Two-Dimensional Fuzzy Spatial Relations: A New Way of Computing and Representation

Algorithm 1

Algorithm for defuzzification of 2D fuzzy topological and directional relations.

for 𝑖,𝑗=1 to 8 do

 if 𝐶(3,𝑗)≠0 then

  topological relation is overlap and directional relation is

  max_𝑗(𝐶(2,𝑗),𝐶(3,𝑗),𝐶(4,𝑗),𝐶(6,𝑗))

 else if 𝐶(4,𝑗)≠0 then

  topological relation is TPP and directional relation is max_𝑗(𝐶(4,𝑗))

 else if 𝐶(6,𝑗)≠0 then

  topological relation is TPPI and directional relation is max_𝑗(𝐶(6,𝑗))

 else if all 𝐶(5,∶) are approximately equal for all 𝑗 then

  topological relation will be NTPP

 else if all 𝐶(7,∶) are approximately equal for all 𝑗 then

  topological relation is NTPPI

 else if all 𝐶(8,∶) are approximately equal for all 𝑗 then

  topological relation will be EQ

 else if 𝐶(2,𝑗)≠0∧𝐶(𝑖,𝑗)=0∨𝑖≥3 then

  topological relation is meet M and directional relation is max_𝑗(𝐶(2,𝑗))

 else

  topological relation is Disjoint and directional relation is max_𝑗(𝐶(1,𝑗))

 end if

end for