Linguistic Representation and Membership Function

Variables

Range of Values

Very Low Gain

Low Gain

High Gain

Very High Gain

Positive

Very Low Gain ( V L G r ) 1 < V L G r 5.5

Low Gain ( L G r )

2.1 < L G r 7.9

High Gain ( H G r )

4.6 < H G r 10

Very High Gain( V H G r )

7.0 < V H G r 10

μ ( V L G r ) = { 0 , V L G r < 1 < 1 , 1 V L G r < 2.5 1 , V L G r = 2.5 < 1 , 2.5 < V L G r 5.5

μ ( L G r ) = { 0 , L G r < 2.1 < 1 , 2.1 < L G r < 5.0 1 , L G r = 5.0 < 1 , 5.0 < L G r 7.9

μ ( H G r ) = { 0 , H G r < 4.6 < 1 , 4.6 < H G r < 7.5 1 , H G r = 7.5 < 1 , 7.5 < H G r 10

μ ( V H G r ) = { 0 , V H G r < 7.0 < 1 , 7.0 < V H G r < 10 1 , V H G r = 10

Negative

Very Low Loss ( V L L l ) 1 < V L L l 5.5

Low Loss ( L L l )

2.1 < L L l 7.9

High Loss ( H L l )

4.6 < H L l 10

Very High Loss ( V H L l )

7.0 < V H L l 10

Very Low Loss

Low Loss

High Loss

Very High Loss

μ ( V L L l ) = { 0 , V L L l < 1 < 1 , 1 V L L l < 2.5 1 , V L L l = 2.5 < 1 , 2.5 < V L L l 5.5

μ ( L L l ) = { 0 , L L l < 2.1 < 1 , 2.1 < L L l < 5.0 1 , L L l = 5.0 < 1 , 5.0 < L L l 7.9

μ ( H L l ) = { 0 , H L l < 4.6 < 1 , 4.6 < H L l < 7.5 1 , H L l = 7.5 < 1 , 7.5 < H L l 10

μ ( V H L l ) = { 0 , V H L l < 7.0 < 1 , 7.0 < V H L l < 10 1 , V H L l = 10