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Dynamic Programming and Multi Objective Linear Programming approaches |
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PP: 253-263 |
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Author(s) |
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P. K. De,
Amita Bhincher,
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Abstract |
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| This paper describes two different methods to deal with the fuzzy shortest path problems. The first one
is to study fuzzy shortest path in a network by Bellman dynamic programming approach and the second
one is to study same problems by multi objective linear programming (MOLP) technique. It is
considered that the edge weights of the network as uncertain. To analyze this idea of uncertainty four
examples have been taken with two different network where edge weights have been presented by
triangular fuzzy numbers and trapezoidal fuzzy numbers respectively. Both the problems have been
solved by the above two methods. In the first method sign distance ranking procedure has been applied
to get real value of the fuzzy edge weights where as in the second method MOLP, only 0-1 variables
have been considered to get integer solution without using the Branch and Bound technique. It is
observed that the length of the shortest paths in fuzzy sense as obtained by both the methods are
same/almost same and the shortest path corresponds to the actual path in the network. It is obvious that
fuzzy shortest path is an extension of the crisp problem. |
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