A novel lexicographic optimization method for solving shortest path problems with interval-valued triangular fuzzy arc weights

2020 ◽  
Vol 39 (1) ◽  
pp. 1277-1287 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Somayeh Tabatabaei ◽  
Francisco J. Santos-Arteaga
Keyword(s):  
Shortest Path ◽  
Optimization Method ◽  
Shortest Path Problems ◽  
Lexicographic Optimization ◽  
Interval Valued

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

2019 ◽  
Vol 21 (6) ◽  
pp. 1687-1708 ◽  
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

Application of Floyd's Algorithm in Interval Valued Neutrosophic Setting

2020 ◽  
pp. 77-106
Author(s):  
Nagarajan DeivanayagamPillai ◽  
Lathamaheswari Malayalan ◽  
Said Broumi ◽  
Florentin Smarandache ◽  
Kavikumar Jacob
Keyword(s):  
Comparative Analysis ◽  
Shortest Path ◽  
Shortest Path Problems ◽  
Interval Valued

An algorithm with complete and incremental access is called a Floyd algorithm (FA). It determines shortest path for all the pairs in the network. Though there are many algorithms have been designed for shortest path problems (SPPs), due to the completeness of Floyd's algorithm, it has been improved by considering interval valued neutrosophic numbers as the edge weights to solve neutrosophic SPP (NSPP). Further, the problem is extended to triangular and trapezoidal neutrosophic environments. Also, comparative analysis has been done with the existing method.

scholarly journals Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

2020 ◽  
pp. 53-61
Author(s):  
admin admin ◽  
◽  
◽  
◽  
Said Broumi ◽  
...  
Keyword(s):  
Shortest Path ◽  
Score Function ◽  
Shortest Path Problem ◽  
Destination Node ◽  
A Algorithm ◽  
Shortest Path Problems ◽  
Different Types ◽  
The Cost ◽  
Arc Lengths ◽  
Interval Valued

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length of the shortest path by utilizing ranking function from the source node to the destination node. A* algorithm is executed by applying best first search with the help of this search, it greedily decides which vertex to investigate subsequently. A* is equally complete and optimal if an acceptable heuristic is concerned. The arc lengths in interval valued neutrosophic numbers are defuzzified using the score function. A numerical example is used to illustrate the proposed approach.

scholarly journals An Intelligent and Robust Framework towards Anomaly Detection, Medical Diagnosis, and Shortest Path Problems Based on Interval-Valued T-Spherical Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Huanhuan Jin ◽  
Syed Khurram Jah Rizvi ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Kifayat Ullah ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
Fuzzy Sets ◽  
Shortest Path ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Shortest Path Problem ◽  
Information Modeling ◽  
Research Trend ◽  
Shortest Path Problems ◽  
Interval Valued

The recent emerging advancements in the domain of the fuzzy sets are the framework of the T-spherical fuzzy set (TSFS) and interval valued T-spherical fuzzy set (IVTSFS). Keeping in view the promising significance of the latest research trend in the fuzzy sets and the enabling impact of IVTSFS, we proposed a novel framework for decision assembly using interval valued TSFS based upon encompassing the four impressive dimensions of human judgement including favor, abstinence, disfavor, and refusal degree. Another remarkable contribution is the optimization of information modeling and prevention of information loss by redefining the concept of each membership in interval. Moreover, the proposed research made a worthy contribution work by demonstrating the effective utilization of the interval valued TSFS based framework in anomaly detection, medical diagnosis, and shortest path problem. The proposed work demonstrates the effective remedial measure for the anomaly detection problem based on several parameters using the aggregation operators of IVTSFS. Moreover, the interval valued T-spherical fuzzy relations and their composition are illustrated to investigate the medical diagnosis problem. Furthermore, the notion of interval valued T-spherical fuzzy graph is also presented and fundamental notions of graph theory are also demonstrated with the help of real world instances. In the context of interval valued T-spherical fuzzy graphs (IVTSFGs), a modified Dijkstra Algorithm (DA) is developed and applied to the shortest path problem. The in-depth quantitative assessment and comparative analysis revealed that the proposed notion outpaces contemporary progressive approaches.

A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network: Suggested modifications

2021 ◽  
pp. 1-18
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
S.S. Appadoo
Keyword(s):  
Shortest Path ◽  
Fuzzy Number ◽  
Fuzzy Systems ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Novel Approach ◽  
Shortest Distance ◽  
All Pairs Shortest Path ◽  
Fuzzy Network ◽  
Interval Valued

Enayattabr et al. (Journal of Intelligent and Fuzzy Systems 37 (2019) 6865– 6877) claimed that till now no one has proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems (all-pairs shortest path problems in which distance between every two nodes is represented by an interval-valued trapezoidal fuzzy number). Also, to fill this gap, Enayattabr et al. proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems. In this paper, an interval-valued trapezoidal fuzzy shortest path problem is considered to point out that Enayattabr et al.’s approach fails to find correct shortest distance between two fixed nodes. Hence, it is inappropriate to use Enayattabr et al.’s approach in its present from. Also, the required modifications are suggested to resolve this inappropriateness of Enayattabr et al.’s approach.

scholarly journals Mehar Approach for Finding Shortest Path in Supply Chain Network

2021 ◽  
Vol 13 (7) ◽  
pp. 4016
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
Srimantoorao S. Appadoo ◽  
Yuvraj Gajpal ◽  
Mahesh Kumar Sharma
Keyword(s):  
Shortest Path ◽  
Fuzzy Numbers ◽  
New Approach ◽  
Shortest Path Problems ◽  
Shortest Distance ◽  
Lexicographic Method ◽  
Different Types ◽  
The Cost ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

The aim of each company/industry is to provide a final product to customers at the minimum possible cost, as well as to protect the environment from degradation. Ensuring the shortest travel distance between involved locations plays an important role in achieving the company’s/industry’s objective as (i) the cost of a final product can be minimized by minimizing the total distance travelled (ii) finding the shortest distance between involved locations will require less fuel than the longest distance between involved locations. This will eventually result in lesser degradation of the environment. Hence, in the last few years, various algorithms have been proposed to solve different types of shortest path problems. A recently proposed algorithm for solving interval-valued Pythagorean fuzzy shortest path problems requires excessive computational efforts. Hence, to reduce the computational efforts, in this paper, firstly, an alternative lexicographic method is proposed for comparing interval-valued Pythagorean fuzzy numbers. Then, using the proposed lexicographic comparing method, a new approach (named as Mehar approach) is proposed to solve interval-valued Pythagorean fuzzy shortest path problems. Furthermore, the superiority of the proposed lexicographic comparing method, as well as the proposed Mehar approach, is discussed.

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

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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