library(readxl)
cmcData <- read_excel(path = "datakanker.xlsx")
diagnosis <- as.numeric(cmcData$diagnosis == "M")
cmcData$diagnosis <- diagnosis
cmcData
## # A tibble: 569 × 32
##          id diagnosis radius_m…¹ textu…² perim…³ area_…⁴ smoot…⁵ compa…⁶ conca…⁷
##       <dbl>     <dbl>      <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1   842302         1       18.0    10.4   123.    1001   0.118   0.278   0.300 
##  2   842517         1       20.6    17.8   133.    1326   0.0847  0.0786  0.0869
##  3 84300903         1       19.7    21.2   130     1203   0.110   0.160   0.197 
##  4 84348301         1       11.4    20.4    77.6    386.  0.142   0.284   0.241 
##  5 84358402         1       20.3    14.3   135.    1297   0.100   0.133   0.198 
##  6   843786         1       12.4    15.7    82.6    477.  0.128   0.17    0.158 
##  7   844359         1       18.2    20.0   120.    1040   0.0946  0.109   0.113 
##  8 84458202         1       13.7    20.8    90.2    578.  0.119   0.164   0.0937
##  9   844981         1       13      21.8    87.5    520.  0.127   0.193   0.186 
## 10 84501001         1       12.5    24.0    84.0    476.  0.119   0.240   0.227 
## # … with 559 more rows, 23 more variables: concave_points_mean <dbl>,
## #   symmetry_mean <dbl>, fractal_dimension_mean <dbl>, radius_se <dbl>,
## #   texture_se <dbl>, perimeter_se <dbl>, area_se <dbl>, smoothness_se <dbl>,
## #   compactness_se <dbl>, concavity_se <dbl>, `concave points_se` <dbl>,
## #   symmetry_se <dbl>, fractal_dimension_se <dbl>, radius_worst <dbl>,
## #   texture_worst <dbl>, perimeter_worst <dbl>, area_worst <dbl>,
## #   smoothness_worst <dbl>, compactness_worst <dbl>, concavity_worst <dbl>, …
#data training diambil dari data index ke-100 sampai ke-300 dengan kolom ke-10 sampai ke-16
training <- cmcData[100:200,10:16]
#untuk testing kolom yang dipakai adalah kolom ke-10 sampai ke-15
testing <- cmcData[201:nrow(cmcData),10:15]
#untuk validasi kolom yang dipakai adalah kolom ke-16
validasi <- cmcData[201:nrow(cmcData),16]
#data_research yang digunakan adalah kolom 10(concave_points_mean) dan 15(perimeter_se)
data_research <- cmcData[201:nrow(cmcData),c(10,15)]
training 
## # A tibble: 101 × 7
##    concave_points_mean symmetry_mean fractal_d…¹ radiu…² textu…³ perim…⁴ area_se
##                  <dbl>         <dbl>       <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1              0.0584         0.188      0.0639   0.290   1.85    2.38    26.8 
##  2              0.0449         0.161      0.0587   0.456   1.29    2.86    43.1 
##  3              0              0.193      0.0782   0.224   1.51    1.55     9.83
##  4              0.0177         0.174      0.0568   0.192   1.57    1.18    14.7 
##  5              0.0303         0.194      0.0632   0.180   1.22    1.53    11.8 
##  6              0.0120         0.222      0.0648   0.355   1.53    2.30    23.1 
##  7              0.0960         0.192      0.0769   0.391   0.924   2.41    34.7 
##  8              0.0348         0.180      0.0652   0.306   1.66    2.15    20.6 
##  9              0.0192         0.160      0.0607   0.120   0.894   0.848    9.23
## 10              0.182          0.256      0.0704   1.22    1.54   10.0    170   
## # … with 91 more rows, and abbreviated variable names ¹​fractal_dimension_mean,
## #   ²​radius_se, ³​texture_se, ⁴​perimeter_se
testing
## # A tibble: 369 × 6
##    concave_points_mean symmetry_mean fractal_dimension…¹ radiu…² textu…³ perim…⁴
##                  <dbl>         <dbl>               <dbl>   <dbl>   <dbl>   <dbl>
##  1              0.0411         0.198              0.0601   0.353   1.33     2.31
##  2              0.0749         0.151              0.0549   0.397   0.828    3.09
##  3              0.162          0.22               0.0623   0.554   1.56     4.67
##  4              0.0918         0.225              0.0742   0.565   1.93     3.91
##  5              0.0382         0.192              0.0637   0.396   1.04     2.50
##  6              0.0408         0.159              0.0599   0.271   0.362    1.97
##  7              0.0195         0.193              0.0628   0.214   1.34     1.52
##  8              0.0539         0.203              0.0522   0.586   0.855    4.11
##  9              0.0510         0.185              0.0731   0.193   0.922    1.49
## 10              0.0316         0.136              0.0553   0.213   0.363    1.52
## # … with 359 more rows, and abbreviated variable names ¹​fractal_dimension_mean,
## #   ²​radius_se, ³​texture_se, ⁴​perimeter_se
validasi
## # A tibble: 369 × 1
##    area_se
##      <dbl>
##  1    27.2
##  2    40.7
##  3    83.2
##  4    52.7
##  5    30.3
##  6    26.4
##  7    12.3
##  8    68.5
##  9    15.1
## 10    20  
## # … with 359 more rows
data_research
## # A tibble: 369 × 2
##    concave_points_mean perimeter_se
##                  <dbl>        <dbl>
##  1              0.0411         2.31
##  2              0.0749         3.09
##  3              0.162          4.67
##  4              0.0918         3.91
##  5              0.0382         2.50
##  6              0.0408         1.97
##  7              0.0195         1.52
##  8              0.0539         4.11
##  9              0.0510         1.49
## 10              0.0316         1.52
## # … with 359 more rows
## Define interval of data
range.data <-apply(training, 2, range)
range.data
##      concave_points_mean symmetry_mean fractal_dimension_mean radius_se
## [1,]              0.0000        0.1167                0.05025    0.1199
## [2,]              0.2012        0.2678                0.09296    1.5090
##      texture_se perimeter_se area_se
## [1,]     0.4064       0.8484   8.966
## [2,]     4.8850      10.0500 233.000
## Set the method and its parameters,
## for example, we use Wang and Mendel's algorithm
method.type <- "WM"
control <- list(num.labels = 15, type.mf = "GAUSSIAN", type.defuz = "WAM",
type.tnorm = "MIN", type.snorm = "MAX", type.implication.func = "LUKASIEWICZ",
name = "fourhill")
library(frbs)
## Learning step: Generate an FRBS model
object.reg <- frbs.learn(training, range.data, method.type, control)
## Predicting step: Predict for newdata
res.test <- predict(object.reg, testing)
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## Display the FRBS model
summary(object.reg)
## The name of model:  fourhill 
## Model was trained using:  WM 
## The names of attributes:  concave_points_mean symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se area_se 
## The interval of training data:  
##     concave_points_mean symmetry_mean fractal_dimension_mean radius_se
## min              0.0000        0.1167                0.05025    0.1199
## max              0.2012        0.2678                0.09296    1.5090
##     texture_se perimeter_se area_se
## min     0.4064       0.8484   8.966
## max     4.8850      10.0500 233.000
## Type of FRBS model: 
## [1] "MAMDANI"
## Type of membership functions: 
## [1] "GAUSSIAN"
## Type of t-norm method: 
## [1] "Standard t-norm (min)"
## Type of s-norm method: 
## [1] "Standard s-norm"
## Type of defuzzification technique: 
## [1] "Weighted average method"
## Type of implication function: 
## [1] "LUKASIEWICZ"
## The names of linguistic terms on the input variables:  
##  [1] "v.1_a.1"  "v.1_a.2"  "v.1_a.3"  "v.1_a.4"  "v.1_a.5"  "v.1_a.6" 
##  [7] "v.1_a.7"  "v.1_a.8"  "v.1_a.9"  "v.1_a.10" "v.1_a.11" "v.1_a.12"
## [13] "v.1_a.13" "v.1_a.14" "v.1_a.15" "v.2_a.1"  "v.2_a.2"  "v.2_a.3" 
## [19] "v.2_a.4"  "v.2_a.5"  "v.2_a.6"  "v.2_a.7"  "v.2_a.8"  "v.2_a.9" 
## [25] "v.2_a.10" "v.2_a.11" "v.2_a.12" "v.2_a.13" "v.2_a.14" "v.2_a.15"
## [31] "v.3_a.1"  "v.3_a.2"  "v.3_a.3"  "v.3_a.4"  "v.3_a.5"  "v.3_a.6" 
## [37] "v.3_a.7"  "v.3_a.8"  "v.3_a.9"  "v.3_a.10" "v.3_a.11" "v.3_a.12"
## [43] "v.3_a.13" "v.3_a.14" "v.3_a.15" "v.4_a.1"  "v.4_a.2"  "v.4_a.3" 
## [49] "v.4_a.4"  "v.4_a.5"  "v.4_a.6"  "v.4_a.7"  "v.4_a.8"  "v.4_a.9" 
## [55] "v.4_a.10" "v.4_a.11" "v.4_a.12" "v.4_a.13" "v.4_a.14" "v.4_a.15"
## [61] "v.5_a.1"  "v.5_a.2"  "v.5_a.3"  "v.5_a.4"  "v.5_a.5"  "v.5_a.6" 
## [67] "v.5_a.7"  "v.5_a.8"  "v.5_a.9"  "v.5_a.10" "v.5_a.11" "v.5_a.12"
## [73] "v.5_a.13" "v.5_a.14" "v.5_a.15" "v.6_a.1"  "v.6_a.2"  "v.6_a.3" 
## [79] "v.6_a.4"  "v.6_a.5"  "v.6_a.6"  "v.6_a.7"  "v.6_a.8"  "v.6_a.9" 
## [85] "v.6_a.10" "v.6_a.11" "v.6_a.12" "v.6_a.13" "v.6_a.14" "v.6_a.15"
## The parameter values of membership function on the input variable (normalized):  
##      v.1_a.1    v.1_a.2   v.1_a.3   v.1_a.4   v.1_a.5   v.1_a.6   v.1_a.7
## [1,]   5.000 5.00000000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000
## [2,]   0.000 0.07142857 0.1428571 0.2142857 0.2857143 0.3571429 0.4285714
## [3,]   0.025 0.02500000 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000
## [4,]      NA         NA        NA        NA        NA        NA        NA
## [5,]      NA         NA        NA        NA        NA        NA        NA
##      v.1_a.8   v.1_a.9  v.1_a.10  v.1_a.11  v.1_a.12  v.1_a.13  v.1_a.14
## [1,]   5.000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000
## [2,]   0.500 0.5714286 0.6428571 0.7142857 0.7857143 0.8571429 0.9285714
## [3,]   0.025 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000
## [4,]      NA        NA        NA        NA        NA        NA        NA
## [5,]      NA        NA        NA        NA        NA        NA        NA
##      v.1_a.15 v.2_a.1    v.2_a.2   v.2_a.3   v.2_a.4   v.2_a.5   v.2_a.6
## [1,]    5.000   5.000 5.00000000 5.0000000 5.0000000 5.0000000 5.0000000
## [2,]    1.000   0.000 0.07142857 0.1428571 0.2142857 0.2857143 0.3571429
## [3,]    0.025   0.025 0.02500000 0.0250000 0.0250000 0.0250000 0.0250000
## [4,]       NA      NA         NA        NA        NA        NA        NA
## [5,]       NA      NA         NA        NA        NA        NA        NA
##        v.2_a.7 v.2_a.8   v.2_a.9  v.2_a.10  v.2_a.11  v.2_a.12  v.2_a.13
## [1,] 5.0000000   5.000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000
## [2,] 0.4285714   0.500 0.5714286 0.6428571 0.7142857 0.7857143 0.8571429
## [3,] 0.0250000   0.025 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000
## [4,]        NA      NA        NA        NA        NA        NA        NA
## [5,]        NA      NA        NA        NA        NA        NA        NA
##       v.2_a.14 v.2_a.15 v.3_a.1    v.3_a.2   v.3_a.3   v.3_a.4   v.3_a.5
## [1,] 5.0000000    5.000   5.000 5.00000000 5.0000000 5.0000000 5.0000000
## [2,] 0.9285714    1.000   0.000 0.07142857 0.1428571 0.2142857 0.2857143
## [3,] 0.0250000    0.025   0.025 0.02500000 0.0250000 0.0250000 0.0250000
## [4,]        NA       NA      NA         NA        NA        NA        NA
## [5,]        NA       NA      NA         NA        NA        NA        NA
##        v.3_a.6   v.3_a.7 v.3_a.8   v.3_a.9  v.3_a.10  v.3_a.11  v.3_a.12
## [1,] 5.0000000 5.0000000   5.000 5.0000000 5.0000000 5.0000000 5.0000000
## [2,] 0.3571429 0.4285714   0.500 0.5714286 0.6428571 0.7142857 0.7857143
## [3,] 0.0250000 0.0250000   0.025 0.0250000 0.0250000 0.0250000 0.0250000
## [4,]        NA        NA      NA        NA        NA        NA        NA
## [5,]        NA        NA      NA        NA        NA        NA        NA
##       v.3_a.13  v.3_a.14 v.3_a.15 v.4_a.1    v.4_a.2   v.4_a.3   v.4_a.4
## [1,] 5.0000000 5.0000000    5.000   5.000 5.00000000 5.0000000 5.0000000
## [2,] 0.8571429 0.9285714    1.000   0.000 0.07142857 0.1428571 0.2142857
## [3,] 0.0250000 0.0250000    0.025   0.025 0.02500000 0.0250000 0.0250000
## [4,]        NA        NA       NA      NA         NA        NA        NA
## [5,]        NA        NA       NA      NA         NA        NA        NA
##        v.4_a.5   v.4_a.6   v.4_a.7 v.4_a.8   v.4_a.9  v.4_a.10  v.4_a.11
## [1,] 5.0000000 5.0000000 5.0000000   5.000 5.0000000 5.0000000 5.0000000
## [2,] 0.2857143 0.3571429 0.4285714   0.500 0.5714286 0.6428571 0.7142857
## [3,] 0.0250000 0.0250000 0.0250000   0.025 0.0250000 0.0250000 0.0250000
## [4,]        NA        NA        NA      NA        NA        NA        NA
## [5,]        NA        NA        NA      NA        NA        NA        NA
##       v.4_a.12  v.4_a.13  v.4_a.14 v.4_a.15 v.5_a.1    v.5_a.2   v.5_a.3
## [1,] 5.0000000 5.0000000 5.0000000    5.000   5.000 5.00000000 5.0000000
## [2,] 0.7857143 0.8571429 0.9285714    1.000   0.000 0.07142857 0.1428571
## [3,] 0.0250000 0.0250000 0.0250000    0.025   0.025 0.02500000 0.0250000
## [4,]        NA        NA        NA       NA      NA         NA        NA
## [5,]        NA        NA        NA       NA      NA         NA        NA
##        v.5_a.4   v.5_a.5   v.5_a.6   v.5_a.7 v.5_a.8   v.5_a.9  v.5_a.10
## [1,] 5.0000000 5.0000000 5.0000000 5.0000000   5.000 5.0000000 5.0000000
## [2,] 0.2142857 0.2857143 0.3571429 0.4285714   0.500 0.5714286 0.6428571
## [3,] 0.0250000 0.0250000 0.0250000 0.0250000   0.025 0.0250000 0.0250000
## [4,]        NA        NA        NA        NA      NA        NA        NA
## [5,]        NA        NA        NA        NA      NA        NA        NA
##       v.5_a.11  v.5_a.12  v.5_a.13  v.5_a.14 v.5_a.15 v.6_a.1    v.6_a.2
## [1,] 5.0000000 5.0000000 5.0000000 5.0000000    5.000   5.000 5.00000000
## [2,] 0.7142857 0.7857143 0.8571429 0.9285714    1.000   0.000 0.07142857
## [3,] 0.0250000 0.0250000 0.0250000 0.0250000    0.025   0.025 0.02500000
## [4,]        NA        NA        NA        NA       NA      NA         NA
## [5,]        NA        NA        NA        NA       NA      NA         NA
##        v.6_a.3   v.6_a.4   v.6_a.5   v.6_a.6   v.6_a.7 v.6_a.8   v.6_a.9
## [1,] 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000   5.000 5.0000000
## [2,] 0.1428571 0.2142857 0.2857143 0.3571429 0.4285714   0.500 0.5714286
## [3,] 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000   0.025 0.0250000
## [4,]        NA        NA        NA        NA        NA      NA        NA
## [5,]        NA        NA        NA        NA        NA      NA        NA
##       v.6_a.10  v.6_a.11  v.6_a.12  v.6_a.13  v.6_a.14 v.6_a.15
## [1,] 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000    5.000
## [2,] 0.6428571 0.7142857 0.7857143 0.8571429 0.9285714    1.000
## [3,] 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000    0.025
## [4,]        NA        NA        NA        NA        NA       NA
## [5,]        NA        NA        NA        NA        NA       NA
## The names of linguistic terms on the output variable:  
##  [1] "c.1"  "c.2"  "c.3"  "c.4"  "c.5"  "c.6"  "c.7"  "c.8"  "c.9"  "c.10"
## [11] "c.11" "c.12" "c.13" "c.14" "c.15"
## The parameter values of membership function on the output variable (normalized):  
##        c.1        c.2       c.3       c.4       c.5       c.6       c.7   c.8
## [1,] 5.000 5.00000000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000 5.000
## [2,] 0.000 0.07142857 0.1428571 0.2142857 0.2857143 0.3571429 0.4285714 0.500
## [3,] 0.025 0.02500000 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000 0.025
## [4,]    NA         NA        NA        NA        NA        NA        NA    NA
## [5,]    NA         NA        NA        NA        NA        NA        NA    NA
##            c.9      c.10      c.11      c.12      c.13      c.14  c.15
## [1,] 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000 5.0000000 5.000
## [2,] 0.5714286 0.6428571 0.7142857 0.7857143 0.8571429 0.9285714 1.000
## [3,] 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000 0.0250000 0.025
## [4,]        NA        NA        NA        NA        NA        NA    NA
## [5,]        NA        NA        NA        NA        NA        NA    NA
## The number of linguistic terms on each variables 
##      concave_points_mean symmetry_mean fractal_dimension_mean radius_se
## [1,]                  15            15                     15        15
##      texture_se perimeter_se area_se
## [1,]         15           15      15
## The fuzzy IF-THEN rules:  
##     V1                  V2 V3       V4  V5            V6 V7       V8  V9
## 1   IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.8 and
## 2   IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.5 and
## 3   IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.8 and
## 4   IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.6 and
## 5   IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.8 and
## 6   IF concave_points_mean is  v.1_a.2 and symmetry_mean is v.2_a.11 and
## 7   IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 8   IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 9   IF concave_points_mean is v.1_a.14 and symmetry_mean is v.2_a.14 and
## 10  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 11  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.6 and
## 12  IF concave_points_mean is  v.1_a.6 and symmetry_mean is  v.2_a.6 and
## 13  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.8 and
## 14  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 15  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.6 and
## 16  IF concave_points_mean is  v.1_a.7 and symmetry_mean is v.2_a.10 and
## 17  IF concave_points_mean is  v.1_a.8 and symmetry_mean is v.2_a.10 and
## 18  IF concave_points_mean is  v.1_a.5 and symmetry_mean is v.2_a.10 and
## 19  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.6 and
## 20  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.8 and
## 21  IF concave_points_mean is v.1_a.15 and symmetry_mean is v.2_a.15 and
## 22  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.7 and
## 23  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.3 and
## 24  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 25  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.9 and
## 26  IF concave_points_mean is  v.1_a.9 and symmetry_mean is v.2_a.11 and
## 27  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.8 and
## 28  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.8 and
## 29  IF concave_points_mean is  v.1_a.5 and symmetry_mean is v.2_a.10 and
## 30  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.7 and
## 31  IF concave_points_mean is  v.1_a.6 and symmetry_mean is  v.2_a.6 and
## 32  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.5 and
## 33  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.3 and
## 34  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.6 and
## 35  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.8 and
## 36  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.7 and
## 37  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.8 and
## 38  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.7 and
## 39  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 40  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.3 and
## 41  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.9 and
## 42  IF concave_points_mean is  v.1_a.6 and symmetry_mean is v.2_a.15 and
## 43  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.6 and
## 44  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.6 and
## 45  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.4 and
## 46  IF concave_points_mean is  v.1_a.3 and symmetry_mean is v.2_a.14 and
## 47  IF concave_points_mean is  v.1_a.3 and symmetry_mean is v.2_a.11 and
## 48  IF concave_points_mean is  v.1_a.6 and symmetry_mean is v.2_a.14 and
## 49  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.7 and
## 50  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 51  IF concave_points_mean is  v.1_a.8 and symmetry_mean is  v.2_a.8 and
## 52  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 53  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 54  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.4 and
## 55  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.9 and
## 56  IF concave_points_mean is  v.1_a.8 and symmetry_mean is  v.2_a.6 and
## 57  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.5 and
## 58  IF concave_points_mean is  v.1_a.8 and symmetry_mean is  v.2_a.7 and
## 59  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.3 and
## 60  IF concave_points_mean is  v.1_a.6 and symmetry_mean is  v.2_a.8 and
## 61  IF concave_points_mean is  v.1_a.8 and symmetry_mean is  v.2_a.4 and
## 62  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.7 and
## 63  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.5 and
## 64  IF concave_points_mean is  v.1_a.9 and symmetry_mean is  v.2_a.8 and
## 65  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.5 and
## 66  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.8 and
## 67  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.6 and
## 68  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.6 and
## 69  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.7 and
## 70  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.3 and
## 71  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.4 and
## 72  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.5 and
## 73  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.1 and
## 74  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.6 and
## 75  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.5 and
## 76  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.4 and
## 77  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.6 and
## 78  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.6 and
## 79  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.6 and
## 80  IF concave_points_mean is  v.1_a.1 and symmetry_mean is  v.2_a.6 and
## 81  IF concave_points_mean is  v.1_a.7 and symmetry_mean is  v.2_a.6 and
## 82  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 83  IF concave_points_mean is  v.1_a.6 and symmetry_mean is  v.2_a.7 and
## 84  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.7 and
## 85  IF concave_points_mean is  v.1_a.6 and symmetry_mean is  v.2_a.7 and
## 86  IF concave_points_mean is  v.1_a.8 and symmetry_mean is  v.2_a.8 and
## 87  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.8 and
## 88  IF concave_points_mean is v.1_a.10 and symmetry_mean is  v.2_a.9 and
## 89  IF concave_points_mean is  v.1_a.6 and symmetry_mean is v.2_a.12 and
## 90  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.8 and
## 91  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.5 and
## 92  IF concave_points_mean is v.1_a.14 and symmetry_mean is  v.2_a.7 and
## 93  IF concave_points_mean is v.1_a.11 and symmetry_mean is v.2_a.12 and
## 94  IF concave_points_mean is  v.1_a.4 and symmetry_mean is  v.2_a.8 and
## 95  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.6 and
## 96  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.8 and
## 97  IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.2 and
## 98  IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.4 and
## 99  IF concave_points_mean is  v.1_a.5 and symmetry_mean is  v.2_a.8 and
## 100 IF concave_points_mean is  v.1_a.3 and symmetry_mean is  v.2_a.7 and
## 101 IF concave_points_mean is  v.1_a.2 and symmetry_mean is  v.2_a.4 and
##                        V10 V11      V12 V13       V14 V15      V16 V17
## 1   fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 2   fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.4 and
## 3   fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.2 and
## 4   fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.2 and
## 5   fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 6   fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 7   fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 8   fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.1 and
## 9   fractal_dimension_mean  is  v.3_a.8 and radius_se  is v.4_a.12 and
## 10  fractal_dimension_mean  is  v.3_a.8 and radius_se  is  v.4_a.4 and
## 11  fractal_dimension_mean  is  v.3_a.8 and radius_se  is  v.4_a.3 and
## 12  fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.3 and
## 13  fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.3 and
## 14  fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.1 and
## 15  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 16  fractal_dimension_mean  is  v.3_a.7 and radius_se  is  v.4_a.4 and
## 17  fractal_dimension_mean  is  v.3_a.9 and radius_se  is  v.4_a.5 and
## 18  fractal_dimension_mean  is  v.3_a.1 and radius_se  is  v.4_a.5 and
## 19  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.1 and
## 20  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.7 and
## 21  fractal_dimension_mean  is  v.3_a.7 and radius_se  is v.4_a.15 and
## 22  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 23  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.1 and
## 24  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 25  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.4 and
## 26  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.5 and
## 27  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
## 28  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.5 and
## 29  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.4 and
## 30  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.3 and
## 31  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.6 and
## 32  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 33  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.4 and
## 34  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 35  fractal_dimension_mean  is  v.3_a.5 and radius_se  is v.4_a.13 and
## 36  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.3 and
## 37  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
## 38  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.7 and
## 39  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 40  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.2 and
## 41  fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.4 and
## 42  fractal_dimension_mean  is  v.3_a.9 and radius_se  is  v.4_a.3 and
## 43  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.4 and
## 44  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 45  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.2 and
## 46  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.4 and
## 47  fractal_dimension_mean  is v.3_a.12 and radius_se  is  v.4_a.2 and
## 48  fractal_dimension_mean  is v.3_a.15 and radius_se  is  v.4_a.8 and
## 49  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 50  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 51  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.8 and
## 52  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.5 and
## 53  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 54  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.3 and
## 55  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.5 and
## 56  fractal_dimension_mean  is  v.3_a.1 and radius_se  is v.4_a.10 and
## 57  fractal_dimension_mean  is  v.3_a.7 and radius_se  is  v.4_a.3 and
## 58  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.6 and
## 59  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
## 60  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.6 and
## 61  fractal_dimension_mean  is  v.3_a.5 and radius_se  is v.4_a.11 and
## 62  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.3 and
## 63  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.5 and
## 64  fractal_dimension_mean  is  v.3_a.8 and radius_se  is  v.4_a.4 and
## 65  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
## 66  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.3 and
## 67  fractal_dimension_mean  is  v.3_a.7 and radius_se  is  v.4_a.2 and
## 68  fractal_dimension_mean  is v.3_a.11 and radius_se  is  v.4_a.4 and
## 69  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 70  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.2 and
## 71  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 72  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.4 and
## 73  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.3 and
## 74  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.4 and
## 75  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.2 and
## 76  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 77  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.2 and
## 78  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.2 and
## 79  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.7 and
## 80  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 81  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.3 and
## 82  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.2 and
## 83  fractal_dimension_mean  is  v.3_a.7 and radius_se  is  v.4_a.6 and
## 84  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.6 and
## 85  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.4 and
## 86  fractal_dimension_mean  is v.3_a.10 and radius_se  is  v.4_a.4 and
## 87  fractal_dimension_mean  is  v.3_a.7 and radius_se  is  v.4_a.4 and
## 88  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.7 and
## 89  fractal_dimension_mean  is  v.3_a.9 and radius_se  is  v.4_a.3 and
## 90  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 91  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 92  fractal_dimension_mean  is  v.3_a.3 and radius_se  is  v.4_a.8 and
## 93  fractal_dimension_mean  is  v.3_a.9 and radius_se  is  v.4_a.6 and
## 94  fractal_dimension_mean  is  v.3_a.4 and radius_se  is  v.4_a.2 and
## 95  fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 96  fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
## 97  fractal_dimension_mean  is  v.3_a.8 and radius_se  is  v.4_a.3 and
## 98  fractal_dimension_mean  is  v.3_a.2 and radius_se  is  v.4_a.2 and
## 99  fractal_dimension_mean  is  v.3_a.1 and radius_se  is  v.4_a.7 and
## 100 fractal_dimension_mean  is  v.3_a.5 and radius_se  is  v.4_a.2 and
## 101 fractal_dimension_mean  is  v.3_a.6 and radius_se  is  v.4_a.2 and
##            V18 V19      V20 V21          V22 V23      V24  V25     V26 V27  V28
## 1   texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 2   texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 3   texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 4   texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 5   texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 6   texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 7   texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 8   texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 9   texture_se  is  v.5_a.5 and perimeter_se  is v.6_a.15 THEN area_se  is c.11
## 10  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.2
## 11  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.2
## 12  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.2
## 13  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 14  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 15  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 16  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 17  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.4
## 18  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.4
## 19  texture_se  is  v.5_a.1 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 20  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.6
## 21  texture_se  is  v.5_a.9 and perimeter_se  is v.6_a.15 THEN area_se  is c.15
## 22  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 23  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 24  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 25  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 26  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.4
## 27  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.1
## 28  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 29  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 30  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 31  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.5
## 32  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 33  texture_se  is  v.5_a.8 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.3
## 34  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 35  texture_se  is  v.5_a.4 and perimeter_se  is v.6_a.13 THEN area_se  is  c.7
## 36  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 37  texture_se  is  v.5_a.1 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 38  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.5
## 39  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 40  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 41  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.2
## 42  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 43  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.3
## 44  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 45  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 46  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 47  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 48  texture_se  is  v.5_a.8 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.4
## 49  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 50  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 51  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.8 THEN area_se  is  c.6
## 52  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.3
## 53  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 54  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 55  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.3
## 56  texture_se  is  v.5_a.2 and perimeter_se  is v.6_a.10 THEN area_se  is  c.8
## 57  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 58  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.7
## 59  texture_se  is  v.5_a.1 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 60  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.5
## 61  texture_se  is  v.5_a.4 and perimeter_se  is v.6_a.11 THEN area_se  is  c.8
## 62  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 63  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 64  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 65  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 66  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 67  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 68  texture_se  is  v.5_a.7 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.2
## 69  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 70  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 71  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 72  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.3
## 73  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 74  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.2
## 75  texture_se  is  v.5_a.1 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 76  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 77  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.1 THEN area_se  is  c.1
## 78  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 79  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.4
## 80  texture_se  is v.5_a.15 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 81  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.2
## 82  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 83  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.4
## 84  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.5
## 85  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.4
## 86  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.3
## 87  texture_se  is  v.5_a.5 and perimeter_se  is  v.6_a.4 THEN area_se  is  c.3
## 88  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.7 THEN area_se  is  c.7
## 89  texture_se  is  v.5_a.6 and perimeter_se  is  v.6_a.3 THEN area_se  is  c.2
## 90  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 91  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 92  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.9 THEN area_se  is  c.8
## 93  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.6 THEN area_se  is  c.6
## 94  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 95  texture_se  is  v.5_a.1 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 96  texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.2
## 97  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.5 THEN area_se  is  c.1
## 98  texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 99  texture_se  is  v.5_a.4 and perimeter_se  is  v.6_a.8 THEN area_se  is  c.6
## 100 texture_se  is  v.5_a.2 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## 101 texture_se  is  v.5_a.3 and perimeter_se  is  v.6_a.2 THEN area_se  is  c.1
## Plot the membership functions
plotMF(object.reg)

pred <- predict(object.reg, testing)
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
## [1] "note: Some of your new data are out of the previously specified range"
str(pred)
##  num [1:369, 1] 15.5 40.9 105 28.3 24.9 ...
str(data_research)
## tibble [369 × 2] (S3: tbl_df/tbl/data.frame)
##  $ concave_points_mean: num [1:369] 0.0411 0.0749 0.162 0.0918 0.0382 ...
##  $ perimeter_se       : num [1:369] 2.31 3.09 4.67 3.91 2.5 ...
data_research$predict <- pred
data_research
## # A tibble: 369 × 3
##    concave_points_mean perimeter_se predict[,1]
##                  <dbl>        <dbl>       <dbl>
##  1              0.0411         2.31       15.5 
##  2              0.0749         3.09       40.9 
##  3              0.162          4.67      105.  
##  4              0.0918         3.91       28.3 
##  5              0.0382         2.50       24.9 
##  6              0.0408         1.97       25.0 
##  7              0.0195         1.52        9.47
##  8              0.0539         4.11       64.6 
##  9              0.0510         1.49       26.1 
## 10              0.0316         1.52       25.0 
## # … with 359 more rows
data_research$residual <- (data_research$perimeter_se - data_research$predict)
data_research
## # A tibble: 369 × 4
##    concave_points_mean perimeter_se predict[,1] residual[,1]
##                  <dbl>        <dbl>       <dbl>        <dbl>
##  1              0.0411         2.31       15.5        -13.2 
##  2              0.0749         3.09       40.9        -37.8 
##  3              0.162          4.67      105.        -100.  
##  4              0.0918         3.91       28.3        -24.4 
##  5              0.0382         2.50       24.9        -22.4 
##  6              0.0408         1.97       25.0        -23.0 
##  7              0.0195         1.52        9.47        -7.95
##  8              0.0539         4.11       64.6        -60.5 
##  9              0.0510         1.49       26.1        -24.6 
## 10              0.0316         1.52       25.0        -23.4 
## # … with 359 more rows
mean(data_research$predict != data_research$perimeter_se)
## [1] 1
accuracy <- table(data_research$predict, data_research$perimeter_se)
sum(diag(accuracy))/sum(accuracy)
## [1] 0.008130081
library(ggplot2)
library(reshape2)
x <- 1:9
real_data <- data_research$`perimeter_se`
predict_data <- data_research$predict
df <- data.frame(x, real_data , predict_data )

# melt the data to a long format
df2 <- melt(data = df, id.vars = "x")

# plot, using the aesthetics argument 'colour'
ggplot(data = df2, aes(x = x, y = value, colour = variable))+
  geom_point(alpha = 1/2,size=7) + 
  theme(legend.justification = "top") +
  labs(title = "Graph of Prediction  using Fuzzy logic", 
         subtitle = "Mamdani", 
         y = "", x = "") + theme(axis.text.x = element_text(angle = -45))