fuzzy-rules-generator/temp_density_tree.ipynb

In [70]:

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 [71]:

from src.rules import get_rules


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

27

Out[71]:

[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 [72]:

from src.rules import normalise_rules


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

27

Out[72]:

[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 [73]:

from src.rules import delete_same_rules


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

15

Out[73]:

[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 [74]:

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[74]:

	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 [75]:

from src.rules import simplify_rules

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

15

Out[75]:

[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 [124]:

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(5, variable_type="quant")
temp.view()

/Users/user/Projects/python/fuzzy-rules-generator/.venv/lib/python3.12/site-packages/skfuzzy/control/fuzzyvariable.py:125: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  fig.show()

In [125]:

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[125]:

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

In [126]:

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[lower]
	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[lower] : 0.0

RULE #1:
  IF (density[low] AND ti[low]) AND al[low] THEN temp[low]
	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[low] : 0.5693410286540264

RULE #2:
  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 #3:
  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 #4:
  IF density[low] AND ti[high] THEN temp[higher]
	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[higher] : 0.0

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

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

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

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

RULE #7:
  IF density[average] AND al[low] THEN temp[higher]
	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[higher] : 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[lower]
	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[lower] : 0.0


==============================
 Intermediaries and Conquests 
==============================
Consequent: temp                     = 41.73310616908626
  lower:
    Accumulate using accumulation_max : 0.5693410286540264
  low:
    Accumulate using accumulation_max : 0.5693410286540264
  average:
    Accumulate using accumulation_max : 0.0
  high:
    Accumulate using accumulation_max : 0.43065897134597164
  higher:
    Accumulate using accumulation_max : 0.0

np.float64(41.73310616908626)

In [127]:

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[127]:

	T	Al2O3	TiO2	Density	Real	Inferred	RMSE
0	20	0.00	0.0	1.06250	20	39.276564	19.277
1	25	0.00	0.0	1.05979	25	40.474182	15.474
2	35	0.00	0.0	1.05404	35	43.002194	8.002
3	40	0.00	0.0	1.05103	40	44.373956	4.374
4	45	0.00	0.0	1.04794	45	45.803674	0.804
5	50	0.00	0.0	1.04477	50	47.330811	2.669
6	60	0.00	0.0	1.03826	60	50.888953	9.111
7	65	0.00	0.0	1.03484	65	53.183324	11.817
8	70	0.00	0.0	1.03182	70	55.645272	14.355
9	20	0.05	0.0	1.08755	20	37.043626	17.044
10	45	0.05	0.0	1.07105	45	36.776662	8.223
11	50	0.05	0.0	1.06760	50	38.797623	11.202
12	55	0.05	0.0	1.06409	55	40.347656	14.652
13	65	0.05	0.0	1.05691	65	42.508159	22.492
14	70	0.05	0.0	1.05291	70	43.516405	26.484

In [128]:

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[128]:

	T	Al2O3	TiO2	Density	Real	Inferred	RMSE
0	30	0.00	0.00	1.05696	30	41.707469	11.707
1	55	0.00	0.00	1.04158	55	48.979472	6.021
2	25	0.05	0.00	1.08438	25	35.546123	10.546
3	30	0.05	0.00	1.08112	30	33.702339	3.702
4	35	0.05	0.00	1.07781	35	31.483248	3.517
5	40	0.05	0.00	1.07446	40	34.051564	5.948
6	60	0.05	0.00	1.06053	60	41.554965	18.445
7	35	0.30	0.00	1.17459	35	26.052643	8.947
8	65	0.30	0.00	1.14812	65	51.649578	13.350
9	45	0.00	0.05	1.07424	45	32.924090	12.076
10	50	0.00	0.05	1.07075	50	35.608122	14.392
11	55	0.00	0.05	1.06721	55	37.735219	17.265
12	20	0.00	0.30	1.22417	20	32.475100	12.475
13	30	0.00	0.30	1.21310	30	32.475102	2.475
14	40	0.00	0.30	1.20265	40	32.475114	7.525
15	60	0.00	0.30	1.18265	60	32.475245	27.525
16	70	0.00	0.30	1.17261	70	32.477777	37.522

In [132]:

import matplotlib.pyplot as plt

result_test.hist(bins=30, figsize=(10, 10))
plt.show()

In [130]:

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[130]:

{'RMSE_train': 14.558276689668899,
 'RMSE_test': 15.299814000482547,
 'RMAE_test': 3.543337541765307,
 'R2_test': -0.09732952379343951}