Certain Operations on Complex Picture Fuzzy Graphs

Shoaib, Muhammad; Mahmood, Waqas; Xin, Qin; Tchier, Fairouz; Tawfiq, Ferdous M. O.

doi:10.1109/access.2022.3216615

Cited by 11 publications

(8 citation statements)

References 23 publications

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“…Method Application [31] Complex intuitionistic fuzzy graphs Cellular network provider companies [33] On t-intuitionistic fuzzy graphs Poverty reduction [34] Neutrosophic graph Multicriteria decision-making model [35] Complex picture fuzzy graphs The influence of the countries relationship [17] Complex fermatean neutrosophic graph Education system [6] pentapartitioned neutrosophic graphs Determining safest paths and towns in response to COVID-19…”

Section: Yearmentioning

confidence: 99%

Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design

Alqahtani,

Kaviyarasu,

Al-Masarwah

et al. 2024

Mathematics

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Complex neutrosophic graphs are created by combining complex neutrosophic sets with graph theory ideas. This provides a flexible framework for tackling complex problem-solving circumstances. Various processes, such as union, join, and composition, are thoroughly investigated to improve the administration of complicated neutrosophic graphs. This research also looks into the area of complicated neutrosophic graph homeomorphisms, investigating the transformations and mappings that occur inside these structures. This investigation advances our knowledge of the intrinsic features and linkages found in complicated neutrosophic graphs. Finally, our methodology’s practical usefulness is demonstrated by its use in the design of hospital infrastructure. We illustrate the effectiveness of complicated neutrosophic graphs in addressing difficult design concerns and optimizing infrastructure solutions for practical deployment in this real-world scenario.

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Section: Yearmentioning

confidence: 99%

Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design

Alqahtani,

Kaviyarasu,

Al-Masarwah

et al. 2024

Mathematics

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“…Akram and Naz (2019) proposed complex Pythagorean fuzzy graphs (CPFG). Shoaib et al (2022) introduced the concept of picture fuzzy graphs and their properties. Also, Shoaib et al (2022a) initiated the notion of complex spherical fuzzy graph.…”

Section: Table 2 Complex Fuzzy Sets Under Various Fuzzy Environmentmentioning

confidence: 99%

Complex fermatean neutrosophic graph and application to decision making

Broumi

Mohanaselvi

Witczak

et al. 2023

Decis. Mak. Appl. Manag. Eng.

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A new growing area of neutrosophic set (NS) theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS take values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesian product of CFNG. Moreover, the concept of regular graph under complex fermatean neutrosophic environment is discussed. Finally, an application of multi criteria decision making problem in educational system to evaluate lecturer’s research productivity using CFNG is discussed.

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“…Researchers recently expanded PFGs in numerous types, such as q-rung PFGs [10], balanced PFGs [11], the application of PFGs for selecting best routes in an airlines network [12], picture fuzzy soft graphs [13], complex PFGs [14], regular PFGs [15], and so on. Numerous studies had also been conducted on the use of PFGs in practical issues such as the application of balanced PFGs [11], decision making under picture fuzzy soft graphs [13], the implementation of regular PFGs in communication networks [15], road map design using picture fuzzy multigraphs [16], the application of PFGs in social networks [17], the shortest path algorithm in picture fuzzy digraphs [18], the site selection problem using laplacian energy of PFGs [19], the application of picture fuzzy tolerance graphs [20], the genus of PFGs [21], and multiple attribute decision-making via PFGs [22].…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for Coloring of Picture Fuzzy Graphs Based on Strong and Weak Adjacencies, and Its Application

Rosyida,

Indrati

2023

Algorithms

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The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs), and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no”. Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to these properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is useful when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been carried to evaluate the method.

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Certain Operations on Complex Picture Fuzzy Graphs

Cited by 11 publications

References 23 publications

Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design

Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design

Complex fermatean neutrosophic graph and application to decision making

An Algorithm for Coloring of Picture Fuzzy Graphs Based on Strong and Weak Adjacencies, and Its Application

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