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The fuzzy base rule is as given in the table 1-1. 2 are assumed as mentioned in the table 1-2. Table 1-2. 2 Figure 1-20. Relationship between crisp value and fuzzy membership for the Input variable X in the example 1. 4 ___________________________________________________________ fuzzygv . m posx=[0 3 5 7 10]; maxx=max(posx); posx=posx/max(posx); posy=[0 20 45 65 100]; maxy=max(posy); posy=posy/max(posy); posz=[0 35 70 90 100]; maxz=max(posz); posz=posz/max(posz); i=posx(1):1/999:posx(2); j=(posx(2)):(1/999):posx(3); k=(posx(3)):(1/999):posx(4); l=(posx(4)):(1/999):posx(5); xsmall=[1/posx(2)*i (-1/(posx(3)-posx(2))*(j-posx(3))) zeros(1,length([k l]))]; xmedium =[zeros(1,length([i])) (1/(posx(3)-posx(2))*(j-posx(2))) (-1/(posx(4)posx(3))*(k-posx(4))) zeros(1,length([l]))]; xlarge=[zeros(1,length([i j])) (1/(posx(4)-posx(3))*(k-posx(3))) (-1/(posx(5)-posx(4))*(lposx(5))) ]; figure plot([i j k l]*maxx,xsmall,':'); hold plot([i j k l]*maxx,xmedium,'-'); plot([i j k l]*maxx,xlarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('XINPUT') i=posy(1):1/999:posy(2); j=(posy(2)):(1/999):posy(3); k=(posy(3)):(1/999):posy(4); l=(posy(4)):(1/999):posy(5); ysmall=[1/posy(2)*i (-1/(posy(3)-posy(2))*(j-posy(3))) zeros(1,length([k l]))]; 42 Chapter 1 ymedium =[zeros(1,length([i])) (1/(posy(3)-posy(2))*(j-posy(2))) (-1/(posy(4)posy(3))*(k-posy(4))) zeros(1,length([l]))]; ylarge=[zeros(1,length([i j])) (1/(posy(4)-posy(3))*(k-posy(3))) (-1/(posy(5)-posy(4))*(lposy(5))) ]; figure plot([i j k l]*maxy,ysmall,':'); hold plot([i j k l]*maxy,ymedium,'-'); plot([i j k l]*maxy,ylarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('YINPUT') i=posz(1):1/999:posz(2); j=(posz(2)):(1/999):posz(3); k=(posz(3)):(1/999):posz(4); l=(posz(4)):(1/999):posz(5); zsmall=[1/posz(2)*i (-1/(posz(3)-posz(2))*(j-posz(3))) zeros(1,length([k l]))]; zmedium =[zeros(1,length([i])) (1/(posz(3)-posz(2))*(j-posz(2))) (-1/(posz(4)posz(3))*(k-posz(4))) zeros(1,length([l]))]; zlarge=[zeros(1,length([i j])) (1/(posz(4)-posz(3))*(k-posz(3))) (-1/(posz(5)-posz(4))*(lposz(5))) ]; figure plot([i j k l]*maxz,zsmall,':'); hold plot([i j k l]*maxz,zmedium,'-'); plot([i j k l]*maxz,zlarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('ZOUTPUT') xinput=[6]; xinput=round(((xinput/maxx)*1000)) yinput=[50]; yinput=round(((yinput/maxy)*1000)) %fuzzy values xfuzzy=[xsmall(xinput) xmedium(xinput) xlarge(xinput)]; yfuzzy=[ysmall(yinput) ymedium(yinput) ylarge(yinput)]; 1.

Suppose if q3 is the lowest among the values in the vector, the number 3 is assigned to the variable u8. This is called one iteration. Step 4: • The updating pheromone matrix for the second iteration is computed as described in the step 2 using the set of orders selected by the five ants in the first iteration. This is called as Updating pheromone matrix (2). • Pheromone matrix used in the 2nd iteration is computed as Pheromone matrix (2) = Pheromone matrix (1) +Updating Pheromone matrix (2) Step 5: Next set of orders selected by the five ants are computed as described in the step 3.

The orders selected by the four ants after 50 Iterations are displayed below. ANT1: ANT2: ANT3: ANT4: 1 1 3 4 2 2 2 2 3 3 7 3 4 4 4 7 5 5 1 1 6 6 6 6 7 7 5 5 8 8 8 8 Note that ANT1 and ANT2 found the best order as expected using Ant colony technique. Initially the cost values are having more changes. After 40th iteration, cost value gradually increases and reaches maximum which is the optimum cost corresponding the optimum order selected using Ant colony technique. 1. *Q(max(i,A(i)),min(i,A(i))); end Chapter 2 PROBABILITY AND RANDOM PROCESS Algorithm Collections 1.

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Maple 11 Quick Reference Card
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