An extension principle based solution approach for shortest path problem with fuzzy arc lengths

2016 ◽  
Vol 17 (2) ◽  
pp. 395-411 ◽  
Author(s):  
Sadegh Niroomand ◽  
Ali Mahmoodirad ◽  
Ahmad Heydari ◽  
Fatemeh Kardani ◽  
Abdollah Hadi-Vencheh
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Extension Principle ◽  
Solution Approach ◽  
Arc Lengths

Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

2020 ◽  
Vol 39 (5) ◽  
pp. 7653-7656
Author(s):  
Ranjan Kumar ◽  
SA Edalatpanah ◽  
Hitesh Mohapatra
Keyword(s):  
Shortest Path ◽  
Fuzzy Systems ◽  
Optimal Path ◽  
Vital Role ◽  
Path Selection ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Fuzzy Environment ◽  
Selection Approach ◽  
Arc Lengths

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

Genetic Algorithm for Solving Fuzzy Shortest Path Problem in a Network with mixed fuzzy arc lengths

2011 ◽  
Author(s):  
Iraj Mahdavi ◽  
Ali Tajdin ◽  
Reza Hassanzadeh ◽  
Nezam Mahdavi-Amiri ◽  
Hosna Shafieian ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Shortest Path Problem ◽  
Arc Lengths

scholarly journals A genetic algorithm for the fuzzy shortest path problem in a fuzzy network

2020 ◽  
Author(s):  
Lihua Lin ◽  
Chuzheng Wu ◽  
Li Ma
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Ad Hoc ◽  
Real Life ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Routing Problem ◽  
Path Lengths ◽  
Fuzzy Network ◽  
Arc Lengths

Abstract The shortest path problem (SPP) is an optimization problem of determining a path between specified source vertex s and destination vertex t in a fuzzy network. Fuzzy logic can handle the uncertainties, associated with the information of any real life problem, where conventional mathematical models may fail to reveal proper result. In classical SPP, real numbers are used to represent the arc length of the network. However, the uncertainties related with the linguistic description of arc length in SPP are not properly represented by real number. We need to address two main matters in SPP with fuzzy arc lengths. The first matter is how to calculate the path length using fuzzy addition operation and the second matter is how to compare the two different path lengths denoted by fuzzy parameter. We use the graded mean integration technique of triangular fuzzy numbers to solve this two problems. A common heuristic algorithm to solve the SPP is the genetic algorithm. In this manuscript, we have introduced an algorithmic method based on genetic algorithm for determining the shortest path between a source vertex s and destination vertex t in a fuzzy graph with fuzzy arc lengths in SPP. A new crossover and mutation is introduced to solve this SPP. We also describe the QoS routing problem in a wireless ad hoc network.

A Study of Neutrosophic Shortest Path Problem

2020 ◽  
pp. 148-179 ◽  
Author(s):  
Ranjan Kumar ◽  
Arindam Dey ◽  
Said Broumi ◽  
Florentin Smarandache
Keyword(s):  
Shortest Path ◽  
Real Life ◽  
Shortest Path Problem ◽  
Combinatorial Optimization Problem ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Decision Making Problem ◽  
Theory Uncertainty ◽  
Arc Lengths

Shortest path problem (SPP) is an important and well-known combinatorial optimization problem in graph theory. Uncertainty exists almost in every real-life application of SPP. The neutrosophic set is one of the popular tools to represent and handle uncertainty in information due to imprecise, incomplete, inconsistent, and indeterminate circumstances. This chapter introduces a mathematical model of SPP in neutrosophic environment. This problem is called as neutrosophic shortest path problem (NSPP). The utility of neutrosophic set as arc lengths and its real-life applications are described in this chapter. Further, the chapter also includes the different operators to handle multi-criteria decision-making problem. This chapter describes three different approaches for solving the neutrosophic shortest path problem. Finally, the numerical examples are illustrated to understand the above discussed algorithms.

scholarly journals The shortest-path problem for graphs with random arc-lengths

1985 ◽  
Vol 10 (1) ◽  
pp. 57-77 ◽  
Author(s):  
A.M. Frieze ◽  
G.R. Grimmett
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Arc Lengths

scholarly journals New models for shortest path problem with fuzzy arc lengths

2007 ◽  
Vol 31 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Xiaoyu Ji ◽  
Kakuzo Iwamura ◽  
Zhen Shao
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
New Models ◽  
Arc Lengths

scholarly journals The shortest path problem with discrete fuzzy arc lengths

2005 ◽  
Vol 49 (2-3) ◽  
pp. 263-270 ◽  
Author(s):  
Jung-Yuan Kung ◽  
Tzung-Nan Chuang
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Arc Lengths
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