The solution to solve the assertion error and Value error?

Question

This is my code with some problem.

AssertionError: Total area is zero in defuzzification!

ValueError: Crisp output cannot be calculated, likely because the system is too sparse. Check to make sure this set of input values will activate at least one connected Term in each Antecedent via the current set of Rules. Top of this two error is show after i run my code.

Below the code is the full error message after i run. may i know what and where is the problem ?

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

Temp = ctrl.Antecedent(np.arange(0,101,1),'temperature')
Temp['Low'] = fuzz.trapmf(Temp.universe, [0,0,20,30])
Temp['Medium'] = fuzz.trimf(Temp.universe, [25,50,70])
Temp['High'] = fuzz.trapmf(Temp.universe, [60,80,100,100])

Humidity = ctrl.Antecedent(np.arange(0,101,1),'Humidity')
Humidity['Poor']=fuzz.trapmf(Humidity.universe, [0,0,10,20])
Humidity['Fair']=fuzz.trimf(Humidity.universe, [15,30,50])
Humidity['Good'] = fuzz.trapmf(Humidity.universe, [45,60,100,100])

CO = ctrl.Antecedent(np.arange(0,101,1),'CO')
CO['Low'] = fuzz.trapmf(CO.universe, [0,0,25,35])
CO['Medium'] = fuzz.trimf(CO.universe, [30,50,70])
CO['High'] = fuzz.trapmf(CO.universe, [65,80,100,100])

CO2 = ctrl.Antecedent(np.arange(0,101,1),'CO2')
CO2['Low'] = fuzz.trapmf(CO2.universe, [0,0,10,20])
CO2['Medium'] = fuzz.trimf(CO2.universe, [15,30,50])
CO2['High'] = fuzz.trapmf(CO2.universe, [45,60,100,100])

Condition = ctrl.Consequent(np.arange(0,101,1),'Health Condition')
Condition['Very Good']=fuzz.trapmf(Condition.universe, [0,0,10,30])
Condition['Good']=fuzz.trimf(Condition.universe, [20,30,40])
Condition['Medium']=fuzz.trimf(Condition.universe, [35,50,65])
Condition['Bad']=fuzz.trimf(Condition.universe, [60,70,80])
Condition['Dangerous']=fuzz.trapmf(Condition.universe, [75,90,100,100])

Temp.view()
Humidity.view()
CO.view()
CO2.view()
Condition.view()

rule1 = ctrl.Rule(Temp['Medium'] & Humidity['Fair'] & CO['Low'] & CO2['Low'], Condition['Good'])
rule2 = ctrl.Rule(Temp['Medium'] & Humidity['Good'] & CO['Medium'] & CO2['Low'], Condition['Very Good'])
rule3 = ctrl.Rule(Temp['Low'] & Humidity['Poor'] & CO['High'] & CO2['High'], Condition['Dangerous'])
rule4 = ctrl.Rule(Temp['High'] & Humidity['Poor'] & CO['Medium'] & CO2['Low'], Condition['Bad'])
rule5 = ctrl.Rule(Temp['Low'] & Humidity['Fair'] & CO['Medium'] & CO2['Medium'], Condition['Medium'])

rule1.view()
rule2.view()
rule3.view()
rule4.view()
rule5.view()

Health_ctrl = ctrl.ControlSystem([rule1, rule2, rule3, rule4, rule5])
HealthResult = ctrl.ControlSystemSimulation(Health_ctrl)

HealthResult.input['temperature'] =45
HealthResult.input['Humidity'] =40
HealthResult.input['CO'] =50
HealthResult.input['CO2'] =75

HealthResult.compute()

print(HealthResult.output['Health Condition'])
Condition.view(sim=HealthResult)



---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
/usr/local/lib/python3.6/dist-packages/skfuzzy/control/controlsystem.py in defuzz(self)
    586                 return defuzz(ups_universe, output_mf,
--> 587                               self.var.defuzzify_method)
    588             except AssertionError:

3 frames
/usr/local/lib/python3.6/dist-packages/skfuzzy/defuzzify/defuzz.py in defuzz(x, mfx, mode)
    247         zero_truth_degree = mfx.sum() == 0  # Approximation of total area
--> 248         assert not zero_truth_degree, 'Total area is zero in defuzzification!'
    249 

AssertionError: Total area is zero in defuzzification!

During handling of the above exception, another exception occurred:
ValueError                                Traceback (most recent call last)
<ipython-input-4-f358e5f1a15d> in <module>()
     56 HealthResult.input['CarbonDioxide'] =75
     57 
---> 58 HealthResult.compute()
     59 
     60 print(HealthResult.output['Health Condition'])

/usr/local/lib/python3.6/dist-packages/skfuzzy/control/controlsystem.py in compute(self)
    371         for consequent in self.ctrl.consequents:
    372             consequent.output[self] = \
--> 373                 CrispValueCalculator(consequent, self).defuzz()
    374             self.output[consequent.label] = consequent.output[self]
    375 

/usr/local/lib/python3.6/dist-packages/skfuzzy/control/controlsystem.py in defuzz(self)
    587                               self.var.defuzzify_method)
    588             except AssertionError:
--> 589                 raise ValueError("Crisp output cannot be calculated, likely "
    590                                  "because the system is too sparse. Check to "
    591                                  "make sure this set of input values will "

ValueError: Crisp output cannot be calculated, likely because the system is too sparse. Check to make sure this set of input values will activate at least one connected Term in each Antecedent via the current set of Rules.

Answer 1

When it says "too sparse" is saying that there are zones where no rule is activated, therefore no area can be calculated (hiper-area), so no center of gravity can be calculated (division by zero basically). In your case:

Rule 1: C0 and C02 have 0 membership

Rule 2: Humidity and C02 have 0 membership

Rule 3: Temperature, Humidity and CO have 0 membership

Rule 4: Tempreature and CO2 have 0 membership.

Therefore no area is generated