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

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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An approach towards decision making and shortest path problems using the concepts of interval‐valued Pythagorean fuzzy information

International Journal of Intelligent Systems ◽

10.1002/int.22154 ◽

2019 ◽

Vol 34 (10) ◽

pp. 2403-2428 ◽

Cited By ~ 4

Author(s):

Naeem Jan ◽

Muhammad Aslam ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Jun Wang

Keyword(s):

Decision Making ◽

Shortest Path ◽

Fuzzy Information ◽

Shortest Path Problems ◽

Interval Valued

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Analysis of Social Networks by Using Pythagorean Cubic Fuzzy Einstein Weighted Geometric Aggregation Operators

Journal of Mathematics ◽

10.1155/2021/5516869 ◽

2021 ◽

Vol 2021 ◽

pp. 1-18

Author(s):

Tehreem ◽

Amjad Hussain ◽

Jung Rye Lee ◽

Muhammad Sajjad Ali Khan ◽

Dong Yun Shin

Keyword(s):

Decision Making ◽

Social Networks ◽

Fuzzy Set ◽

Group Decision ◽

Aggregation Operators ◽

Pythagorean Fuzzy Set ◽

Operational Laws ◽

Multiple Attribute ◽

Analysis Of Social Networks ◽

Interval Valued

Pythagorean cubic set (PCFS) is the combination of the Pythagorean fuzzy set (PFS) and interval-valued Pythagorean fuzzy set (IVPFS). PCFS handle more uncertainties than PFS and IVPFS and thus are more extensive in their applications. The objective of this paper is under the PCFS to establish some novel operational laws and their corresponding Einstein weighted geometric aggregation operators. We describe some novel Pythagorean cubic fuzzy Einstein weighted geometric (PCFEWG) operators to handle multiple attribute group decision-making problems. The desirable relationship and the characteristics of the proposed operator are discussed in detail. Finally, a descriptive case is given to describe the practicality and the feasibility of the methodology established.

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Application of Floyd's Algorithm in Interval Valued Neutrosophic Setting

Advances in Data Mining and Database Management - Neutrosophic Graph Theory and Algorithms ◽

10.4018/978-1-7998-1313-2.ch003 ◽

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.

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Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

10.54216/ijns.0110104 ◽

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.

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

Mathematical Problems in Engineering ◽

10.1155/2020/9656909 ◽

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.

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