Optimal Path Problem with Possibilistic Weights - Geoinformatics for Intelligent Transportation - page 47

Fig. 3 Results of case study compared in a graph

Table 2 Comparison of the resulting paths
Comparison Possibility Necessity

a → b → d ≥ a → c → d 0.875 0.349

a → c → d ≥ a → d 0 0

a → c → d ≥ a → b → d 1 0.651

a → c → d ≥ a → d 0.304 0

a → d ≥ a → b → d 1 1

a → d ≥ a → c → d 1 1

overlap. But even such solutions can be ordered, there is higher both possibility and
necessity of a → c → d ≥ a → b → d than a → b → d ≥ a → c → d. Than can be

interpreted as a d being more suitable solution. However the fact that

neither of indices is equal to 1 means that the solutions can not be distinguished
very well, in fact they are rather similar (Fig. 3 ). According to those facts the results
of the algorithm can be shortly summarized by de

→ b →

ning solutions a → b → d and

a d is unacceptable solution (Table 3 ).

Such cases are classic situations when presenting both solution and their ranking
would be useful for decision maker. Mainly because the solutions are quite similar
and there is possibility that choosing any of those might lead to optimal decision.
Unfortunately because of the presented uncertainty the solutions can not be ranked
directly.

→ c → d as acceptable solutions, while a →

Table 3 Results of the
algorithm

Path Status

a → b → d Accepted

a → c → d Accepted

a → d Not accepted