Vertex rough graphs

Mathew, Bibin; John, Sunil Jacob; Garg, Harish

doi:10.1007/s40747-020-00133-8

Cited by 19 publications

(11 citation statements)

References 18 publications

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“…Jan et al [9] discussed some root-level modifications in interval-valued FGs. Mathew et al [10] introduced vertex rough graphs. Certain types of FGs such as fuzzy threshold graphs, fuzzy tolerance graphs, and Bipolar fuzzy hypergraphs were given by Samanta and Pal [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

2021

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In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with their certain properties. The number of operations including Cartesian product (CP), composition, tensor product, and normal product in an IFIGs are also investigated. The method to compute the degree of IFIGs obtained by CP, composition, tensor product, and the normal product is discussed. Some important theorems to calculate the degree of the vertices of IFIGs acquired by CP, composition, tensor product, and normal product are elaborated. An application of CP and composition of two IFIGs in the textile industry to find the best combinations of departments expressing the highest percentage of progress and the lowest percentage of nonprogress is provided. A comparative analysis of our study with the existing study is discussed. Our study will be beneficial to comprehend and understand the further characteristics of IFIGs in detail. Another advantage of our study is that it will be helpful to find the maximum percentage of progress and minimum percentage of nonprogress in different departments of universities, garment factories, and hospitals.

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Section: Introductionmentioning

confidence: 99%

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

2021

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“…Harisha et al [3] discussed degree sequence and join operations in graphs. Mathew et al [4] introduced vertex rough graphs and the membership function of vertex rough graphs. For more detailed study on graphs, we may suggest to the reader [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

Nazeer

Rashid

Guirao

2021

Mathematical Problems in Engineering

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Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been recognized as being an effective tool to tackle real-world problems in which vague data and information are essential. Dominating sets (DSs) have multiple applications in diverse areas of life. In wireless networking, DSs are being used to find efficient routes with ad hoc mobile networks. In this paper, we extend the concept of domination of FGs to the FIGs and show some of their important properties. We propose the idea of order, size, and domination in FIGs. Two types of domination, namely, strong fuzzy incidence domination and weak fuzzy incidence domination, for FIGs are discussed. A relationship between strong fuzzy incidence domination and weak fuzzy incidence domination for complete fuzzy incidence graphs (CFIGs) is also introduced. An algorithm to find a fuzzy incidence dominating set (FIDS) and a fuzzy incidence domination number (FIDN) is discussed. Finally, an application of fuzzy incidence domination (FID) is provided to choose the best medical lab among different labs for the conduction of tests for the coronavirus.

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“…The recent conceptual developments in picture fuzzy graphs are the shortest path algorithm, newly defined using the picture fuzzy digraphs (Mani et al 2021), domination in picture fuzzy graphs (MohamedIsmayil and AshaBoslley 2019), using competition in graphs on picture fuzzy environment with applications in the medical field (Das and Ghorai 2020) and a genus of graphs in the picture fuzzy environment (Das et al 2021). In recent, many researchers are working on the development of the picture sets in Garg and Kaur (2021), , Bibin et al (2020), Khalil et al (2019, Riaz et al (2021), Akram et al (2020Akram et al ( , 2021, Akram and Habib (2019). The introduction of this new Picture fuzzy soft graphs is an emerging new concept that can be rather developed into various graph theoretical concepts.…”

Section: Introductionmentioning

confidence: 99%

An approach to decision-making via picture fuzzy soft graphs

2021

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Fuzzy soft graphs are effective mathematical tools that are used to model the vagueness of the real world. A fuzzy soft graph is a fusion of the fuzzy soft set and the graph model and is widely used across different fields. In this current research, the concept of picture fuzzy soft graphs is presented by combining the theory of picture soft sets with graphs. The introduction of this new picture fuzzy soft graphs is an emerging concept that can be rather developed into various graph theoretical concepts. Since soft sets are most usable in real-life applications, the newly combined concepts of the picture and fuzzy soft sets will lead to many possible applications in the fuzzy set theoretical area by adding extra fuzziness in analyzing. The notions of picture soft graphs, strong and complete picture soft fuzzy graphs, a few types of product picture fuzzy soft graphs, and regular, totally regular picture fuzzy soft graphs are discussed and validated using real-world scenarios. In addition, an application of decision-making for medical diagnosis in the current COVID scenario using the picture fuzzy soft graph has been illustrated.

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Vertex rough graphs

Cited by 19 publications

References 18 publications

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

An approach to decision-making via picture fuzzy soft graphs

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