Novel Applications of Intuitionistic Fuzzy Digraphs in Decision Support Systems

Algorithm 3

IF in vulnerability assessment of gas pipeline networks.

(1) void fuzzyPipelineVulnerability() {

(2)  𝐹 = Intuitionistic fuzzy set of pipeline fitting;

(3)  𝑐𝑜𝑢𝑛𝑡𝐹𝑖𝑡𝑡 = count(𝐹);

(4)  𝑃 = Empty intuitionistic fuzzy set;

(5)  for (int 𝑥=0; 𝑥<𝑐𝑜𝑢𝑛𝑡𝐹𝑖𝑡𝑡;𝑥++) {

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

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

(8)     𝜇_{𝑃(𝑥𝑦)}=min(𝜇_𝐹(𝑥),𝜇_𝐹(𝑦));

(9)     𝜈_{𝑃(𝑥𝑦)}=max(𝜈_𝐹(𝑥),𝜈_𝐹(𝑦));

(10)    }

(11)   }

(12)  }

(13)  𝑃 = Intuitionistic fuzzy set of edges;

(14)  𝐺 = Intuitionistic fuzzy relation (adjacency matrix of 𝐹×𝐹);

(15)  𝑊𝐺 = Weighted relation (adjacency matrix of 𝐹×𝐹;

(16)  𝑛𝑜𝑂𝑓𝐸𝑑𝑔𝑒𝑠 = count(𝑃);

(17)  for (int 𝑖=0;𝑖<𝑛𝑜𝑂𝑓𝐸𝑑𝑔𝑒𝑠; 𝑖++) {

(18)   𝑆_𝑖=𝜇_𝑃𝑖−𝜈_𝑃𝑖∗𝜋_𝑃𝑖;

(19)   𝑥 = Adjacent from Node of 𝑃_𝑖;

(20)   𝑦 = Adjacent to Node of 𝑃_𝑖;

(21)   𝑊𝐺_𝑥𝑦=𝑆_𝑖;

(22)  }

(23)  print 𝑊𝐺;

(24)  Calculate Vulnerability using 𝑊𝐺;

(25) }