A Study of Complex Dombi Fuzzy Graph With Application in Decision Making Problems

Butt, Ehsan Mehboob Ahmed; Mahmood, Waqas; Tawfiq, Ferdous M. O.; Xin, Qin; Shoaib, Muhammad

doi:10.1109/access.2022.3208279

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Motivated by these works we initiated the concept, complex fermatean neutrosophic fuzzy sets (CFNS) and complex fermatean neutrosophic fuzzy graph (CFNG). Butt et al (2022) established a complex dombi fuzzy graph and their properties. In the single valued neutrosophic environment, regular graphs are explored by Samina et al (2017).…”

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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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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“…Shoaib et al (4) , elaborated on the basic operations in complex spherical fuzzy graphs (CSFG) along with applications, which gives us the ability to deal with problems in three directions. E.M. Ahamed Buttet et al (5) , implemented the dombi operators in complex fuzzy sets to extend the graph to a complex dombi fuzzy graph (CDFG). They discussed the https://www.indjst.org/ concepts of homomorphism, weak isomorphism, and co-weak isomorphism between two CDFGs and established the application of CDFG in decision-making problems.…”

Section: Introductionmentioning

confidence: 99%

Isomorphism on Complex Fuzzy Graph

Ismayil,

Azhagendran

2024

IJST

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Objective: To investigate isomorphism between two complex fuzzy graphs and prove it is an equivalence relation. The major objective of this research paper is to elucidate weak and strong isomorphism, and the study also endeavours to look at the complement of complex fuzzy graphs. Methods: Isomorphism is examined by comparing the membership values of nodes and arcs (both amplitude and phase). The same technique also proves further validation of the equivalence relation, which is also proven by the same technique. This criterion helps us to identify and formalise the isomorphic relationship between complex fuzzy graphs. Findings: This study demonstrates that isomorphism in complex fuzzy graphs allows for consideration of graph structures' differences and similarities. It provides for a better understanding of significant connections between complex fuzzy graphs. Novelty: By offering an elaborate perception of the idea of isomorphism in complex fuzzy graphs, this work advances the discipline. It seeks a better understanding of the complexities of equivalency determination for complicated structures, as well as the application of isomorphism theory to complex fuzzy graphs. Keywords: Complex fuzzy graph, Homomorphism, Isomorphism, Partial order relation, Self complementary

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“…mining [1] and is the basis for various applications,including community mining [2], picture feature selection [3], decision making [4], graph computing systems [5], and action recognition [6] and so on.…”

Section: Introductionmentioning

confidence: 99%

Efficient Densest Subgraphs Discovery in Large Dynamic Graphs by Greedy Approximation

Han¹

2023

IEEE Access

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Densest subgraph detection has become an important primitive in graph mining tasks when analyzing communities and detecting events in a wide range of application domains. Currently, it is a challenging and practically crucial research issue to develop efficient densest subgraphs mining approaches that can handle both very large and continuously evolving graphs. Although large-scale or dynamic methods have been proposed to find the densest subgraphs, there is still a lack of a promising method to deal with largescale and dynamically evolving graphs. In this paper, the problem is formulated and proved to be NP-Hard, an incremental greedy approximation approach is proposed, and its running time is O(m+n). In order to find the densest subgraph effectively by heuristically merging the local densest subgraphs, firstly, the edge flow of a dynamic graph is divided into several subgraphs in a given period of T . Secondly, a local candidate set is generated by local denser subgraph discovery. Third, the global densest subgraph candidates are collected by heuristically merging. Last, the densest subgraphs are induced from the global densest subgraph candidates with constraints by static densest subgraph discovery algorithm. This incremental approach enables us to scale up the existing densest subgraph discovery algorithms, which focus mainly on small and static graphs and thus can handle very large dynamic graphs. Experiments on real-world networks with billions of nodes for comprehensive evaluations present excellent improvement in efficiency and accuracy: it reduces about 25% running time on average and presents a more accurate estimation of the structure of a graph with more compact subgraphs than the static method.It also performs well when dealing with graphs of varying densities. INDEX TERMSDensest subgraphs, incremental greedy approximation, heuristically merging, local candidate, global densest subgraph candidates.

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A Study of Complex Dombi Fuzzy Graph With Application in Decision Making Problems

Cited by 4 publications

References 15 publications

Complex fermatean neutrosophic graph and application to decision making

Complex fermatean neutrosophic graph and application to decision making

Isomorphism on Complex Fuzzy Graph

Efficient Densest Subgraphs Discovery in Large Dynamic Graphs by Greedy Approximation

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