Let R and S be two fuzzy relations defined as : Then, the resulting relation,…

Use the max-min composition:

T(x,z) = max over y of min( R(x,y), S(y,z) ).

1. Compute row for x1:

   • T(x1,z1) = max{ min(0.7,0.9), min(0.5,0.1) } = max{ 0.7, 0.1 } = 0.7

   • T(x1,z2) = max{ min(0.7,0.6), min(0.5,0.7) } = max{ 0.6, 0.5 } = 0.6

   • T(x1,z3) = max{ min(0.7,0.2), min(0.5,0.5) } = max{ 0.2, 0.5 } = 0.5

2. Compute row for x2:

   • T(x2,z1) = max{ min(0.8,0.9), min(0.4,0.1) } = max{ 0.8, 0.1 } = 0.8

   • T(x2,z2) = max{ min(0.8,0.6), min(0.4,0.7) } = max{ 0.6, 0.4 } = 0.6

   • T(x2,z3) = max{ min(0.8,0.2), min(0.4,0.5) } = max{ 0.2, 0.4 } = 0.4

Therefore the resulting relation T (rows x1,x2 and columns z1,z2,z3) is:

T = [ x1: 0.7 0.6 0.5 ; x2: 0.8 0.6 0.4 ]