## Nonsingleton input - A Fuzzy logic problem

### Emanuel (view profile)

on 5 Dec 2012

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=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

### Walter Roberson (view profile)

on 5 Dec 2012

price is "loud" ??

Emanuel

### Emanuel (view profile)

on 6 Dec 2012

price is high. Could you see my program?

clear all

clc

close all

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

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')

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);

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

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