New Concepts of Interval-Valued Fuzzy Graphs with Application

Rashmanlou, Hossein; Jouybari, Mostafa Nouri

doi:10.22457/jmi.v8a8

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…To analyze world problems, boundedness between the nodes exists due to a few relations. Many researchers [10][11][12][13][14][15][16][17][18][19][20][21][22] participated in improving fuzzy concepts in di erent elds.…”

Section: Introductionmentioning

confidence: 99%

Notion of Complex Spherical Fuzzy Graph with Application

Shoaib

Mahmood

Albalawi

et al. 2022

Journal of Function Spaces

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A complex spherical fuzzy set (CSFS) is a generalization of a spherical fuzzy set (CFS). CSFS handles vagueness more explicitly, and its range is expanded from the real subset to the complex with unit disc. The major goal of this research is to present the foundation of a complex spherical fuzzy graph (CSFG) due to the limitation of the complex neutral membership function in a complex Pythagorean fuzzy graph (CPFG). Complex spherical fuzzy models have more flexibility as compared to complex fuzzy models, complex intuitionistic fuzzy models, and complex Pythagorean fuzzy models due to their coverage in three directions: complex membership functions, neutral membership functions, and complex non-membership functions. Firstly, we present the motivation for CSFG. Furthermore, we define the order, degree of a vertex, size, and total degree of a vertex of CSFG. We elaborate on primary operations, including complement, join, and the union of CSFG. This research study introduces some operations, namely, strong product, composition, Cartesian product, and semi-strong product, on CSFG. Moreover, we present the application of CSFG, which ensures the ability to deal with problems in three directions.

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Section: Introductionmentioning

confidence: 99%

Notion of Complex Spherical Fuzzy Graph with Application

Shoaib

Mahmood

Albalawi

et al. 2022

Journal of Function Spaces

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“…In 2020, Talebi et al [ 30 ] also introduced new concepts of interval-valued intuitionistic fuzzy graphs (IVIFG). Rashmanlou and Jun [ 31 ] discussed complete IVFG. Talebi et al [ 32 ] discussed interval-valued intuitionistic fuzzy competition graph of an interval-valued intuitionistic fuzzy digraph.…”

Section: Introductionmentioning

confidence: 99%

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Shi,

Kosari,

Hameed

et al. 2024

PLoS ONE

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Fuzzy graphs are very important when we are trying to understand and study complex systems with uncertain and not exact information. Among different types of fuzzy graphs, cubic fuzzy graphs are special due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. To figure out how things are connected in cubic fuzzy graphs, we need to know about cubic α−strong, cubic β−strong and cubic δ−weak edges. These concepts better help in making decisions, solving problems and analyzing things like transportation, social networks and communication systems. The applicability of connectivity and comprehension of cubic fuzzy graphs have urged us to discuss connectivity in the domain of cubic fuzzy graphs. In this paper, the terms partial cubic α−strong and partial cubic δ−weak edges are introduced for cubic fuzzy graphs. The bounds and exact expression of connectivity index for several cubic fuzzy graphs are estimated. The average connectivity index for cubic fuzzy graphs is also defined and some results pertaining to these concepts are proved in this paper. The results demonstrate that removing some vertices or edges may cause a change in the value of connectivity index or average connectivity index, but the change will not necessarily be related to both values. This paper also defines the concepts of partial cubic connectivity enhancing node and partial cubic connectivity reducing node and some related results are proved. Furthermore, the concepts of cubic α−strong, cubic β− strong, cubic δ−weak edge, partial cubic α−strong and partial cubic δ−weak edges are utilized to identify areas most affected by a tsunami resulting from an earthquake. Finally, the research findings are compared with the existing methods to demonstrate their suitability and creativity.

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“…They also discussed some of the properties of influence pairs and influence cut-nodes. Rashmanlou and Jun [20] defined three new operations on interval-valued FGs; namely, direct product, semi-strong product, and strong product. Likewise, they gave sufficient conditions for each one of them to be complete and show that if any of these products is complete, then at least one factor is a complete interval-valued FG.…”

Section: Introductionmentioning

confidence: 99%

Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

et al. 2021

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Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are M[γs(Cl(σ,ϕ,η))]=⌈l3⌉. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization.

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New Concepts of Interval-Valued Fuzzy Graphs with Application

Cited by 6 publications

References 24 publications

Notion of Complex Spherical Fuzzy Graph with Application

Notion of Complex Spherical Fuzzy Graph with Application

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

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