A Method Based on Picture Fuzzy Graph Coloring for Determining Traffic Signal Phasing on an Intersection

Rosyida, Isnaini; Indrati, Ch. Rini; Kalayathankal, Sunny Joseph

doi:10.1007/978-3-031-39774-5_36

Cited by 1 publication

(3 citation statements)

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“…The terms "strong adjacency" and "weak adjacency" have been defined in an IFG by [4]. We expand upon these ideas in terms of PFGs in the previous work [32].…”

Section: Strong and Weak Adjacencies Between Vertices In Pfgsmentioning

confidence: 99%

“…Strong and weak adjacencies-two different forms of adjacencies-between vertices in fuzzy graphs and IFGs are crucial in decision-making issues. Hence, we generalized strong and weak adjacencies into PFGs and proposed a concept to color PFGs based on strong and weak adjacencies [32]. When we work with PFGs with many vertices and edges, we need a computational tool to identify the strong and weak adjacencies and find the chromatic number of PFGs.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, we initiated a coloring method of PFGs based on (α, β, δ)-cut of PFGs [31]. Since the computation of PFG's coloring through the cuts was complicated in determining the chromatic number, we propose a coloring method of PFGs based on strong and weak adjacencies between vertices in [32].…”

mentioning

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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“…The terms "strong adjacency" and "weak adjacency" have been defined in an IFG by [4]. We expand upon these ideas in terms of PFGs in the previous work [32].…”

Section: Strong and Weak Adjacencies Between Vertices In Pfgsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%