Genus of graphs under picture fuzzy environment with applications

Das, Sankar; Ghorai, Ganesh; Pal, Madhumangal

doi:10.1007/s12652-020-02887-y

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…Also, the concept of m-step PF competition graphs was proposed by Das et al [31] with their applications in education system, ecosystem and job competition. After that, they worked on the embedding of PFGs in various surfaces based on genus values and applying it to design electronic circuits in [32]. They also studied on PF tolerance graphs with application in sports competition in [33].…”

Section: Related Workmentioning

confidence: 99%

Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

Das

Ghorai

Xin

2022

Entropy

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In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources.

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Section: Related Workmentioning

confidence: 99%

Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

Das

Ghorai

Xin

2022

Entropy

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“…Recently, Das and Ghorai [8] have defined picture FPGs and applied it to construct road map designs. They have also applied the idea of PF sets to CGs, PF genus graphs [9][10][11]. Xiao et al studied on regular PFG and its application in communication networks in [49].…”

Section: Research Backgroundmentioning

confidence: 99%

Picture fuzzy tolerance graphs with application

Das

Ghorai

Pal

2021

Complex Intell. Syst.

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In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy $$\phi $$ ϕ -tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking $$\phi $$ ϕ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy $$\phi $$ ϕ -tolerance chaingraphs which is the picture fuzzy $$\phi $$ ϕ -tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs.

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“…Moreover, Chen et al [15] discussed linguistic Znumber. Liu [16] assessed the logistics efficiency of agriculture produced under intuitionistic FS, and Das et al [17] devised 𝜙-tolerance competition graphs under picture fuzzy information along with its applications. Zhang [18] devised the notion of the bipolar fuzzy set (BFS) by expanding the notion of FS.…”

Section: Introductionmentioning

confidence: 99%

Selection of Software Development Methodology by Employing a Multi-Criteria Decision-Making Approach Based on Logarithmic Bipolar Complex Fuzzy Aggregation Operators

Song,

Mahmood,

Rehman

2024

IEEE Access

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Numerous factors, including project complexity, team size, customer collaboration, and development pace, must be taken into consideration while choosing a software development methodology. This problem is a multi-criteria decision-making dilemma since the many criteria frequently fight with one another and fluctuate in priority. To systematically select the best methodology, the multi-criteria decisionmaking technique assists in quantifying and assessing these factors. This ensures that decisions are made in a fair and informed manner within the context of the challenging software development environment. Thus, in this article, we develop a multi-criteria decision-making approach in the setting of bipolar complex fuzzy information for the prioritization and selection of optimal software development methodology. For this, we first, invent logarithmic operational laws and associated results for the bipolar complex fuzzy set. Then, we invent four aggregation operators by utilizing these logarithmic operational laws under the structure of bipolar complex fuzzy information, that is, logarithmic bipolar complex fuzzy weighted averaging, logarithmic bipolar complex fuzzy ordered weighted averaging, logarithmic bipolar complex fuzzy weighted geometric, and logarithmic bipolar complex fuzzy ordered weighted geometric. After that, we solve a multi-criteria decision-making dilemma related to the prioritization and selection of software development methodology by considering the artificial data in the setting of bipolar complex fuzzy information and achieve that "Agile" is the optimal software development methodology among the considered four different software development methodologies, i.e., Waterfall, DevOps, Spiral, and Agile. In the last, we investigate the comparison study of the deduced theory to a few current theories to reveal the importance and supremacy of the constructed theory.INDEX TERMS Software development methodology; logarithmic operations; bipolar complex fuzzy set; MCDM.

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Genus of graphs under picture fuzzy environment with applications

Cited by 11 publications

References 26 publications

Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

Picture fuzzy tolerance graphs with application

Selection of Software Development Methodology by Employing a Multi-Criteria Decision-Making Approach Based on Logarithmic Bipolar Complex Fuzzy Aggregation Operators

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