| Membership functions name | 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 descending order, respectively. | M1F1, M1F2 | fnf5, 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 descending order, respectively. | M2F1, M2F2 | snf5, 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 frequencies for second mode of vibration in ascending order, respectively. | L3F1, L3F2, L3F3, L3F4 | tnf1 to 4 | Low ranges of relative natural frequencies for third mode of vibration in descending order, respectively. | M3F1, M3F2 | tnf5, 6 | Medium ranges of relative natural frequencies for third mode of vibration in ascending order, respectively. | H3F1, H3F2, H3F3, H3F4 | tnf7 to 10 | Higher ranges of relative natural frequencies for third mode of vibration in ascending order, respectively. | S1M1, S1M2, S1M3, S1M4 | fmd1 to 4 | Small ranges of first relative mode shape difference in descending order, respectively. | M1M1, M1M2 | fmd5, 6 | Medium ranges of first relative mode shape difference in ascending order, respectively. | H1M1, H1M2, H1M3, H1M4 | fmd7 to 10 | Higher ranges of first relative mode shape difference in ascending order, respectively. | S2M1, S2M2, S2M3, S2M4 | smd1 to 4 | Small ranges of second relative mode shape difference in descending order, respectively. | M2M1, M2M2 | smd5, 6 | Medium ranges of second relative mode shape difference in ascending order, respectively. | H2M1, H2M2, H2M3, H2M4 | smd7 to 10 | Higher ranges of second relative mode shape difference in ascending order, respectively. | S3M1, S3M2, S3M3, S3M4 | tmd1 to 4 | Small ranges of third relative mode shape difference in descending order, respectively. | M3M1, M3M2 | tmd5, 6 | Medium ranges of third relative mode shape difference in ascending order, respectively. | H3M1, H3M2, H3M3, H3M4 | tmd7 to 10 | Higher ranges of third relative mode shape difference in ascending order, respectively. | S1L1, S1L2,…, S1L22 | rcl11 to 22 | Small ranges of relative crack location in descending order, respectively. | M1L1, M1L2 | rcl123, 24 | Medium ranges of relative crack location in ascending order, respectively. | B1L1, B1L2,…, B1L22 | rcl125 to 46 | Bigger ranges of relative crack location in ascending order, respectively. | S1D1, S1D2,…, S1D9 | rcd11 to 9 | Small ranges of relative crack depth in descending order, respectively. | M1D | rcd110 | Medium relative crack depth. | L1D1, L1D2,…, L1D9 | rcd111 to 19 | Larger ranges of relative crack depth in ascending order, respectively. | S2L1, S2L2,…, S2L22 | rcl21 to 22 | Small ranges of relative crack location in descending order, respectively. | M2L1, M2L2 | rcl223, 24 | Medium ranges of relative crack location in ascending order, respectively. | B2L1, B2L2,…, B2L22 | rcl225 to 46 | Bigger ranges of relative crack location in ascending order, respectively. | S2D1, S2D2,…, S2D9 | rcd21 to 9 | Small ranges of relative crack depth in descending order, respectively. | M2D | rcd210 | Medium relative crack depth. | L2D1, L2D2,…, L2D9 | rcd211 to 19 | Larger ranges of relative crack depth in ascending order, respectively. |
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