Shortest path on interval- valued nether trapezoidal neutrosophic fuzzy graphs

2020 ◽

pp. 437-468

Author(s):

Michael G. Voskoglou ◽

Tarasankar Pramanik

Keyword(s):

Graph Theory ◽

Complex Networks ◽

Shortest Path ◽

Building Block ◽

Shortest Path Problem ◽

Fuzzy Graph ◽

The Core ◽

Fuzzy Graphs ◽

Fuzzy Hypergraphs ◽

Interval Valued

Relationship is the core building block of a network, and today's world advances through the complex networks. Graph theory deals with such problems more efficiently. But whenever vagueness or imprecision arises in such relationships, fuzzy graph theory helps. However, fuzzy hypergraphs are more advanced generalization of fuzzy graphs. Whenever there is a need to define multiary relationship rather than binary relationship, one can use fuzzy hypergraphs. In this chapter, interval-valued fuzzy hypergraph is discussed which is a generalization of fuzzy hypergraph. Several approaches to find shortest path between two given nodes in an interval-valued fuzzy graphs is described here. Many researchers have focused on fuzzy shortest path problem in a network due to its importance to many applications such as communications, routing, transportation, etc.

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Analysis of Social Networks, Communication Networks and Shortest Path Problems in the Environment of Interval-Valued q-Rung Ortho Pair Fuzzy Graphs

International Journal of Fuzzy Systems ◽

10.1007/s40815-019-00643-9 ◽

2019 ◽

Vol 21 (6) ◽

pp. 1687-1708 ◽

Cited By ~ 5

Author(s):

Naeem Jan ◽

Tahir Mahmood ◽

Lemnaouar Zedam ◽

Kifayat Ullah ◽

José Carlos Rodríguez Alcantud ◽

...

Keyword(s):

Social Networks ◽

Communication Networks ◽

Shortest Path ◽

Shortest Path Problems ◽

Fuzzy Graphs ◽

Analysis Of Social Networks ◽

Interval Valued

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Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem

Complex & Intelligent Systems ◽

10.1007/s40747-021-00278-0 ◽

2021 ◽

Author(s):

Ali Ebrahimnejad ◽

Mohammad Enayattabr ◽

Homayun Motameni ◽

Harish Garg

Keyword(s):

Shortest Path ◽

Artificial Bee Colony ◽

Fuzzy Numbers ◽

Pso Algorithm ◽

Convergence Time ◽

Bee Colony ◽

Different Types ◽

Implementation Time ◽

Fuzzy Network ◽

Interval Valued

AbstractIn recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm.

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