Abstract
We present a novel approach for computing a shortest path in a mixed fuzzy network, network having various fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using -cuts. Then, we present a dynamic programming method for finding a shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Four examples are worked out to illustrate the applicability of the proposed approach as compared to two other methods in the literature as well as demonstrate the novel feature offered by our algorithm to find a fuzzy shortest path in mixed fuzzy networks with various settings for the fuzzy arc lengths.
Highlights
Determination of shortest distance and shortest path between two vertices is one of the most fundamental problems in graph theory
We present a novel approach for computing a shortest path in a mixed fuzzy network, network having various fuzzy arc lengths
Four examples are worked out to illustrate the applicability of the proposed approach as compared to two other methods in the literature as well as demonstrate the novel feature offered by our algorithm to find a fuzzy shortest path in mixed fuzzy networks with various settings for the fuzzy arc lengths
Summary
Determination of shortest distance and shortest path between two vertices is one of the most fundamental problems in graph theory. Okada and Soper [18] proposed an algorithm to find the shortest path in a network with fuzzy edge weights. In proposing an algorithm for solving the problem, we are first faced with the comparison or ordering of fuzzy numbers, a task not considered to be routine For this reason, fuzzy shortest path problems have rarely been studied despite their potential application to many problems [18,26]. We propose a new approach and an algorithm to find a shortest path in a mixed network having various fuzzy arc lengths.
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