Closure axioms for a class of fuzzy matroids and co-towers of matroids

Li, Shenggang; Xin, Xiu; Li, Yaolong

doi:10.1016/j.fss.2007.01.003

Cited by 18 publications

(5 citation statements)

References 9 publications

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“…Later on, bases and circuits of the fuzzy matroids were also defined by them [33][34][35][36]. As time progressed, different FSs were used to define different fuzzy matroids, and their properties were also discussed by different researchers [37][38][39][40][41][42]. Recently, we proposed the idea of Pythagorean fuzzy matroids (PFMs) and described their application to decision making [43].…”

Section: Introductionmentioning

confidence: 99%

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

Asif

Kattan

Pamučar

et al. 2021

Discrete Dynamics in Nature and Society

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The theory of q -rung orthopair fuzzy sets ( q -ROFSs) is emerging for the provision of more comprehensive and useful information in comparison to their counterparts like intuitionistic and Pythagorean fuzzy sets, especially when responding to the models of vague data with membership and non-membership grades of elements. In this study, a significant generalized model q -ROFS is used to introduce the concept of q -rung orthopair fuzzy vector spaces ( q -ROFVSs) and illustrated by an example. We further elaborate the q -rung orthopair fuzzy linearly independent vectors. The study also involves the results regarding q -rung orthopair fuzzy basis and dimensions of q -ROFVSs. The main focus of this study is to define the concepts of q -rung orthopair fuzzy matroids ( q -ROFMs) and apply them to explore the characteristics of their basis, dimensions, and rank function. Ultimately, to show the significance of our proposed work, we combine these ideas and offer an application. We provide an algorithm to solve the numerical problems related to human flow between particular regions to ensure the increased government response action against frequently used path (heavy path) for the countries involved via directed q -rung orthopair fuzzy graph ( q -ROFG). At last, a comparative study of the proposed work with the existing theory of Pythagorean fuzzy matroids is also presented.

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Section: Introductionmentioning

confidence: 99%

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

Asif

Kattan

Pamučar

et al. 2021

Discrete Dynamics in Nature and Society

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“…They also discussed basis, circuits, and other concepts related to the fuzzy matroids in their subsequent work [29,30]. With the passage of time, different kind of fuzzy matroids were presented, based on varied definitions of fuzzy sets and their axioms [31][32][33][34][35][36][37]. Sarwar and Akram [38], highlighted the idea of m-polar fuzzy matroids and also discussed their pivotal properties.…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Fuzzy Matroids with Application

2020

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The Pythagorean fuzzy models deal with graphical and algebraic structures in case of vague information related to membership and non-membership grades. Here, we use Pythagorean fuzzy sets to generalize the concept of vector spaces and discuss their basis and dimensions. We also highlight the concept of Pythagorean fuzzy matroids and examine some of their fundamental characteristics like circuits, basis, dimensions, and rank functions. Additionally, we explore the concept of Pythagorean fuzzy matroids in linear algebra, graph theory, and combinatorics. Finally, we demonstrate the use of Pythagorean fuzzy matroids for minimizing the time taken by a salesman in delivering given products.

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“…The notion of fuzzy independent set was also explored in [3,4]. Some constructions, fuzzy spanning sets, fuzzy rank and fuzzy closure axioms were also studied in [5][6][7][8]. Several other fuzzifications of matroids were also discussed in [9,10].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Closure Matroids

Al-Hawary¹

2016

MATEMATIKA

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In 1988, Geotschel and Voxman [1] introduced and explored the concept of fuzzy matroids via the notion of fuzzy independent sets. In 2013, Al-Hawary [2] introduced fuzzy matroids via the notion of fuzzy flats. In this paper, we introduce the notion of fuzzy closure matroids, a new class of fuzzy matroids. We study properties of this class and classify it. In addition, the class of fuzzy modular matroids is defined and characterized.

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Closure axioms for a class of fuzzy matroids and co-towers of matroids

Cited by 18 publications

References 9 publications

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

Pythagorean Fuzzy Matroids with Application

Fuzzy Closure Matroids

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Closure axioms for a class of fuzzy matroids and co-towers of matroids

Cited by 18 publications

References 9 publications

q -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

q -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

Pythagorean Fuzzy Matroids with Application

Fuzzy Closure Matroids

Contact Info

Product

Resources

About

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking

$q$ -Rung Orthopair Fuzzy Matroids with Application to Human Trafficking