The shortest path problem with discrete fuzzy arc lengths

Abstract

In the past, the fuzzy shortest path problem in a network has attracted attention from many researchers for its importance to various applications. In this paper, we propose a new algorithm to deal with the fuzzy shortest path problem. It is composed of fuzzy shortest path length procedure and similarity measure. The former is presented to determine the fuzzy shortest path length from source node to the destination node in the network, and the latter is used to measure the similarity degree between fuzzy length sets. This algorithm not only can yield shortest length but also can offer the actual shortest path to decision makers. An illustrative example is also included to demonstrate our proposed algorithm. (~)

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

“…(iii) Put = 1, 2, 3, = 4; (iv) Put = 1, 2, 3, 4, = 5; (6,7,8,9) ⊕ (4,7,6,8), (8,10,4,12) ⊕ (3, 6, 7, 8)}; 5 = min{ (10,14,14,17), (11,16,11,20)}; 5 = (10, 14, 14, 17) and 5 = min{ 1 ⊕ 15 , 2 ⊕ 25 , 3 ⊕ 35 , 4 ⊕ 45 }; 5 = min{ (7,8,9,10)⊕ (6,8,7,9), (11,13,8,17)⊕ (5,8,9,12) (13,16,16,19), (16,21,17,29)}; 5 = (13, 16, 16, 19) ∴ 2 = 2 → 5.…”

“…(v) Put = 1, 2, 3, 4, 5, = 6; (8,10,4,12) ⊕ (2,3,5,6), (10,14,14,17) ⊕ (5, 10, 11, 12)}; 6 = min{ (10,13,9,18), (15,24,25,29)}; 6 = (10, 13,9,18) Steps 4, 5, and 6. Table 1 shows the results of membership and nonmembership functions, direct/indirect link with source node, and direct/indirect link with destination node from Steps 2 and 3.…”

“…Szmidt and Kacprzyk [7] found distance between intuitionistic fuzzy sets using Hamming distance, the normalized Hamming distance, the Euclidean distance, and the normalized Euclidean distance. Kung and Chuang [8] pointed out that there are several methods to solve this kind of problem in the available literature. Przemysław Grzegorzewski [9] discussed two families of metrics in space of intuitionistic fuzzy numbers.…”

Routing Urban Transport Network With Weighing Arcs Fuzzy Numbers and Application in Emergency Medical Aid

“…This is a method for modeling the type of of instability associated with ambiguity. In this paper is used proposed in [5] modification of Dijkstra's algorithm, as permanent marks of each vertex (the shortest distance from vertex source) also fuzzy numbers. Despite the intensive development of the theory of fuzzy sets.…”

“…Despite the intensive development of the theory of fuzzy sets. There is no single formula formulation of the problem [13], [5], [11], [6], due to various assumptions, aims and forms of fuzzy numbers. In this paper an approach is used for finding the shortest path from s to all other nodes of the graph, similar to that in [13].…”