Laporan Praktikum

SISTEM KENDALI CERDAS

CRISP SETS DAN FUZZY SETS

Oleh:

Ahmad Fajar Nugroho (12518241040)

I. Tujuan

Menentukan identitas dasar dalam fuzzy sets.

II. Hasil dan Analisis

Modul sqrmf :

% modul sqrmf.m

function [val] = sqrmf(x,a,b)

val = max(min(min((x-a)/0.001,(b-x)/0.001),1),0);

return;

Modul gbellmf :

% modul gbellmf.m

function [y] = gbellmf(x,a,b,c)

y = 1./(1+(((x-c)/a).^2).^b);

return;

Modul Crisp sets dan Fuzzy set

x=0:10:600; %semesta (kedalaman laut)

%crisp sets

A=sqrmf(x,0,200);

B=sqrmf(x,200,400);

C=sqrmf(x,400,600);

%fuzzy sets

Az=gbellmf(x,60,2.5,100);

Bz=gbellmf(x,60,2.5,300);

Cz=gbellmf(x,60,2.5,500);

%Crisp Sets and Fuzzy Sets (Set A, Set B, And Set C)

figure(1)

clf

hold on

grid on

plot(x,A,'g--',x,B,'y--',x,C,'r--',x,Az,'g',x,Bz,'y',x,Cz,'r');

axis([-inf inf 0 1.2]);

title('Fuzzy dan Crisp Sets (Kedalaman Laut)');

ylabel('Nilai Himpunan Fuzzy');

text(87,1.1,'Dangkal'); text(288,1.1,'Sedang'); text(490,1.1,'Dalam');

hold off

Figure 1, Set nilai Fuzzy dan Crisp sets

Sub Modul 2 : Contradiction and Excluded Middle

%Contradiction and Excluded Middle

figure(2)

clf

hold on

subplot(221)

plot(x,A,'--',x,1-A,'-.',x,min(A,1-A),'r');

axis ([-inf inf 0 1.2]);

title('A And (Not A)');

subplot(222)

plot(x,Az,'--',x,1-Az,'-.',x,min(Az,1-Az),'r');

axis ([-inf inf 0 1.2]);

title('A And (Not A)');

subplot(223)

plot(x,A,'--',x,1-A,'-.',x,max(A,1-A),'r');

axis ([-inf inf 0 1.2]);

title('A Or (Not A)');

subplot(224)

plot(x,Az,'--',x,1-Az,'-.',x,max(Az,1-Az),'r');

axis ([-inf inf 0 1.2]);

title('A Or (Not A)');

hold off

Figure 2, Contradiction and Excluded Middle

Sub Modul 3 : Indempotency Law

%Indempotency Law

figure(3)

clf

hold on

subplot(221)

plot(x,A,'b',x,Az,'r');

axis([-inf inf 0 1.2]);

title('A');

set(gca ,'xtick', [0 200 400 600]);

subplot(222)

plot(x,min(A,A),'b',x,min(Az,Az),'r');

axis([-inf inf 0 1.2]);

title('A and A');

set(gca ,'xtick', [0 200 400 600]);

subplot(223)

plot(x,max(A,A),'b',x,max(Az,Az),'r');

axis([-inf inf 0 1.2]);

title('A or A');

set(gca ,'xtick', [0 200 400 600]);

subplot(224)

plot(x,1-(1-A),'b',x,1-(1-Az),'r');

axis([-inf inf 0 1.2]);

title('Not (Not A)');

set(gca ,'xtick', [0 200 400 600]);

hold off

Figure 3, Indempotency Law

Sub Modul 4 : Comutative Law

% Comutative Law

figure(4)

clf

hold on

subplot(221)

plot(x,min(A,B),'b',x,min(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('A and B');

set(gca ,'xtick', [0 200 400 600]);

subplot(222)

plot(x,min(B,A),'b',x,min(Bz,Az),'r');

axis([-inf inf 0 1.2]);

title('B and A');

set(gca ,'xtick', [0 200 400 600]);

subplot(223)

plot(x,max(A,B),'b',x,max(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('A or B');

set(gca ,'xtick', [0 200 400 600]);

subplot(224)

plot(x,max(B,A),'b',x,max(Bz,Az),'r');

axis([-inf inf 0 1.2]);

title('B or A');

set(gca ,'xtick', [0 200 400 600]);

hold off

Figure 4, Comutative Law

Sub Modul 5 : Associative Law

%Associative Law

figure(5)

clf

hold on

subplot(221)

plot(x,min(min(A,B),C),'b',x,min(min(Az,Bz),Cz),'r');

axis([-inf inf 0 1.2]);

title('(A and B) and C');

set(gca ,'xtick', [0 200 400 600]);

subplot(222)

plot(x,min(A,min(B,C)),'b',x,min(Az,min(Bz,Cz)),'r');

axis([-inf inf 0 1.2]);

title('A and (B and C)');

set(gca ,'xtick', [0 200 400 600]);

subplot(223)

plot(x,max(max(A,B),C),'b',x,max(max(Az,Bz),Cz),'r');

axis([-inf inf 0 1.2]);

title('(A or B) or C');

set(gca ,'xtick', [0 200 400 600]);

subplot(224)

plot(x,max(A,max(B,C)),'b',x,max(Az,max(Bz,Cz)),'r');

axis([-inf inf 0 1.2]);

title('A or (B or C)');

set(gca ,'xtick', [0 200 400 600]);

hold off

Figure 5, Associative Law

Sub Modul 6 : Distributive Law

%Distributive Law

figure(6)

clf

hold on

subplot(221)

plot(x,max(A,min(B,C)),'b',x,max(Az,min(Bz,Cz)),'r');

axis([-inf inf 0 1.2]);

title('(A or B) and C');

set(gca ,'xtick', [0 200 400 600]);

subplot(222)

plot(x,min(max(A,B),max(A,C)),'b',x,min(max(Az,Bz),max(Az,Cz)),'r');

axis([-inf inf 0 1.2]);

title('(A or B) and (A or C)');

set(gca ,'xtick', [0 200 400 600]);

subplot(223)

plot(x,min(A,max(B,C)),'b',x,min(Az,max(Bz,Cz)),'r');

axis([-inf inf 0 1.2]);

title('A and (B or C)');

set(gca ,'xtick', [0 200 400 600]);

subplot(224)

plot(x,max(min(A,B),min(A,C)),'b',x,max(min(Az,Bz),min(Az,Cz)),'r');

axis([-inf inf 0 1.2]);

title('(A and B) or (A and C)');

set(gca ,'xtick', [0 200 400 600]);

hold off

Figure 6, Distributive Law

Sub Modul 7 : Absorption Law

%Abrsorption

figure(7)

clf

hold on

subplot(221)

plot(x,A,'b',x,Az,'r');

axis([-inf inf 0 1.2]);

title('A');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(222)

plot(x,max(A,min(A,B)),'b',x,max(Az,min(Az,Bz)),'r');

axis([-inf inf 0 1.2]);

title('A or (A and B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(223)

plot(x,A,'b',x,Az,'r');

axis([-inf inf 0 1.2]);

title('A');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(224)

plot(x,min(A,max(A,B)),'b',x,min(Az,max(Az,Bz)),'r');

axis([-inf inf 0 1.2]);

title('A and (A or B)');

set(gca, 'xtick', [ 0 200 400 600]);

hold off

Figure 7, Absorption Law

Sub Modul 8 : Absorption of Complement Law

%Absorbtion of complement

figure(8)

clf

hold on

subplot(221)

plot(x,max(A,min((1-A),B)),'b',x,max(Az,min((1-Az),Bz)),'r');

axis([-inf inf 0 1.2]);

title('A or (Not A and B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(222)

plot(x,max(A,B),'b',x,max(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('A or B');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(223)

plot(x,min(A,max((1-A),B)),'b',x,min(Az,max((1-Az),Bz)),'r');

axis([-inf inf 0 1.2]);

title('A and (Not A or B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(224)

plot(x,min(A,B),'b',x,min(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('A and B');

set(gca, 'xtick', [ 0 200 400 600]);

hold off

Figure 8, Absorption of Complement Law

Sub Modul 9 : DeMorgan Law

%DeMorgan

figure(9)

clf

hold on

subplot(221)

plot(x,1-max(A,B),'b',x,1-max(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('Not (A or B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(222)

plot(x,min(1-A,1-B),'b',x,min(1-Az,1-Bz),'r');

axis([-inf inf 0 1.2]);

title('(Not A) and (Not B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(223)

plot(x,1-min(A,B),'b',x,1-min(Az,Bz),'r');

axis([-inf inf 0 1.2]);

title('Not (A and B)');

set(gca, 'xtick', [ 0 200 400 600]);

subplot(224)

plot(x,max(1-A,1-B),'b',x,max(1-Az,1-Bz),'r');

axis([-inf inf 0 1.2]);

title('(Not A) or (Not B)');

set(gca, 'xtick', [ 0 200 400 600]);

hold off

Figure 9, DeMorgan law

III. Kesimpulan

Dari hasil praktikum di atas, gambar 8, pada bagian 3 dan 4 tidak dapat dipakai karena kurva

yang dihasilan tidak sama, sedangkan pada sub modul dan figur lainnya, masing-masing

memiliki kesamaan pada perbandingan himpunan sesuai dengan hukum yang terdapat

pada modul 1 (fuzzy set dan crips set).