fuzzy-rules-generator/density_fuzzy.ipynb at 99a4c21f6e7b0c014dd5c498ee32a5d05a9862b7

In [58]:

import pandas as pd

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

display(density_train.head(3))
display(density_test.head(3))

	T	Density
0	20	1.06250
1	25	1.05979
2	35	1.05404

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

In [59]:

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

temp = ctrl.Antecedent(density_train["T"].sort_values().unique(), "temp")
al = ctrl.Antecedent(np.arange(0, 0.3, 0.005), "al")
ti = ctrl.Antecedent(np.arange(0, 0.3, 0.005), "ti")
density = ctrl.Consequent(np.arange(1.03, 1.22, 0.00001), "density")

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

c:\Users\user\Projects\python\fuzzy\.venv\Lib\site-packages\skfuzzy\control\fuzzyvariable.py:125: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  fig.show()

In [60]:

rule11 = ctrl.Rule(
    temp["low"] & al["low"] & ti["low"],
    density["low"],
)
rule12 = ctrl.Rule(
    temp["average"] & al["low"] & ti["low"],
    density["lower"],
)
rule13 = ctrl.Rule(
    temp["high"] & al["low"] & ti["low"],
    density["lower"],
)

rule21 = ctrl.Rule(
    temp["low"] & al["average"] & ti["low"],
    density["low"],
)
rule22 = ctrl.Rule(
    temp["average"] & al["average"] & ti["low"],
    density["low"],
)
rule23 = ctrl.Rule(
    temp["high"] & al["average"] & ti["low"],
    density["lower"],
)

rule31 = ctrl.Rule(
    temp["low"] & al["high"] & ti["low"],
    density["high"],
)
rule32 = ctrl.Rule(
    temp["low"] & al["high"] & ti["low"],
    density["high"],
)
rule33 = ctrl.Rule(
    temp["high"] & al["high"] & ti["low"],
    density["average"],
)

rule41 = ctrl.Rule(
    temp["low"] & al["low"] & ti["average"],
    density["low"],
)
rule42 = ctrl.Rule(
    temp["average"] & al["low"] & ti["average"],
    density["low"],
)
rule43 = ctrl.Rule(
    temp["high"] & al["low"] & ti["average"],
    density["lower"],
)

rule51 = ctrl.Rule(
    temp["low"] & al["low"] & ti["high"],
    density["higher"],
)
rule52 = ctrl.Rule(
    temp["average"] & al["low"] & ti["high"],
    density["high"],
)
rule53 = ctrl.Rule(
    temp["high"] & al["low"] & ti["high"],
    density["high"],
)

In [61]:

fuzzy_rules = [
    rule11,
    rule12,
    rule13,
    rule21,
    rule22,
    rule23,
    rule31,
    rule32,
    rule33,
    rule41,
    rule42,
    rule43,
    rule51,
    rule52,
    rule53,
]

density_cntrl = ctrl.ControlSystem(fuzzy_rules)

sim = ctrl.ControlSystemSimulation(density_cntrl)

fuzzy_rules

Out[61]:

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

In [62]:

sim.input["temp"] = 20
sim.input["al"] = 0.3
sim.input["ti"] = 0.0
sim.compute()
sim.print_state()
display(sim.output["density"])

=============
 Antecedents 
=============
Antecedent: temp                    = 20
  - low                             : 1.0
  - average                         : 0.0
  - high                            : 0.0
Antecedent: al                      = 0.295
  - low                             : 0.0
  - average                         : 0.0
  - high                            : 1.0
Antecedent: ti                      = 0.0
  - low                             : 1.0
  - average                         : 0.0
  - high                            : 0.0

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

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

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

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

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

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

RULE #3:
  IF (temp[low] AND al[average]) AND ti[low] THEN density[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

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

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

RULE #5:
  IF (temp[high] AND al[average]) AND ti[low] THEN density[lower]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #6:
  IF (temp[low] AND al[high]) AND ti[low] THEN density[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

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

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

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

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

RULE #9:
  IF (temp[low] AND al[low]) AND ti[average] THEN density[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #10:
  IF (temp[average] AND al[low]) AND ti[average] THEN density[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #11:
  IF (temp[high] AND al[low]) AND ti[average] THEN density[lower]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #12:
  IF (temp[low] AND al[low]) AND ti[high] THEN density[higher]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #13:
  IF (temp[average] AND al[low]) AND ti[high] THEN density[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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

RULE #14:
  IF (temp[high] AND al[low]) AND ti[high] THEN density[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

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


==============================
 Intermediaries and Conquests 
==============================
Consequent: density                  = 1.1724924997377486
  lower:
    Accumulate using accumulation_max : 0.0
  low:
    Accumulate using accumulation_max : 0.0
  average:
    Accumulate using accumulation_max : 0.0
  high:
    Accumulate using accumulation_max : 1.0
  higher:
    Accumulate using accumulation_max : 0.0

np.float64(1.1724924997377486)

In [63]:

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

In [65]:

result_train = density_train.copy()

result_train["DensityPred"] = result_train.apply(fuzzy_pred, axis=1)

result_train.head(15)

Out[65]:

	T	Al2O3	Density	DensityPred
0	20	0.00	1.06250	1.077498
1	25	0.00	1.05979	1.076593
2	35	0.00	1.05404	1.069156
3	40	0.00	1.05103	1.061106
4	45	0.00	1.04794	1.045833
5	50	0.00	1.04477	1.046360
6	60	0.00	1.03826	1.047642
7	65	0.00	1.03484	1.046360
8	70	0.00	1.03182	1.045833
9	20	0.05	1.08755	1.077498
10	45	0.05	1.07105	1.067145
11	50	0.05	1.06760	1.067145
12	55	0.05	1.06409	1.067988
13	65	0.05	1.05691	1.062538
14	70	0.05	1.05291	1.047191

In [66]:

result_test = density_test.copy()

result_test["DensityPred"] = result_test.apply(fuzzy_pred, axis=1)

result_test

Out[66]:

	T	Al2O3	TiO2	Density	DensityPred
0	30	0.00	0.00	1.05696	1.073918
1	55	0.00	0.00	1.04158	1.047642
2	25	0.05	0.00	1.08438	1.076518
3	30	0.05	0.00	1.08112	1.073918
4	35	0.05	0.00	1.07781	1.069156
5	40	0.05	0.00	1.07446	1.067145
6	60	0.05	0.00	1.06053	1.067988
7	35	0.30	0.00	1.17459	1.172492
8	65	0.30	0.00	1.14812	1.124995
9	45	0.00	0.05	1.07424	1.067145
10	50	0.00	0.05	1.07075	1.067145
11	55	0.00	0.05	1.06721	1.067988
12	20	0.00	0.30	1.22417	1.204157
13	30	0.00	0.30	1.21310	1.180834
14	40	0.00	0.30	1.20265	1.173397
15	60	0.00	0.30	1.18265	1.172492
16	70	0.00	0.30	1.17261	1.172492

In [67]:

import math
from sklearn import metrics


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

rmetrics

Out[67]:

{'RMSE_train': 0.0156766544822719,
 'RMSE_test': 0.014603864614526584,
 'RMAE_test': 0.1057231829134674,
 'R2_test': 0.9436578668511394}

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