Fuzzy Optimization and Decision Making

, Volume 4, Issue 4, pp 293–312

# Shortest Path Problem on a Network with Imprecise Edge Weight

• SK. MD. Abu. Nayeem
Article

## Abstract

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.

## Key words

fuzzy shortest path interval numbers triangular fuzzy numbers network

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