Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network

Table 1

Tabular representation of link between source and destination nodes.

𝑗	𝑚𝑝𝑖	𝑛𝑝𝑖	D/ID link with source node	D/ID link with destination node	Direct/indirect link with source and destination nodes	Distance
2	𝑚𝑝1= 1→2	𝑛𝑝1= 1→2	Yes; DIR; Link	No	Discard	Discard
3	𝑚𝑝1= 1→3	𝑛𝑝1= 1→3	Yes; DIR; Link	Yes; ID; Link	Yes	⟨3,2,1,5⟩⟨5,4,3,7⟩
4	𝑚𝑝3= 3→4	𝑛𝑝3= 3→4	Yes; ID; Link	Yes; ID; Link	Yes	⟨8,10,4,12⟩⟨11,13,8,17⟩
5	𝑚𝑝2= 2→5	𝑛𝑝2= 2→5	Yes; ID; Link	No	Discard	Discard
6	𝑚𝑝4= 4→6	𝑛𝑝4= 4→6	Yes; ID; Link	Yes; DIR; Link	Yes	⟨10,13,9,18⟩⟨14,18,14,25⟩

Hence the required path is 1→3→4→6.
Required shortest distance is (⟨10,13,9,18⟩ ⟨14,18,14,25⟩).