H2M4 | sms7 to 10 | Higher ranges of mode shape deflection for second mode of vibration in ascending order, respectively | | L3M1, L3M2, L3M3, L3M4 | tms1 to 4 | Low ranges of mode shape deflection for third mode of vibration in ascending order, respectively | | M3M1, M3M2 | tms5 to 6 | Medium ranges of mode shape deflection for third mode of vibration in ascending order, respectively | | H3M1, H3M2, H3M3, H3M4 | tms7 to 10 | Higher ranges of mode shape deflection for third mode of vibration in ascending order, respectively | | SD1, SD2, SD3, SD4 | rcd1 to 4 | Small ranges of relative crack depth in ascending order, respectively | | MD1, MD2 | rcd5 to 6 | Medium ranges of relative crack depth in ascending order, respectively | | HD1, HD2, HD3, HD4 | rcd7 to 10 | Larger ranges of relative crack depth in ascending order, respectively | | SL1, SL2, SL3, SL4 | rcl1 to 4 | Small ranges of relative crack location in ascending order, respectively | | ML1, ML2 | rcl5 to 6 | Medium ranges of relative crack location in ascending order, respectively | | HL1, HL2, HL3, HL4 | rcl7 to 10 | Bigger ranges of relative crack location in ascending order |
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