Novel Applications of Intuitionistic Fuzzy Digraphs in Decision Support Systems

Algorithm 4

IF digraph in travel time.

(1) void fuzzyShortestPath(){

(2)  𝐶 = Intuitionistic fuzzy set of crossings;

(3)  𝑛𝑜𝑂𝑓𝐶𝑟𝑜𝑠𝑠𝑖𝑛𝑔 = count(𝐶);

(4)  𝐿 = Empty intuitionistic fuzzy set of roads;

(5)  for (int 𝑥=0;𝑥<𝑛𝑜𝑂𝑓𝐶𝑟𝑜𝑠𝑠𝑖𝑛𝑔; 𝑥++) {

(6)   for (int 𝑦=0;𝑦<𝑛𝑜𝑂𝑓𝐶𝑟𝑜𝑠𝑠𝑖𝑛𝑔; 𝑦++) {

(7)    if (𝐶(𝑥) is adjacent to 𝐶(𝑦)) {

(8)     𝜇_{𝐿(𝑥𝑦)}=min(𝜇_𝐶(𝑥),𝜇_𝐶(𝑦));

(9)     𝜈_{𝐿(𝑥𝑦)}=max(𝜈_𝐶(𝑥),𝜈_𝐶(𝑦)));

(10)    }

(11)   }

(12)  }

(13)  𝐿 = Intuitionistic fuzzy set of edges;

(14)  𝑅 = Intuitionistic fuzzy relation (Adjacency matrix of 𝐶×𝐶);

(15)  𝑊𝑅 = Weighted relation (adjacency matrix of 𝐶×𝐶;

(16)  𝑛𝑜𝑂𝑓𝐸𝑑𝑔𝑒𝑠 = count(𝐿);

(17)  for (int 𝑖=0;𝑖<𝑛𝑜𝑂𝑓𝐸𝑑𝑔𝑒𝑠;𝑖++) {

(18)   𝑆_𝑖=𝜇_𝐿𝑖−𝜈_𝐿𝑖∗𝜋_𝐿𝑖;

(19)   𝑥 = Adjacent from Node of 𝐿_𝑖;

(20)   𝑦 = Adjacent to Node of 𝐿_𝑖;

(21)   𝑊𝑅_𝑥𝑦=𝑆_𝑖;

(22)  }

(23)  print 𝑊𝑅;

(24)  Calculate Optimal path using 𝑊𝑅;

(25) }