How to create relation from each rule

How to create fuzzy relation from multi input variable? My fuzzy system has four input from QRS duration, QTP interval, Raton RR and Area A ST. After I obtain membership function, I need to crate fuzzy operation in each rule for obtain relation between input and output.

Assume my rule is " IF QRS-duration is PM and QTR-interval is PS and Ratio RR is PB and Area R ST is PM THEN Heart beat case is NORM"

I need to use min operation for combine each variable, and finally I will obtain relation between input and output.

%%%%%%%%%%%%%%%%%%%%%%______________________________%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%The membership function of the input variable%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%The Fuzzy Set of QRS Duration%%%%%%%%%%%%%%%%

x1=0:250;

%%%%%%Positive Small Set%%%%%%

for i=1:length(x1)

   if (x1(i)>34) && (x1(i)<=54.3)

   PS(i)=((x1(i)-34.0)/(54.3-34.0));

   elseif (x1(i)>54.3) && (x1(i)<=61.0)

   PS(i)=((61.0-x1(i))/(61.0-54.3));

   else

   PS(i)=0;

 end

end

plot(x1,PS);

%%%%%%Positive Median Set%%%%%%

for i=1:length(x1)

    if (x1(i)>33)&&(x1(i)<=55)

        PM(i)=(x1(i)-33)/(55-33);

    elseif (x1(i)>55)&&(x1(i)<=79)

        PM(i)=(79-x1(i))/(79-55);

    else

        PM(i)=0;

    end

end

hold on;

plot(x1,PM,'r');

%%%%%%Positive Big Set%%%%%%

for i=1:length(x1)

if x1(i)>46 && x1(i)<=74.6

    PB(i)=(x1(i)-46)/(74.6-46.0);

elseif x1(i)>74.6 && x1(i)<=130

    PB(i)=(130-x1(i))/(130-74.6);

else

    PB(i)=0;

end

end

hold on;

plot(x1,PB,'g');

%%%%%%Positive Very-Big Set%%%%%%

for i=1:length(x1)

if x1(i)>52&& x1(i)<=120.4

    PV(i)=(x1(i)-52)/(120.4-52);

elseif x1(i)>120.4 && x1(i)<=210

    PV(i)=(210-x1(i))/(210-120.4);

else

    PV(i)=0;

end

end

hold on;

plot(x1,PV,'m');

%%%%%%Positive Enormous Set%%%%%%

for i=1:length(x1)

if x1(i)>86&& x1(i)<=109.2

    PE(i)=(x1(i)-86)/(109.2-86);

elseif x1(i)>109.2 && x1(i)<=153

    PE(i)=(153-x1(i))/(153-109.2);

else

    PE(i)=0;

end

end

hold on;

plot(x1,PE,'c');

xlabel('Feature Value (mV)');

ylabel('Degree of Membership');

title('QRS Duration');

legend('PS','PM','PB','PV','PE');

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

%%%%%%%%%%%%%%%%The Fuzzy Set of QTP Interval%%%%%%%%%%%%%%%%

x2=0:500;

%%%%%%Positive Small Set%%%%%%

for i=1:length(x2)

   if (x2(i)>43) && (x2(i)<=73)

       PS2(i)=((x2(i)-43)/(73-43.0));

   elseif (x2(i)>73) && (x2(i)<=90.0)

       PS2(i)=((90-x2(i))/(90-73));

   else

       PS2(i)=0;

   end

end

figure;

plot(x2,PS2);

%%%%%%Positive Median Set%%%%%%

for i=1:length(x2)

   if (x2(i)>52.5) && (x2(i)<=90)

       PM2(i)=((x2(i)-52.5)/(90-52.5));

   elseif (x2(i)>90) && (x2(i)<=112.5)

       PM2(i)=((112.5-x2(i))/(112.5-90));

   else

       PM2(i)=0;

   end

end

hold on;

plot(x2,PM2,'r');

%%%%%%Positive Big Set%%%%%%

for i=1:length(x2)

   if (x2(i)>97.5) && (x2(i)<=143)

       PB2(i)=((x2(i)-97.5)/(143-97.5));

   elseif (x2(i)>143) && (x2(i)<=212)

       PB2(i)=((212-x2(i))/(212-143));

   else

       PB2(i)=0;

   end

end

hold on;

plot(x2,PB2,'g');

%%%%%%Positive Very-Big Set%%%%%%

for i=1:length(x2)

   if (x2(i)>120) && (x2(i)<=294)

       PV2(i)=((x2(i)-120)/(294-120));

   elseif (x2(i)>294) && (x2(i)<=482)

       PV2(i)=((482-x2(i))/(482-294));

   else

       PV2(i)=0;

   end

end

hold on;

plot(x2,PV2,'m');

%%%%%%Positive Enormous Set%%%%%%

for i=1:length(x2)

   if (x2(i)>135) && (x2(i)<=172.5)

       PE2(i)=((x2(i)-135)/(172.5-135));

   elseif (x2(i)>172.5) && (x2(i)<=233)

       PE2(i)=((233-x2(i))/(233-172.5));

   else

       PE2(i)=0;

   end

end

hold on;

plot(x2,PE2,'c');

xlabel('Feature Value (ms)');

ylabel('Degree of Membership');

title('QTR Interval');

legend('PS','PM','PB','PV','PE');

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

%%%%%%%%%%%%%%%% Ratio R-R%%%%%%%%%%%%%%%%

x3=0:160;

%%%%%%Positive Small Set%%%%%%

for i=1:length(x3)

    xa=x3/100;

    if (xa(i)>0.440) && (xa(i)<=0.640)

       PS3(i)=((xa(i)-0.440)/(0.640-0.440));    

   elseif (xa(i)>0.640) && (xa(i)<=0.760)

       PS3(i)=((0.760-xa(i))/((0.760-0.640)));

   else

       PS3(i)=0;

   end

end

figure;

plot(x3/100,PS3);

%%%%%%Positive Median Set%%%%%%

for i=1:length(x3)

    xa=x3/100;

    if (xa(i)>0.400) && (xa(i)<=0.690)

       PM3(i)=((xa(i)-0.400)/(0.690-0.400));

   elseif (xa(i)>0.690) && (xa(i)<=0.760)

       PM3(i)=((0.760-xa(i))/((0.760-0.690)));

   else

       PM3(i)=0;

   end

end

hold on;

plot(x3/100,PM3,'r');

%%%%%%Positive Big Set%%%%%%

for i=1:length(x3)

    xa=x3/100;

    if (xa(i)>0.800) && (xa(i)<=0.990)

       PB3(i)=((xa(i)-0.800)/(0.990-0.800));

   elseif (xa(i)>0.990) && (xa(i)<=1.200)

       PB3(i)=((1.200-xa(i))/((1.200-0.990)));

   else

       PB3(i)=0;

   end

end

hold on;

plot(x3/100,PB3,'g');

%%%%%%Positive Very-Big Set%%%%%%

for i=1:length(x3)

    xa=x3/100;

    if (xa(i)>0.77) && (xa(i)<=1.02)

       PV3(i)=((xa(i)-0.77)/(1.02-0.77));

   elseif (xa(i)>1.02) && (xa(i)<=1.500)

       PV3(i)=((1.500-xa(i))/((1.500-1.02)));

   else

       PV3(i)=0;

   end

end

hold on;

plot(x3/100,PV3,'m');

%%%%%%Positive Enormous Set%%%%%%

for i=1:length(x3)

    xa=x3/100;

    if (xa(i)>0.840) && (xa(i)<=1.010)

       PE3(i)=((xa(i)-0.840)/(1.010-0.840));

   elseif (xa(i)>1.010) && (xa(i)<=1.300)

       PE3(i)=((1.300-xa(i))/((1.300-1.010)));

   else

       PE3(i)=0;

   end

end

hold on;

plot(x3/100,PE3,'c');

xlabel('Feature Value ');

ylabel('Degree of Membership');

title('Ration R-R');

legend('PS','PM','PB','PV','PE');

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

%%%%%%%%%%%%%%%% Area -R'ST'%%%%%%%%%%%%%%%%

x4=0:300;

%%%%%%Positive Small Set%%%%%%

for i=1:length(x4)

   if (x4(i)>0) && (x4(i)<=8)

       PS4(i)=((x4(i)-0)/(8-0));

   elseif (x4(i)>8) && (x4(i)<=155)

       PS4(i)=((155-x1(i))/(155-8));

   else

       PS4(i)=0;

   end

end

figure;

plot(x4,PS4);

%%%%%%Positive Median Set%%%%%%

for i=1:length(x4)

   if (x4(i)>0) && (x4(i)<=10)

       PM4(i)=((x4(i)-0)/(10));

   elseif (x4(i)>10) && (x4(i)<=24.50)

       PM4(i)=((24.50-x4(i))/(24.50-10));

   else

       PM4(i)=0;

   end

end

hold on;

plot(x4,PM4,'r');

%%%%%%Positive Big Set%%%%%%

for i=1:length(x4)

   if (x4(i)>18) && (x4(i)<=25)

       PB4(i)=((x4(i)-18)/(25-18));

   elseif (x4(i)>25) && (x4(i)<=34)

       PB4(i)=((34-x4(i))/(34-25));

   else

       PB4(i)=0;

   end

end

hold on;

plot(x4,PB4,'g');

%%%%%%Positive Very-Big Set%%%%%%

for i=1:length(x4)

   if (x4(i)>0) && (x4(i)<=150)

       PV4(i)=((x4(i)-0)/(150-0));

   elseif (x4(i)>150) && (x4(i)<=265)

       PV4(i)=((265-x4(i))/(265-150));

   else

       PV4(i)=0;

   end

end

hold on;

plot(x4,PV4,'m');

%%%%%%Positive Enormous Set%%%%%%

for i=1:length(x4)

   if (x4(i)>32) && (x4(i)<=55)

       PE4(i)=((x4(i)-32)/(55-32));

   elseif (x4(i)>55) && (x4(i)<=88)

       PE4(i)=((88-x4(i))/(88-55));

   else

       PE4(i)=0;

   end

end

hold on;

plot(x4,PE4,'c');

xlabel('Feature Value mVxms');

ylabel('Degree of Membership');

title('Area-R ST');

legend('PS','PM','PB','PV','PE');

%%%%%%%%%%%%%%%%%%%%%%______________________________%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%The membership function of the output variable%%%%%%%%%%%%%%%%

x5=0:12;

for i=1:length(x5)

   if x5(i)==2

       NORM(i)=1;

   elseif  x5(i)~= 2

       NORM(i)=0;

   else

       NORM(i)=0;

   end

end

figure;

plot(x5,NORM);

for i=1:length(x5)

   if x5(i)==4

       LBBB(i)=1;

   elseif  x5(i)~= 4

       LBBB(i)=0;

   else

       LBBB(i)=0;

   end

end

hold on;

plot(x5,LBBB,'r');

for i=1:length(x5)

   if x5(i)==6

       RBBB(i)=1;

   elseif  x5(i)~=6

       RBBB(i)=0;

   else

       RBBB(i)=0;

   end

end

hold on;

plot(x5,RBBB,'r');

for i=1:length(x5)

   if x5(i)==8

       VPC(i)=1;

   elseif  x5(i)~=8

       VPC(i)=0;

   else

       VPC(i)=0;

   end

end

hold on;

plot(x5,VPC,'g');

for i=1:length(x5)

   if x5(i)==10

       APC(i)=1;

   elseif  x5(i)~=10

       APC(i)=0;

   else

       APC(i)=0;

   end

end

hold on;

plot(x5,APC,'m');

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

Answer 1

[Salaheddin Hosseinzadeh]

Great now I can read something. I see you're writing a code from ground zero and defined a lot of membership functions, which seem that they all have the same length. good job.

Is your problem on how to apply fuzzy max min (intersection and union) to the membership functions and you're looking for a easy way?

if so, then

make the membership functions as columns, so the size will be n x 1 then you can easily use max and min command.

max(mf1,mf2); % this gives u the union if i'm right ;)

To form the consequent you can make can to the same thing, and max or min it with the consequent mf.

Please let me know if this helps.

Good luck!

[Salaheddin Hosseinzadeh]

Any good?!

[KoolMU]

Thanks for your advice, it can use to find relation between two membership functions.