How to determine the firing level for non-singleton inputs - A fuzzy logic problem

Hi, i'm a new student of Fuzzy theory, and i'm trying to resolve the following Mamdani problem, considering that the input are nonsigleton.

I have 2 inputs: Temperature (low, medium, high) and price (low, medium, high), that are built using Gaussian and triangular functions, respectively:

% temperature
temperature=15:0.1:45;
tlow = gaussmf(temperature, [2.1 15]);%
tmedium = gaussmf(temperature, [2.1 24]);
thigh = gaussmf(temperature, [2.1 36.5]);

% price
price=1:0.1:6;
plow = trimf(price, [-0.3 1 2.4]);
pmedium = trimf(price, [1.7 3 4.3]);
phigh = trimf(price, [3.7 6 8.3]);

The output function of the problem is the soda consumption (low, medium, high), and is a triangular function:

% consumption
consumption=500:0.1:6000;
clow = trimf(consumption, [-1000 500 2000]);
cmedium = trimf(consumption, [1500 3000 4500]);
chigh = trimf(consumption, [4000 6000 8000]);

Rules:

1) if TEMPERATURE is low and PRICE is low then CONSUMPTION is big;

2) if TEMPERATURE is low and PRICE is medium then CONSUMPTION is medium;

3) if TEMPERATURE is low and PRICE is high then CONSUMPTION is small;

4) if TEMPERATURE is medium and PRICE is low then CONSUMPTION is big;

5) if TEMPERATURE is medium and PRICE is medium then CONSUMPTION is medium;

6) if TEMPERATURE is medium and PRICE is high then CONSUMPTION is small;

7) if TEMPERATURE is high and PRICE is low then CONSUMPTION is big;

8) if TEMPERATURE is high and PRICE is medium then CONSUMPTION is medium;

9) if TEMPERATURE is high and PRICE is high then CONSUMPTION is small.

I know that first it is necessary calculate the firing level, but i don't know how. Somebody can help me with this problem?

[Walter Roberson]

price is "loud" ??

[Emanuel]

price is high. Could you see my program?

% OPERADOR MAMDANI

clear all

clc

close all

%1ª entrada - Temperatura

t=15:0.1:45;

tbaixa = gaussmf(t, [2.1 15]);%gaussiana = A

tmedia = gaussmf(t, [2.1 24]);%gaussiana = A

talta = gaussmf(t, [2.1 36.5]);%gaussiana = A

plot(t,tbaixa,'b')

hold

plot(t,tmedia,'r')

plot(t,talta,'g')

legend('tbaixa','tmedia','talta')

%1ª entrada - F1 - Temperatura

t=18:0.1:48;

tbaixan = gaussmf(t, [2.2 18]);%gaussiana = A

tmedian = gaussmf(t, [2.2 27]);%gaussiana = A

taltan = gaussmf(t, [2.2 39.5]);%gaussiana = A

figure

plot(t,tbaixan,'b')

hold

plot(t,tmedian,'r')

plot(t,taltan,'g')

legend('tbaixa','tmedia','talta')

tfiringb=min(tbaixa,tbaixan);

tfiringb=max(tfiringb);%firing level

tfiringm=min(tmedia,tmedian);

tfiringm=max(tfiringm);%firing level

tfiringa=min(talta,taltan);

tfiringa=max(tfiringa);%firing level

%2ª entrada - Preço

pr=1:0.1:6;

pbaixo = trimf(pr, [-0.3 1 2.4]);%triangular=B

pmedio = trimf(pr, [1.7 3 4.3]);%triangular=B

palto = trimf(pr, [3.7 6 8.3]);%triangular=B

figure

plot(pr,pbaixo,'b')

hold

plot(pr,pmedio,'r')

plot(pr,palto,'g')

legend('pbaixo','pmedio','palto')

%2ª entrada -F2- Preço

pr=0:0.1:5;

pbaixon = trimf(pr, [-0.1 0.8 2]);%

pmedion = trimf(pr, [1.9 3.3 4.7]);%triangular=B

palton = trimf(pr, [3.2 5.6 8]);%triangular=B

figure

plot(pr,pbaixon,'b')

hold

plot(pr,pmedion,'r')

plot(pr,palton,'g')

legend('pbaixo','pmedio','palto')

%Achando o ponto

pfiringb=min(pbaixo,pbaixon);

pfiringb=max(pfiringb);%firing level

pfiringm=min(pmedio,pmedion);

pfiringm=max(pfiringm);%firing level

pfiringa=min(palton,palton);

pfiringa=max(pfiringa);%firing level

%Saída - Consumo

consumo=500:0.1:6000;

cbaixo = trimf(consumo, [-1000 500 2000]);%

cmedio = trimf(consumo, [1500 3000 4500]);%

calto = trimf(consumo, [4000 6000 8000]);%

figure

plot(consumo,cbaixo,'b')

hold

plot(consumo,cmedio,'r')

plot(consumo,calto,'g')

legend('cbaixo','cmedio','calto')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

A1=min(tfiringb,pfiringb);%firing level para 1ª regra

con1=combvec(calto,A1);%

con1=min(con1);

plot(con1)

A2=min(tfiringb,pfiringm);%firing level para 2ª regra

con2=combvec(cmedio,A2);

con2=min(con2);

A3=min(tfiringb,pfiringa);%firing level para 3ª regra

con3=combvec(cbaixo,A2);

con3=min(con3);

 A4=min(tfiringm,pfiringb);%firing level para 4ª regra

con4=combvec(calto,A4);

con4=min(con4);

 A5=min(tfiringm,pfiringm);%firing level para 5ª regra

 con5=combvec(cmedio,A5);

con5=min(con5);

A6=min(tfiringm,pfiringa);%firing level para 6ª regra

con6=combvec(cbaixo,A6);

con6=min(con6);

A7=min(tfiringa,pfiringb);%firing level para 7ª regra

con7=combvec(calto,A7);

con7=min(con7);

A8=min(tfiringa,pfiringm);%firing level para 8ª regra

con8=combvec(cmedio,A8);

con8=min(con8);

A9=min(tfiringa,pfiringa);%firing level par 9ª regra

con9=combvec(cbaixo,A9);

con9=min(con9);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Answer 1

[Sam Chak]

Hi @Emanuel

With all the membership functions well-defined and the number of fuzzy rules sufficient (), using specific functions from the Fuzzy Logic Toolbox, or better yet, directly designing the fuzzy system using the Fuzzy Logic Designer app, can skip the computation of firing level, and thus simplifying the process of fuzzy system design. However, the firing level can be computed using evalfis() command.

fis = mamfis;

%% input 1: Temperature
fis = addInput(fis, [15, 45], 'Name', 'Temperature');
fis = addMF(fis, 'Temperature', 'gaussmf', [2.1 15.0], 'Name', 'Low');   
fis = addMF(fis, 'Temperature', 'gaussmf', [2.1 24.0], 'Name', 'Medium');
fis = addMF(fis, 'Temperature', 'gaussmf', [2.1 36.5], 'Name', 'High');  

%% input 2: Price
fis = addInput(fis, [1, 6], 'Name', 'Price');
fis = addMF(fis, 'Price', 'trimf', [-0.3 1 2.4], 'Name', 'Low');  
fis = addMF(fis, 'Price', 'trimf', [ 1.7 3 4.3], 'Name', 'Medium');
fis = addMF(fis, 'Price', 'trimf', [ 3.7 6 8.3], 'Name', 'High');   

%% Output: Consumption
fis = addOutput(fis, [500, 6000], 'Name', 'Consumption');
fis = addMF(fis, 'Consumption', 'trimf', [-1000  500 2000], 'Name', 'Small');
fis = addMF(fis, 'Consumption', 'trimf', [ 1500 3000 4500], 'Name', 'Medium');
fis = addMF(fis, 'Consumption', 'trimf', [ 4000 6000 8000], 'Name', 'Big');

%% Fuzzy rules
rules = [
    "If Temperature is Low    and Price is Low    then Consumption is Big"      % Rule 1
    "If Temperature is Low    and Price is Medium then Consumption is Medium"   % Rule 2
    "If Temperature is Low    and Price is High   then Consumption is Small"    % Rule 3
    "If Temperature is Medium and Price is Low    then Consumption is Big"      % Rule 4
    "If Temperature is Medium and Price is Medium then Consumption is Medium"   % Rule 5
    "If Temperature is Medium and Price is High   then Consumption is Small"    % Rule 6
    "If Temperature is High   and Price is Low    then Consumption is Big"      % Rule 7
    "If Temperature is High   and Price is Medium then Consumption is Medium"   % Rule 8
    "If Temperature is High   and Price is High   then Consumption is Small"    % Rule 9
    ];
fis   = addRule(fis, rules);

figure
subplot(211)
plotmf(fis, 'input', 1, 3001), grid on, title('Input fuzzy sets for Temperature')
subplot(212)
plotmf(fis, 'input', 2, 5001), grid on, title('Input fuzzy sets for Price')

●

figure
plotmf(fis, 'output', 1, 55001), grid on, title('Output fuzzy sets for Consumption')

figure
opt = gensurfOptions('NumGridPoints', 51);
gensurf(fis, opt); view(-37.5, 135)

figure
in_Temp  = 25;  % input value of Temperature
in_Price =  3;  % input value of Price
[~, ~, ~, ~, ruleFiring] = evalfis(fis, [in_Temp, in_Price])

ruleFiring = 9×1

0 0.0000 0 0 0.8928 0 0 0.0000 0

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plotrule(fis, Inputs=[in_Temp, in_Price])