Zeeshan Saleem Mufti, A. H. Tedjani, R. Anjum, Turki Alsuraiheed
In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by Sie(Λ,t), already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph Sie(Λ,t). In the second step, we extract some degree-based indices of a generalized Sierpinski graph Sie(Λ,t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph Sie(Λ,t) by using the Randić index.
1997 年，克拉夫扎尔和米卢蒂诺维奇得到了西尔平斯基图 S(n,k)。图 S(1,k) 代表完整图 Kk，S(n,3) 被称为河内塔图。通过对西尔平斯基图的概念进行广义化，文献中已经存在一种名为广义西尔平斯基图的图，用 Sie(Λ,t) 表示。对于每个图，人们都在研究许多多项式，如色度多项式、匹配多项式、独立性多项式和 M 多项式。对于每一个多项式，都有一个基本的几何对象，它可以提取出隐藏在共同框架的多项式中的一切。现在，我们介绍一下完成任务的步骤。第一步，我们生成广义西尔平斯基图 Sie(Λ,t) 的 M 多项式。第二步，利用第一步生成的 M 多项式提取广义 Sierpinski 图 Sie(Λ,t) 的一些基于度的指数。第三步，利用兰迪克指数生成广义西尔平斯基图 Sie(Λ,t) 的熵。
{"title":"Entropy and Multi-Fractal Analysis in Complex Fractal Systems Using Graph Theory","authors":"Zeeshan Saleem Mufti, A. H. Tedjani, R. Anjum, Turki Alsuraiheed","doi":"10.3390/axioms12121126","DOIUrl":"https://doi.org/10.3390/axioms12121126","url":null,"abstract":"In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by Sie(Λ,t), already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph Sie(Λ,t). In the second step, we extract some degree-based indices of a generalized Sierpinski graph Sie(Λ,t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph Sie(Λ,t) by using the Randić index.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"12 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139000379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results.
{"title":"Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays","authors":"Tingting Xie, Mengmeng Li","doi":"10.3390/axioms12121129","DOIUrl":"https://doi.org/10.3390/axioms12121129","url":null,"abstract":"This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"210 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138997075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Evgeniya Egorova, Aleksey Mokryakov, Vladimir Tsurkov
In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice.
{"title":"The Algebra of Signatures for Extreme Two-Uniform Hypergraphs","authors":"Evgeniya Egorova, Aleksey Mokryakov, Vladimir Tsurkov","doi":"10.3390/axioms12121123","DOIUrl":"https://doi.org/10.3390/axioms12121123","url":null,"abstract":"In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"19 11","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138999862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under q-ROFPRs is established to minimize their deviation from the MCq-ROFPRs and minimize the weight uncertainty. Further, a group goal programming model of ideal MCq-ROFPRs is constructed to obtain the expert weights using the compatibility measure between the ideal MCq-ROFPRs and the individual q-ROFPRs. Finally, a GDM method with unknown expert weights is solved by combining the group goal programming model and the simple q-rung orthopair fuzzy weighted geometric (Sq-ROFWG) operator. The effectiveness and practicality of the proposed GDM method are verified by solving the crucial factors in crowdsourcing task recommendation. The results show that the developed GDM method effectively considers the important measures of experts and identifies the crucial factors that are more reliable than two other methods.
{"title":"Multiplicative Consistent q-Rung Orthopair Fuzzy Preference Relations with Application to Critical Factor Analysis in Crowdsourcing Task Recommendation","authors":"Xicheng Yin, Zhenyu Zhang","doi":"10.3390/axioms12121122","DOIUrl":"https://doi.org/10.3390/axioms12121122","url":null,"abstract":"This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under q-ROFPRs is established to minimize their deviation from the MCq-ROFPRs and minimize the weight uncertainty. Further, a group goal programming model of ideal MCq-ROFPRs is constructed to obtain the expert weights using the compatibility measure between the ideal MCq-ROFPRs and the individual q-ROFPRs. Finally, a GDM method with unknown expert weights is solved by combining the group goal programming model and the simple q-rung orthopair fuzzy weighted geometric (Sq-ROFWG) operator. The effectiveness and practicality of the proposed GDM method are verified by solving the crucial factors in crowdsourcing task recommendation. The results show that the developed GDM method effectively considers the important measures of experts and identifies the crucial factors that are more reliable than two other methods.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"144 3","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. E. Borges, Sammy Cristopher Paredes Puelles, Marija Demicoli, E. Padilla
The presence of particles with a small but finite size, suspended in viscous fluids with low volumetric concentrations, is observed in many applications. The present study focuses on the tridimensional and incompressible lid-driven flow of Newtonian fluids through the application of the immersed boundary method and the Euler–Lagrange approach. These methods are used to numerically predict three-dimensional particle motion by considering nearly neutrally buoyant conditions as well as all relevant elementary processes (drag and lift forces, particle rotation, particle–wall interactions, and coupling between phases). Considering the current stage of the numerical platform, two coupling approaches between phases are considered: one-way and two-way coupling. A single particle is inserted in the cavity after steady-state conditions are achieved. Its three-dimensional motion is obtained from numerical simulations and compared with research data, considering the same conditions, evidently showing that the particle trajectory follows the experimental data until the first collision with a solid surface. After this first contact, there is a deviation between the results, with the two-way coupling results better representing the experimental data than the one-way coupling results. The dimensionless forces’ peaks acting on the particles are associated with the relative velocity of the particle near the wall–particle collision position. In terms of magnitude, in general, the drag force has shown greater influence on the particle’s motion, followed by the rotation-induced and shear-induced lift forces. Finally, a special application is presented, in which 4225 particles are released into the domain and their dynamic is evaluated throughout dimensionless time, showing similar behavior for both couplings between phases, with variations in local concentrations observed in certain regions. The mean square displacement used to quantify the dispersion evolution of the particles showed that the particulate flow reaches an approximately homogeneous distribution from the moment of dimensionless time tU/S = 130.
{"title":"Application of the Euler–Lagrange Approach and Immersed Boundary Method to Investigate the Behavior of Rigid Particles in a Confined Flow","authors":"J. E. Borges, Sammy Cristopher Paredes Puelles, Marija Demicoli, E. Padilla","doi":"10.3390/axioms12121121","DOIUrl":"https://doi.org/10.3390/axioms12121121","url":null,"abstract":"The presence of particles with a small but finite size, suspended in viscous fluids with low volumetric concentrations, is observed in many applications. The present study focuses on the tridimensional and incompressible lid-driven flow of Newtonian fluids through the application of the immersed boundary method and the Euler–Lagrange approach. These methods are used to numerically predict three-dimensional particle motion by considering nearly neutrally buoyant conditions as well as all relevant elementary processes (drag and lift forces, particle rotation, particle–wall interactions, and coupling between phases). Considering the current stage of the numerical platform, two coupling approaches between phases are considered: one-way and two-way coupling. A single particle is inserted in the cavity after steady-state conditions are achieved. Its three-dimensional motion is obtained from numerical simulations and compared with research data, considering the same conditions, evidently showing that the particle trajectory follows the experimental data until the first collision with a solid surface. After this first contact, there is a deviation between the results, with the two-way coupling results better representing the experimental data than the one-way coupling results. The dimensionless forces’ peaks acting on the particles are associated with the relative velocity of the particle near the wall–particle collision position. In terms of magnitude, in general, the drag force has shown greater influence on the particle’s motion, followed by the rotation-induced and shear-induced lift forces. Finally, a special application is presented, in which 4225 particles are released into the domain and their dynamic is evaluated throughout dimensionless time, showing similar behavior for both couplings between phases, with variations in local concentrations observed in certain regions. The mean square displacement used to quantify the dispersion evolution of the particles showed that the particulate flow reaches an approximately homogeneous distribution from the moment of dimensionless time tU/S = 130.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"22 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hao Guan, Waheed Ahmad Khan, Shazia Saleem, Waqar Arif, J. Shafi, Aysha Khan
Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.
{"title":"Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications","authors":"Hao Guan, Waheed Ahmad Khan, Shazia Saleem, Waqar Arif, J. Shafi, Aysha Khan","doi":"10.3390/axioms12121120","DOIUrl":"https://doi.org/10.3390/axioms12121120","url":null,"abstract":"Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"9 2","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139005533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed in this paper. First, take 30 provincial capitals in China for example, the cities are divided into seven regions by LFIG_DTW_HC algorithm, and descriptive statistics of PM2.5 concentration in each region are carried out. Secondly, it is found that the influencing factors of PM2.5 concentration are different in different regions. The input variables of the PM2.5 concentration forecasting model in each region are determined by combining the variable correlation with the generalized additive model, and the main influencing factors of PM2.5 concentration in each region are analyzed. Finally, the empirical analysis is conducted based on the input variables selected above, the generalized additive model is established to forecast PM2.5 concentration in each region, the comparison of the evaluation indexes of the training set and the test set proves that the novel PM2.5 concentration forecasting method achieves better prediction effect. Then, the generalized additive model is established by selecting cities from each region, and compared with the auto-regressive integrated moving average (ARIMA) model. The results show that the novel PM2.5 concentration forecasting method can achieve better prediction effect on the premise of ensuring high accuracy.
{"title":"A Novel PM2.5 Concentration Forecasting Method Based on LFIG_DTW_HC Algorithm and Generalized Additive Model","authors":"Hong Yang, Han Zhang","doi":"10.3390/axioms12121118","DOIUrl":"https://doi.org/10.3390/axioms12121118","url":null,"abstract":"As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed in this paper. First, take 30 provincial capitals in China for example, the cities are divided into seven regions by LFIG_DTW_HC algorithm, and descriptive statistics of PM2.5 concentration in each region are carried out. Secondly, it is found that the influencing factors of PM2.5 concentration are different in different regions. The input variables of the PM2.5 concentration forecasting model in each region are determined by combining the variable correlation with the generalized additive model, and the main influencing factors of PM2.5 concentration in each region are analyzed. Finally, the empirical analysis is conducted based on the input variables selected above, the generalized additive model is established to forecast PM2.5 concentration in each region, the comparison of the evaluation indexes of the training set and the test set proves that the novel PM2.5 concentration forecasting method achieves better prediction effect. Then, the generalized additive model is established by selecting cities from each region, and compared with the auto-regressive integrated moving average (ARIMA) model. The results show that the novel PM2.5 concentration forecasting method can achieve better prediction effect on the premise of ensuring high accuracy.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"203 S613","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139006278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jocivania Pinheiro, R. Santiago, Benjamín Bedregal, F. Bergamaschi
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨⊆g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation.
{"title":"Developing Constrained Interval Operators for Fuzzy Logic with Interval Values","authors":"Jocivania Pinheiro, R. Santiago, Benjamín Bedregal, F. Bergamaschi","doi":"10.3390/axioms12121115","DOIUrl":"https://doi.org/10.3390/axioms12121115","url":null,"abstract":"A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨⊆g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"85 2","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rosa Maza-Quiroga, Karl Thurnhofer-Hemsi, Domingo López-Rodríguez, Ezequiel López-Rubio
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.
本文研究了 T1 MRI 图像中傅立叶、离散余弦和离散正弦变换系数的分布特征。本文揭示了它们遵循本福德定律的情况，即首位数字呈对数分布。本文研究了里森噪声对首位数字分布的影响，这种噪声会导致首位数字偏离理想分布。利用巴塔查里亚距离、库尔贝克-莱布勒发散、总变异距离、海林格距离和詹森-香农发散等指标，提出了一种用于噪声水平估计的新方法。监督学习技术利用这些指标作为回归因子。对来自 1.5 T 和 3 T 不同采集设备的多个数据集（包括数百名患者）的磁共振成像扫描进行评估，验证了无噪声 T1 磁共振成像频域系数与本福德定律的一致性。通过严格的实验，我们的方法证明了与现有噪声估计技术的竞争力，甚至在大量实验中超过了它们。这项研究从经验上支持了本福德定律在变换中的应用，为去噪算法中的噪声估计提供了一种可靠的方法，并推进了图像质量评估。
{"title":"Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit","authors":"Rosa Maza-Quiroga, Karl Thurnhofer-Hemsi, Domingo López-Rodríguez, Ezequiel López-Rubio","doi":"10.3390/axioms12121117","DOIUrl":"https://doi.org/10.3390/axioms12121117","url":null,"abstract":"This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"28 11","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junchi Ma, Bart Wiegmans, Xifu Wang, Kai Yang, Lijun Jiang
Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone.
{"title":"A Hybrid DEMATEL and Bayesian Best–Worst Method Approach for Inland Port Development Evaluation","authors":"Junchi Ma, Bart Wiegmans, Xifu Wang, Kai Yang, Lijun Jiang","doi":"10.3390/axioms12121116","DOIUrl":"https://doi.org/10.3390/axioms12121116","url":null,"abstract":"Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"23 12","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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