Certain Concepts of Vague Graphs With Applications to Medical Diagnosis

Shao, Zehui; Kosari, Saeed; Shoaib, Muhammad; Rashmanlou, Hossein

doi:10.3389/fphy.2020.00357

Cited by 12 publications

(8 citation statements)

References 11 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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“…Shao et al [18] described bondage and non-bondage number of intuitionistic fuzzy graph (IFG). Shao et al [19] studied some properties of vague graph. Gulzar et al [7]- [10] worked on fuzzy group.…”

Section: Introductionmentioning

confidence: 99%

Certain Operations on Complex Picture Fuzzy Graphs

et al. 2022

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A complex picture fuzzy set (Com-PFS) is a motivating tool for more precisely interpreting fuzzy notions. Recently, all extensions of complex fuzzy graphs (Com-FGs) have become a growing research topic as they handle ambiguous situations more explicitly than complex intuitionistic fuzzy graphs (Comp-IFG) and picture fuzzy graphs (PFG). The primary goal of this study is to demonstrate the foundation of Com-PFG due to the drawback of the complex neutral membership function in Com-IFG. This paper introduces the concept of Com-PFGs and explains many of the approaches to their development. A Com-PFG has three complex membership functions. We define the order, size, degree of vertex, and total degree of vertex in Com-PFGs. We elaborate on primary operations including: complement, join, union, Cartesian product, direct product, and composition of Com-PFG. Finally, we discuss its use in decision-making problems.

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“…Rashmanlou et al [14] defined PVGs and studied new concepts such as the complete-PVG, complement of a PVG, and the edge regular PVG with several examples. Shao et al [15][16][17][18][19][20] proposed new concepts in vague graph structures and vague incidence graphs such as the maximal product, residue product, irregular vague graphs, valid degree, isolated vertex, vague incidence irredundant set, Laplacian energy, adjacency matrix, and Laplacian matrix in VGs and investigated their properties with several examples. Also, they described several applications of these concepts in the medical sciences.…”

Section: Introductionmentioning

confidence: 99%

Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

Shi

Kosari

2021

Front. Phys.

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The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

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Certain Concepts of Vague Graphs With Applications to Medical Diagnosis

Cited by 12 publications

References 11 publications

Notion of Complex Spherical Fuzzy Graph with Application

Notion of Complex Spherical Fuzzy Graph with Application

Certain Operations on Complex Picture Fuzzy Graphs

Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

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