Balanced picture fuzzy graph with application

Amanathulla, Sk; Bera, Biswajit; Pal, Madhumangal

doi:10.1007/s10462-021-10020-4

Cited by 29 publications

(8 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another interesting concept of fuzzy cross-entropy for picture hesitant fuzzy sets and introduction of polarity in addressing of attributes using Bipolar soft sets were developed by Mahmood et al for addressing attributes of different nature in decision making problems [ 49 , 50 ]. A generalized concept of picture fuzzy soft set alongside its application was put forward by Khan et al [ 50 , 51 ]. Intuitionistic multiplicative set operational laws and their associated aggregation operators for processing was developed by Garg alongside its application in decision support systems [ 40 ].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Intuitionistic multiplicative set operational laws and their associated aggregation operators for processing was developed by Garg alongside its application in decision support systems [40]. Balanced Picture Fuzzy Graphs were explored in 2021 by Amanathulla et al [51,52]. Numerous related hybrid fuzzy graph theoretical concepts relating to different aspects of their applications are presented in the following studies [53][54][55][56][57][58].…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

2023

View full text Add to dashboard Cite

Risk evaluation has always been of great interest for individuals wanting to invest in various businesses, especially in the marketing and product sale centres. A finely detailed evaluation of the risk factor can lead to better returns in terms of investment in a particular business. Considering this idea, this paper aims to evaluate the risk factor of investing in different nature of products in a supermarket for a better proportioning of investment based on the product’s sales. This is achieved using novel Picture fuzzy Hypersoft Graphs. Picture Fuzzy Hypersoft set (PFHSs) is employed in this technique, a hybrid structure of Picture Fuzzy set and Hypersoft Set. These structures work best for evaluating uncertainty using membership, non-membership, neutral, and multi-argument functions, making them ideal for Risk Evaluation studies. Also, the concept of the PFHS graph with the help of the PFHS set is introduced with some operations like the cartesian product, composition, union, direct product, and lexicographic product. This method presented in the paper provides new insight into product sale risk analysis with a pictorial representation of its associated factors.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

2023

View full text Add to dashboard Cite

show abstract

“…Subsequently, picture fuzzy multigraphs (PFMGs) has been introduced in literature [25]. Recently, the further extensions of PFGs like constant picture fuzzy graphs [26] and balanced picture fuzzy graphs [27] are also introduced. First and third authors (with Babir Ali) have introduced the notion of bipolar picture fuzzy graphs and bipolar picture fuzzy acquaintanceship graph in [28].…”

Section: Introductionmentioning

confidence: 99%

Cayley Picture Fuzzy Graphs and Interconnected Networks

Khan¹,

Faiz²,

Taouti³

2023

Intelligent Automation &Amp; Soft Computing

View full text Add to dashboard Cite

Theory of the Cayley graphs is directly linked with the group theory. However, if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance. In this perspective, numbers of generalizations of fuzzy graphs have been explored in the literature. Among the others, picture fuzzy graph (PFG) has its own importance. A picture fuzzy graph (PFG) is a pair G ¼ ðC; DÞ defined on a H Ã = ðA; BÞ, where C = ð C ; C ; # C Þ is a picture fuzzy set on A and D = ð D ; D ; # D Þ is a picture fuzzy set over the set B A Â A such that for any edge mn 2 B with D ðm; nÞ minð C ðmÞ; C ðnÞÞ, D ðm; nÞ minð C ðmÞ; C ðnÞÞ and # D ðm; nÞ ! maxð# C ðmÞ; # C ðnÞÞ: In this manuscript, we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs. Firstly, we discuss few important characteristics of the Cayley picture fuzzy graphs. We show that Cayley picture fuzzy graphs are vertex transitive and hence regular. Then, we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts. We extensively discuss the term connectivity of the Cayley picture fuzzy graphs. Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed. We also investigate the linkage between these two. Throughout, we provide the extensions of some characteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs. Finally, we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.

show abstract

“…After the introduction of fuzzy sets in 1965, the researchers modified the fuzzy set in various ways to manage the unexpected situations, which are unable to handle by the fuzzy sets. Some of the extension of fuzzy sets are fuzzy soft sets (Cagman et al 2011 ), intuitionistic fuzzy sets (Das et al 2018 ), inter value fuzzy sets (Gorzałczany, 1987 ), multi-fuzzy sets (Das et al 2013 ), fuzzy multi sets (Das et al 2013 ), picture fuzzy sets (Si et al 2019 ; Amanathulla et al 2021 ), and adaptive neuro-fuzzy (Cabalar et al 2012 ). The fuzzy set was generalized by Atanassov ( 1986 ) and converted into intuitionistic fuzzy sets (IFS).…”

Section: Introductionmentioning

confidence: 99%

Preferred hospitalization of COVID-19 patients using intuitionistic fuzzy set-based matching approach

Das

Kar

2022

Granul. Comput.

View full text Add to dashboard Cite

Preferable hospitalization of COVID-19 patients has become an urgent and challenging task to save lives amidst the unexpected rising of the 3rd wave, where fuzzy set and matching techniques are considered due to their inherent capability to deal with uncertain suitable pair selection. The matching technique has been widely used to solve decision-making problems due to its capability to determine the suitable pair between the objects of two disjoint sets, whereas fuzzy set is well known to manage uncertain situations. This paper extends the matching technique using fuzzy set and proposes a novel fuzzy matching approach to solve uncertain decision-making problems. We also extend the fuzzy matching approach in the framework of an intuitionistic fuzzy set. A relation between the matching technique and fuzzy set theory is established by developing the preference sequence of the elements. The fuzzy entropy is used to measure the closeness among the elements between two distinct sets. Applicability of the proposed approach is measured by providing an illustrative case study concerned with the preferred hospitalization of the COVID-19 patients. Finally, a comparative study is given to analyze the effectiveness of the proposed approach, where the intuitionistic fuzzy set-based matching approach shows better performance compared to fuzzy and conventional matching based approach. For experimentation purpose, this study uses 9424 patients and 234 hospitals with a total available capacity of 18,024 beds.

show abstract

Balanced picture fuzzy graph with application

Cited by 29 publications

References 19 publications

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

Theoretical framework for a decision support system for micro-enterprise supermarket investment risk assessment using novel picture fuzzy hypersoft graph

Cayley Picture Fuzzy Graphs and Interconnected Networks

Preferred hospitalization of COVID-19 patients using intuitionistic fuzzy set-based matching approach

Contact Info

Product

Resources

About