Hesitancy Fuzzy Graph Coloring

Prasanna, A.; Rifayathali, M.A.; Mohideen, S. Ismail

doi:10.22457/ijfma.v14n2a2

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…Each element in IFG has membership and non-membership degrees. Numerous studies had been conducted on intuitionistic fuzzy graphs (IFGs), including the coloring of IFGs ( [3,4]), the application of wiener index for IFGs in water pipeline network [5], interval-valued intuitionistic (S, T)-fuzzy graphs [6], and interval-valued intuitionistic fuzzy competition graphs [7].…”

Section: Introductionmentioning

confidence: 99%

“…Some researchers proposed various generalizations of graph coloring such as the coloring of fuzzy graphs based on strong and weak adjacencies [23], fuzzy graph coloring based on δ-fuzzy independent vertex sets [24], the fuzzy fractional coloring of fuzzy graphs [25], the fuzzy coloring of fuzzy graphs [26], the fuzzy colouring of m-polar fuzzy graphs [27], the chromatic number and perfectness of fuzzy graphs [28], and the edge coloring of fuzzy graphs [29]. Several researchers have also proposed the coloring methods through the α-cut approach and two forms of adjacencies (strong and weak) in fuzzy graphs and IFGs, as seen in [3,4,23,30]. The fact that a PFG is an extension of an IFG inspired us to generalize the vertex coloring from IFGs into PFGs in 2021 [31].…”

Section: Introductionmentioning

confidence: 99%

“…An essential idea that can be used in making decisions on various networks of realworld problems is the coloring method of fuzzy graphs and IFGs ( [3,4,25,33]). 2.…”

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confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Ramakrishna [10] introduced the concepts of vague graphs and analysed some of their properties. Recently, new papers have published about fuzzy graphs in [7,9,11].…”

Section: Introductionmentioning

confidence: 99%

Some Operations on Complex Vague Graphs with Application

P.K¹,

Manshath²,

Rashmanlou³

et al. 2021

IJFMA

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Vague graphs has found its importance in most recent years. It has played the vital role in many real life applications. The mathematical approach of blending different aspects of vague graphs gives a more generalized approach. As a result of it, we introduce the concepts of Complex vague graphs (CVG). In this chapter, we introduce certain notions including union, join, complement and composition of complex vague graphs. This helps in manipulating the real life applications in decision making problems. We also investigate on the ideas of homomorphisms of complex vague graphs. Finally we provide an application of CVG in launching a water reservoir in different locations.

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

Rosyida,

Indrati

2023

Preprint

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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 the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull 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 done to evaluate the method.

show abstract

Hesitancy Fuzzy Graph Coloring

Cited by 4 publications

References 7 publications

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

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

Some Operations on Complex Vague Graphs with Application

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

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