fuzzy-rules-generator/temp_density_tree.ipynb

In [44]:

import pickle
import pandas as pd
from sklearn import tree

model = pickle.load(open("data/temp_density_tree.model.sav", "rb"))
features = (
    pd.read_csv("data/density_train.csv", sep=";", decimal=",")
    .drop(["T"], axis=1)
    .columns.values.tolist()
)

rules = tree.export_text(model, feature_names=features)
print(rules)

|--- Density <= 1.04
|   |--- Density <= 1.03
|   |   |--- value: [70.00]
|   |--- Density >  1.03
|   |   |--- Density <= 1.04
|   |   |   |--- value: [65.00]
|   |   |--- Density >  1.04
|   |   |   |--- value: [60.00]
|--- Density >  1.04
|   |--- Density <= 1.07
|   |   |--- TiO2 <= 0.03
|   |   |   |--- Al2O3 <= 0.03
|   |   |   |   |--- Density <= 1.05
|   |   |   |   |   |--- Density <= 1.05
|   |   |   |   |   |   |--- value: [50.00]
|   |   |   |   |   |--- Density >  1.05
|   |   |   |   |   |   |--- value: [42.50]
|   |   |   |   |--- Density >  1.05
|   |   |   |   |   |--- Density <= 1.06
|   |   |   |   |   |   |--- value: [35.00]
|   |   |   |   |   |--- Density >  1.06
|   |   |   |   |   |   |--- value: [22.50]
|   |   |   |--- Al2O3 >  0.03
|   |   |   |   |--- Density <= 1.06
|   |   |   |   |   |--- Density <= 1.05
|   |   |   |   |   |   |--- value: [70.00]
|   |   |   |   |   |--- Density >  1.05
|   |   |   |   |   |   |--- value: [65.00]
|   |   |   |   |--- Density >  1.06
|   |   |   |   |   |--- Density <= 1.07
|   |   |   |   |   |   |--- value: [55.00]
|   |   |   |   |   |--- Density >  1.07
|   |   |   |   |   |   |--- value: [50.00]
|   |   |--- TiO2 >  0.03
|   |   |   |--- Density <= 1.06
|   |   |   |   |--- value: [70.00]
|   |   |   |--- Density >  1.06
|   |   |   |   |--- Density <= 1.06
|   |   |   |   |   |--- value: [65.00]
|   |   |   |   |--- Density >  1.06
|   |   |   |   |   |--- value: [60.00]
|   |--- Density >  1.07
|   |   |--- Density <= 1.12
|   |   |   |--- Density <= 1.08
|   |   |   |   |--- Density <= 1.07
|   |   |   |   |   |--- value: [45.00]
|   |   |   |   |--- Density >  1.07
|   |   |   |   |   |--- Density <= 1.08
|   |   |   |   |   |   |--- value: [40.00]
|   |   |   |   |   |--- Density >  1.08
|   |   |   |   |   |   |--- value: [35.00]
|   |   |   |--- Density >  1.08
|   |   |   |   |--- Density <= 1.09
|   |   |   |   |   |--- value: [30.00]
|   |   |   |   |--- Density >  1.09
|   |   |   |   |   |--- Al2O3 <= 0.03
|   |   |   |   |   |   |--- value: [22.50]
|   |   |   |   |   |--- Al2O3 >  0.03
|   |   |   |   |   |   |--- value: [20.00]
|   |   |--- Density >  1.12
|   |   |   |--- Density <= 1.18
|   |   |   |   |--- Density <= 1.15
|   |   |   |   |   |--- value: [70.00]
|   |   |   |   |--- Density >  1.15
|   |   |   |   |   |--- Al2O3 <= 0.15
|   |   |   |   |   |   |--- value: [65.00]
|   |   |   |   |   |--- Al2O3 >  0.15
|   |   |   |   |   |   |--- value: [50.00]
|   |   |   |--- Density >  1.18
|   |   |   |   |--- Al2O3 <= 0.15
|   |   |   |   |   |--- Density <= 1.20
|   |   |   |   |   |   |--- value: [50.00]
|   |   |   |   |   |--- Density >  1.20
|   |   |   |   |   |   |--- value: [30.00]
|   |   |   |   |--- Al2O3 >  0.15
|   |   |   |   |   |--- Density <= 1.18
|   |   |   |   |   |   |--- value: [30.00]
|   |   |   |   |   |--- Density >  1.18
|   |   |   |   |   |   |--- value: [22.50]

In [45]:

from src.rules import get_rules


rules = get_rules(model, features)
display(len(rules))
rules

27

Out[45]:

[if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density > 1.083) and (Density > 1.086) and (Al2O3 > 0.025) -> 20.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) and (Density > 1.053) and (Density > 1.057) -> 22.5,
 if (Density <= 1.042) and (Density > 1.033) and (Density > 1.037) -> 60.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) and (Density <= 1.053) and (Density <= 1.046) -> 50.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) and (Density <= 1.053) and (Density > 1.046) -> 42.5,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) and (Density > 1.053) and (Density <= 1.057) -> 35.0,
 if (Density <= 1.042) and (Density > 1.033) and (Density <= 1.037) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) and (Density <= 1.061) and (Density <= 1.055) -> 70.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) and (Density <= 1.061) and (Density > 1.055) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) and (Density > 1.061) and (Density <= 1.066) -> 55.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) and (Density > 1.061) and (Density > 1.066) -> 50.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) and (Density <= 1.058) -> 70.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) and (Density > 1.058) and (Density <= 1.062) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) and (Density > 1.058) and (Density > 1.062) -> 60.0,
 if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density <= 1.083) and (Density <= 1.074) -> 45.0,
 if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density <= 1.083) and (Density > 1.074) and (Density <= 1.079) -> 40.0,
 if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density <= 1.083) and (Density > 1.074) and (Density > 1.079) -> 35.0,
 if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density > 1.083) and (Density <= 1.086) -> 30.0,
 if (Density > 1.042) and (Density > 1.069) and (Density <= 1.118) and (Density > 1.083) and (Density > 1.086) and (Al2O3 <= 0.025) -> 22.5,
 if (Density <= 1.042) and (Density <= 1.033) -> 70.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density <= 1.179) and (Density <= 1.148) -> 70.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density <= 1.179) and (Density > 1.148) and (Al2O3 <= 0.15) -> 65.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density <= 1.179) and (Density > 1.148) and (Al2O3 > 0.15) -> 50.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density > 1.179) and (Al2O3 <= 0.15) and (Density <= 1.203) -> 50.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density > 1.179) and (Al2O3 <= 0.15) and (Density > 1.203) -> 30.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density > 1.179) and (Al2O3 > 0.15) and (Density <= 1.182) -> 30.0,
 if (Density > 1.042) and (Density > 1.069) and (Density > 1.118) and (Density > 1.179) and (Al2O3 > 0.15) and (Density > 1.182) -> 22.5]

In [46]:

from src.rules import normalise_rules


rules = normalise_rules(rules)
display(len(rules))
rules

27

Out[46]:

[if (Density > 1.042) and (Density <= 1.118) and (Al2O3 > 0.025) -> 20.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) -> 22.5,
 if (Density <= 1.042) and (Density > 1.033) -> 60.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) -> 50.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) -> 42.5,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) -> 35.0,
 if (Density <= 1.042) and (Density > 1.033) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) -> 70.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) -> 55.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) -> 50.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) -> 70.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) -> 65.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) -> 60.0,
 if (Density > 1.042) and (Density <= 1.118) -> 45.0,
 if (Density > 1.042) and (Density <= 1.118) -> 40.0,
 if (Density > 1.042) and (Density <= 1.118) -> 35.0,
 if (Density > 1.042) and (Density <= 1.118) -> 30.0,
 if (Density > 1.042) and (Density <= 1.118) and (Al2O3 <= 0.025) -> 22.5,
 if (Density <= 1.042) -> 70.0,
 if (Density > 1.042) and (Density <= 1.179) -> 70.0,
 if (Density > 1.042) and (Density <= 1.179) and (Al2O3 <= 0.15) -> 65.0,
 if (Density > 1.042) and (Density <= 1.179) and (Al2O3 > 0.15) -> 50.0,
 if (Density > 1.042) and (Density <= 1.203) and (Al2O3 <= 0.15) -> 50.0,
 if (Density > 1.042) and (Al2O3 <= 0.15) -> 30.0,
 if (Density > 1.042) and (Density <= 1.182) and (Al2O3 > 0.15) -> 30.0,
 if (Density > 1.042) and (Al2O3 > 0.15) -> 22.5]

In [47]:

from src.rules import delete_same_rules


rules = delete_same_rules(rules)
display(len(rules))
rules

15

Out[47]:

[if (Density > 1.042) and (Density <= 1.118) and (Al2O3 > 0.025) -> 20.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 <= 0.025) -> 37.5,
 if (Density <= 1.042) and (Density > 1.033) -> 62.5,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 <= 0.025) and (Al2O3 > 0.025) -> 60.0,
 if (Density > 1.042) and (Density <= 1.069) and (TiO2 > 0.025) -> 65.0,
 if (Density > 1.042) and (Density <= 1.118) -> 37.5,
 if (Density > 1.042) and (Density <= 1.118) and (Al2O3 <= 0.025) -> 22.5,
 if (Density <= 1.042) -> 70.0,
 if (Density > 1.042) and (Density <= 1.179) -> 70.0,
 if (Density > 1.042) and (Density <= 1.179) and (Al2O3 <= 0.15) -> 65.0,
 if (Density > 1.042) and (Density <= 1.179) and (Al2O3 > 0.15) -> 50.0,
 if (Density > 1.042) and (Density <= 1.203) and (Al2O3 <= 0.15) -> 50.0,
 if (Density > 1.042) and (Al2O3 <= 0.15) -> 30.0,
 if (Density > 1.042) and (Density <= 1.182) and (Al2O3 > 0.15) -> 30.0,
 if (Density > 1.042) and (Al2O3 > 0.15) -> 22.5]

In [48]:

train = pd.read_csv("data/density_train.csv", sep=";", decimal=",")
test = pd.read_csv("data/density_test.csv", sep=";", decimal=",")

train["Density"] = train["Density"]
test["Density"] = test["Density"]

display(train.head(3))
display(test.head(3))
train.describe().transpose()

	T	Al2O3	TiO2	Density
0	20	0.0	0.0	1.06250
1	25	0.0	0.0	1.05979
2	35	0.0	0.0	1.05404

	T	Al2O3	TiO2	Density
0	30	0.00	0.0	1.05696
1	55	0.00	0.0	1.04158
2	25	0.05	0.0	1.08438

Out[48]:

	count	mean	std	min	25%	50%	75%	max
T	38.0	45.526316	16.513282	20.00000	31.25000	45.000000	60.000000	70.0000
Al2O3	38.0	0.078947	0.126080	0.00000	0.00000	0.000000	0.050000	0.3000
TiO2	38.0	0.057895	0.108133	0.00000	0.00000	0.000000	0.050000	0.3000
Density	38.0	1.108180	0.060772	1.03182	1.05763	1.082755	1.169058	1.2186

In [49]:

from src.rules import simplify_rules

rules = simplify_rules(train, rules)
display(len(rules))
rules

15

Out[49]:

[if (Density = 1.08) and (Al2O3 = 0.3) -> 20.0,
 if (Density = 1.055) and (TiO2 = 0.0) and (Al2O3 = 0.0) -> 37.5,
 if (Density = 1.037) -> 62.5,
 if (Density = 1.055) and (TiO2 = 0.0) and (Al2O3 = 0.3) -> 60.0,
 if (Density = 1.055) and (TiO2 = 0.3) -> 65.0,
 if (Density = 1.08) -> 37.5,
 if (Density = 1.08) and (Al2O3 = 0.0) -> 22.5,
 if (Density = 1.032) -> 70.0,
 if (Density = 1.11) -> 70.0,
 if (Density = 1.11) and (Al2O3 = 0.0) -> 65.0,
 if (Density = 1.11) and (Al2O3 = 0.3) -> 50.0,
 if (Density = 1.122) and (Al2O3 = 0.0) -> 50.0,
 if (Density = 1.219) and (Al2O3 = 0.0) -> 30.0,
 if (Density = 1.112) and (Al2O3 = 0.3) -> 30.0,
 if (Density = 1.219) and (Al2O3 = 0.3) -> 22.5]

In [64]:

import numpy as np
from skfuzzy import control as ctrl
import skfuzzy as fuzz

al = ctrl.Antecedent(np.arange(0, 0.3, 0.1), "al")
ti = ctrl.Antecedent(np.arange(0, 0.3, 0.1), "ti")
density = ctrl.Antecedent(np.arange(1.03, 1.22, 0.001), "density")
# temp = ctrl.Consequent(train["T"].sort_values().unique(), "temp")
temp = ctrl.Consequent(np.arange(20, 70, 0.1), "temp")

al.automf(3, variable_type="quant")
al.view()
ti.automf(3, variable_type="quant")
ti.view()
density.automf(5, variable_type="quant")
density.view()
temp.automf(3, variable_type="quant")
temp.view()

In [65]:

from src.rules import get_fuzzy_rules

fuzzy_variables = {"Al2O3": al, "TiO2": ti, "Density": density, "consequent": temp}
fuzzy_rules = get_fuzzy_rules(rules, fuzzy_variables)
fuzzy_rules.remove(fuzzy_rules[5])

fuzzy_cntrl = ctrl.ControlSystem(fuzzy_rules)

sim = ctrl.ControlSystemSimulation(fuzzy_cntrl, lenient=False)

display(len(fuzzy_rules))
fuzzy_rules

11

Out[65]:

[IF density[low] AND al[high] THEN temp[low]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF (density[low] AND ti[low]) AND al[low] THEN temp[average]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF (density[low] AND ti[low]) AND al[high] THEN temp[high]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[low] AND ti[high] THEN temp[high]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[low] THEN temp[average]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[lower] THEN temp[high]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[average] THEN temp[high]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[average] AND al[low] THEN temp[high]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[average] AND al[high] THEN temp[average]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[higher] AND al[low] THEN temp[low]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax,
 IF density[higher] AND al[high] THEN temp[low]
 	AND aggregation function : fmin
 	OR aggregation function  : fmax]

In [66]:

sim.input["al"] = 0.0
sim.input["ti"] = 0.0
sim.input["density"] = 1.0569013636039
sim.compute()
sim.print_state()
display(sim.output["temp"])
temp.view(sim=sim)

=============
 Antecedents 
=============
Antecedent: density                 = 1.0569013636039
  - lower                           : 0.43065897134597164
  - low                             : 0.5693410286540264
  - average                         : 0.0
  - high                            : 0.0
  - higher                          : 0.0
Antecedent: al                      = 0.0
  - low                             : 1.0
  - average                         : 0.0
  - high                            : 0.0
Antecedent: ti                      = 0.0
  - low                             : 1.0
  - average                         : 0.0
  - high                            : 0.0

=======
 Rules 
=======
RULE #0:
  IF density[low] AND al[high] THEN temp[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[low]                                           : 0.5693410286540264
  - al[high]                                               : 0.0
                                 density[low] AND al[high] = 0.0
  Activation (THEN-clause):
                                                 temp[low] : 0.0

RULE #1:
  IF (density[low] AND ti[low]) AND al[low] THEN temp[average]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[low]                                           : 0.5693410286540264
  - ti[low]                                                : 1.0
  - al[low]                                                : 1.0
                    (density[low] AND ti[low]) AND al[low] = 0.5693410286540264
  Activation (THEN-clause):
                                             temp[average] : 0.5693410286540264

RULE #2:
  IF (density[low] AND ti[low]) AND al[high] THEN temp[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[low]                                           : 0.5693410286540264
  - ti[low]                                                : 1.0
  - al[high]                                               : 0.0
                   (density[low] AND ti[low]) AND al[high] = 0.0
  Activation (THEN-clause):
                                                temp[high] : 0.0

RULE #3:
  IF density[low] AND ti[high] THEN temp[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[low]                                           : 0.5693410286540264
  - ti[high]                                               : 0.0
                                 density[low] AND ti[high] = 0.0
  Activation (THEN-clause):
                                                temp[high] : 0.0

RULE #4:
  IF density[low] THEN temp[average]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[low]                                           : 0.5693410286540264
                                              density[low] = 0.5693410286540264
  Activation (THEN-clause):
                                             temp[average] : 0.5693410286540264

RULE #5:
  IF density[lower] THEN temp[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[lower]                                         : 0.43065897134597164
                                            density[lower] = 0.43065897134597164
  Activation (THEN-clause):
                                                temp[high] : 0.43065897134597164

RULE #6:
  IF density[average] THEN temp[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[average]                                       : 0.0
                                          density[average] = 0.0
  Activation (THEN-clause):
                                                temp[high] : 0.0

RULE #7:
  IF density[average] AND al[low] THEN temp[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[average]                                       : 0.0
  - al[low]                                                : 1.0
                              density[average] AND al[low] = 0.0
  Activation (THEN-clause):
                                                temp[high] : 0.0

RULE #8:
  IF density[average] AND al[high] THEN temp[average]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[average]                                       : 0.0
  - al[high]                                               : 0.0
                             density[average] AND al[high] = 0.0
  Activation (THEN-clause):
                                             temp[average] : 0.0

RULE #9:
  IF density[higher] AND al[low] THEN temp[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[higher]                                        : 0.0
  - al[low]                                                : 1.0
                               density[higher] AND al[low] = 0.0
  Activation (THEN-clause):
                                                 temp[low] : 0.0

RULE #10:
  IF density[higher] AND al[high] THEN temp[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - density[higher]                                        : 0.0
  - al[high]                                               : 0.0
                              density[higher] AND al[high] = 0.0
  Activation (THEN-clause):
                                                 temp[low] : 0.0


==============================
 Intermediaries and Conquests 
==============================
Consequent: temp                     = 47.13412979960593
  low:
    Accumulate using accumulation_max : 0.0
  average:
    Accumulate using accumulation_max : 0.5693410286540264
  high:
    Accumulate using accumulation_max : 0.43065897134597164

np.float64(47.13412979960593)

In [67]:

from sklearn import metrics
import math


def fuzzy_pred(row):
    sim.input["al"] = row["Al2O3"]
    sim.input["ti"] = row["TiO2"]
    sim.input["density"] = row["Density"]
    sim.compute()
    return sim.output["temp"]


def rmse(row):
    return math.sqrt(metrics.mean_squared_error([row["Real"]], [row["Inferred"]]))


result_train = train.copy()
result_train["Real"] = result_train["T"]
result_train["Inferred"] = result_train.apply(fuzzy_pred, axis=1)
result_train["RMSE"] = result_train.apply(rmse, axis=1)
result_train = result_train.round({"RMSE": 3})
result_train.head(15)

Out[67]:

	T	Al2O3	TiO2	Density	Real	Inferred	RMSE
0	20	0.00	0.0	1.06250	20	46.094987	26.095
1	25	0.00	0.0	1.05979	25	46.553081	21.553
2	35	0.00	0.0	1.05404	35	47.812656	12.813
3	40	0.00	0.0	1.05103	40	48.650748	8.651
4	45	0.00	0.0	1.04794	45	49.664863	4.665
5	50	0.00	0.0	1.04477	50	50.899825	0.900
6	60	0.00	0.0	1.03826	60	54.286981	5.713
7	65	0.00	0.0	1.03484	65	56.744067	8.256
8	70	0.00	0.0	1.03182	70	59.521802	10.478
9	20	0.05	0.0	1.08755	20	45.513146	25.513
10	45	0.05	0.0	1.07105	45	45.157215	0.157
11	50	0.05	0.0	1.06760	50	45.445257	4.555
12	55	0.05	0.0	1.06409	55	45.863334	9.137
13	65	0.05	0.0	1.05691	65	47.132241	17.868
14	70	0.05	0.0	1.05291	70	48.111432	21.889

In [68]:

result_test = test.copy()
result_test["Real"] = result_test["T"]
result_test["Inferred"] = result_test.apply(fuzzy_pred, axis=1)
result_test["RMSE"] = result_test.apply(rmse, axis=1)
result_test = result_test.round({"RMSE": 3})
result_test

Out[68]:

	T	Al2O3	TiO2	Density	Real	Inferred	RMSE
0	30	0.00	0.00	1.05696	30	47.121319	17.121
1	55	0.00	0.00	1.04158	55	52.390781	2.609
2	25	0.05	0.00	1.08438	25	45.222921	20.223
3	30	0.05	0.00	1.08112	30	45.031722	15.032
4	35	0.05	0.00	1.07781	35	44.952086	9.952
5	40	0.05	0.00	1.07446	40	44.992751	4.993
6	60	0.05	0.00	1.06053	60	46.419899	13.580
7	35	0.30	0.00	1.17459	35	32.104404	2.896
8	65	0.30	0.00	1.14812	65	47.920831	17.079
9	45	0.00	0.05	1.07424	45	44.999669	0.000
10	50	0.00	0.05	1.07075	50	45.177446	4.823
11	55	0.00	0.05	1.06721	55	45.485450	9.515
12	20	0.00	0.30	1.22417	20	28.316733	8.317
13	30	0.00	0.30	1.21310	30	28.432013	1.568
14	40	0.00	0.30	1.20265	40	29.056559	10.943
15	60	0.00	0.30	1.18265	60	31.098758	28.901
16	70	0.00	0.30	1.17261	70	32.363220	37.637

In [69]:

rmetrics = {}
rmetrics["RMSE_train"] = math.sqrt(
    metrics.mean_squared_error(result_train["Real"], result_train["Inferred"])
)
rmetrics["RMSE_test"] = math.sqrt(
    metrics.mean_squared_error(result_test["Real"], result_test["Inferred"])
)
rmetrics["RMAE_test"] = math.sqrt(
    metrics.mean_absolute_error(result_test["Real"], result_test["Inferred"])
)
rmetrics["R2_test"] = metrics.r2_score(result_test["Real"], result_test["Inferred"])

rmetrics

Out[69]:

{'RMSE_train': 15.354573113986062,
 'RMSE_test': 15.530460096876435,
 'RMAE_test': 3.4741778705724395,
 'R2_test': -0.13066358713988602}