By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.
{"title":"Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics","authors":"Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu, Xueping Chen","doi":"10.3390/math12182860","DOIUrl":"https://doi.org/10.3390/math12182860","url":null,"abstract":"By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"39 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249149","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}
Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.
{"title":"Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets","authors":"Batyr Orazbayev, Kulman Orazbayeva, Yerbol Ospanov, Salamat Suleimenova, Lyailya Kurmangaziyeva, Valentina Makhatova, Yerlan Izbassarov, Aigerim Otebaeva","doi":"10.3390/math12182856","DOIUrl":"https://doi.org/10.3390/math12182856","url":null,"abstract":"Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"186 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249145","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}
Emerging deep learning-based fault diagnosis methods have advanced in the current industrial scenarios of various working conditions. However, the prerequisite of obtaining target data in advance limits the application of these models to practical engineering scenarios. To address the challenge of fault diagnosis under unseen working conditions, a domain generation framework for unseen conditions fault diagnosis is proposed, which consists of an Adaptive Feature Fusion Domain Generation Network (AFFN) and a Mix-up Augmentation Method (MAM) for both the data and domain spaces. AFFN is utilized to fuse domain-invariant and domain-specific representations to improve the model’s generalization performance. MAM enhances the model’s exploration ability for unseen domain boundaries. The diagnostic framework with AFFN and MAM can effectively learn more discriminative features from multiple source domains to perform different generalization tasks for unseen working loads and machines. The feasibility of the proposed unseen conditions diagnostic framework is validated on the SDUST and PU datasets and achieved peak diagnostic accuracies of 94.15% and 93.27%, respectively.
基于深度学习的新兴故障诊断方法在当前各种工况的工业场景中取得了进展。然而，提前获取目标数据的前提条件限制了这些模型在实际工程场景中的应用。为了应对在未知工况下进行故障诊断的挑战，本文提出了一种用于未知工况故障诊断的域生成框架，该框架由数据空间和域空间的自适应特征融合域生成网络（AFFN）和混合增强方法（MAM）组成。AFFN 用于融合域不变和域特定的表征，以提高模型的泛化性能。MAM 增强了模型对未知领域边界的探索能力。带有 AFFN 和 MAM 的诊断框架可以有效地从多个源域中学习更多的判别特征，从而针对未知的工作负载和机器执行不同的泛化任务。我们在 SDUST 和 PU 数据集上验证了所提出的未知工况诊断框架的可行性，其峰值诊断准确率分别达到 94.15% 和 93.27%。
{"title":"A Domain Generation Diagnosis Framework for Unseen Conditions Based on Adaptive Feature Fusion and Augmentation","authors":"Tong Zhang, Haowen Chen, Xianqun Mao, Xin Zhu, Lefei Xu","doi":"10.3390/math12182865","DOIUrl":"https://doi.org/10.3390/math12182865","url":null,"abstract":"Emerging deep learning-based fault diagnosis methods have advanced in the current industrial scenarios of various working conditions. However, the prerequisite of obtaining target data in advance limits the application of these models to practical engineering scenarios. To address the challenge of fault diagnosis under unseen working conditions, a domain generation framework for unseen conditions fault diagnosis is proposed, which consists of an Adaptive Feature Fusion Domain Generation Network (AFFN) and a Mix-up Augmentation Method (MAM) for both the data and domain spaces. AFFN is utilized to fuse domain-invariant and domain-specific representations to improve the model’s generalization performance. MAM enhances the model’s exploration ability for unseen domain boundaries. The diagnostic framework with AFFN and MAM can effectively learn more discriminative features from multiple source domains to perform different generalization tasks for unseen working loads and machines. The feasibility of the proposed unseen conditions diagnostic framework is validated on the SDUST and PU datasets and achieved peak diagnostic accuracies of 94.15% and 93.27%, respectively.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"5 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249184","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}
Suppose that A1 is a class of analytic functions f:D={z∈C:|z|<1}→C with normalization f(0)=1. Consider two functions Pl(z)=1+z and ΦNe(z)=1+z−z3/3, which map the boundary of D to a cusp of lemniscate and to a twi-cusped kidney-shaped nephroid curve in the right half plane, respectively. In this article, we aim to construct functions f∈A0 for which (i) f(D)⊂Pl(D)∩ΦNe(D) (ii) f(D)⊂Pl(D), but f(D)⊄ΦNe(D) (iii) f(D)⊂ΦNe(D), but f(D)⊄Pl(D). We validate the results graphically and analytically. To prove the results analytically, we use the concept of subordination. In this process, we establish the connection lemniscate (and nephroid) domain and functions, including gα(z):=1+αz2, |α|≤1, the polynomial gα,β(z):=1+αz+βz3, α,β∈R, as well as Lerch’s transcendent function, Incomplete gamma function, Bessel and Modified Bessel functions, and confluent and generalized hypergeometric functions.
{"title":"On the Containment of the Unit Disc Image by Analytical Functions in the Lemniscate and Nephroid Domains","authors":"Saiful R. Mondal","doi":"10.3390/math12182869","DOIUrl":"https://doi.org/10.3390/math12182869","url":null,"abstract":"Suppose that A1 is a class of analytic functions f:D={z∈C:|z|<1}→C with normalization f(0)=1. Consider two functions Pl(z)=1+z and ΦNe(z)=1+z−z3/3, which map the boundary of D to a cusp of lemniscate and to a twi-cusped kidney-shaped nephroid curve in the right half plane, respectively. In this article, we aim to construct functions f∈A0 for which (i) f(D)⊂Pl(D)∩ΦNe(D) (ii) f(D)⊂Pl(D), but f(D)⊄ΦNe(D) (iii) f(D)⊂ΦNe(D), but f(D)⊄Pl(D). We validate the results graphically and analytically. To prove the results analytically, we use the concept of subordination. In this process, we establish the connection lemniscate (and nephroid) domain and functions, including gα(z):=1+αz2, |α|≤1, the polynomial gα,β(z):=1+αz+βz3, α,β∈R, as well as Lerch’s transcendent function, Incomplete gamma function, Bessel and Modified Bessel functions, and confluent and generalized hypergeometric functions.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"9 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249187","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}
Semicircles and circular sectors are both ubiquitous in the natural realm. However, mathematically speaking they have represented an enigma since antiquity. In recent years, the author has worked in integral equations with sections of spheres as related to radiative heat transfer and their associated form factors, to the point of defining new postulates. The main theorems thus far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted. As is known, to find the exact expression of the configuration factor by integration is complex. In the above mentioned problem of the circular sectors, the author reached the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approach for the third and fourth integrals which still remain unsolved, once we have been able to find the preliminary integrals. This possibility had not been identified by former research and the output provides us with an ample variety of unexpected scenarios. As a consequence, we are able to analyze with more precision the spatial transference of radiant heat for figures composed of circular sectors. We already know that spherical shapes cannot be discretized with any accuracy. Therefore, we would be able to reduce a considerable amount of hindrance in the progress of thermal radiation science. Important sequels will be derived for radiation in the entrance to tunnels, aircraft design and lighting as well.
{"title":"New Geometric Theorems Derived from Integral Equations Applied to Radiative Transfer in Spherical Sectors and Circular Segments","authors":"Joseph Cabeza-Lainez","doi":"10.3390/math12182875","DOIUrl":"https://doi.org/10.3390/math12182875","url":null,"abstract":"Semicircles and circular sectors are both ubiquitous in the natural realm. However, mathematically speaking they have represented an enigma since antiquity. In recent years, the author has worked in integral equations with sections of spheres as related to radiative heat transfer and their associated form factors, to the point of defining new postulates. The main theorems thus far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted. As is known, to find the exact expression of the configuration factor by integration is complex. In the above mentioned problem of the circular sectors, the author reached the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approach for the third and fourth integrals which still remain unsolved, once we have been able to find the preliminary integrals. This possibility had not been identified by former research and the output provides us with an ample variety of unexpected scenarios. As a consequence, we are able to analyze with more precision the spatial transference of radiant heat for figures composed of circular sectors. We already know that spherical shapes cannot be discretized with any accuracy. Therefore, we would be able to reduce a considerable amount of hindrance in the progress of thermal radiation science. Important sequels will be derived for radiation in the entrance to tunnels, aircraft design and lighting as well.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"185 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249193","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}
Mario Versaci, Filippo Laganà, Francesco Carlo Morabito, Annunziata Palumbo, Giovanni Angiulli
In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.
{"title":"Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional","authors":"Mario Versaci, Filippo Laganà, Francesco Carlo Morabito, Annunziata Palumbo, Giovanni Angiulli","doi":"10.3390/math12182854","DOIUrl":"https://doi.org/10.3390/math12182854","url":null,"abstract":"In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"8 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223523","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 study addresses the diagnostic challenges of Systemic Lupus Erythematosus (SLE), an autoimmune disease with a complex etiology and varied symptoms. The ANA (antinuclear antibody) test, currently the primary diagnostic tool for SLE, exhibits high sensitivity but low specificity, often leading to inaccurate diagnoses. To enhance diagnostic precision, we propose integrating machine learning algorithms with existing clinical classification guidelines to improve SLE diagnosis accuracy, potentially reducing diagnostic errors and healthcare costs. We analyzed real-world data from a cohort of 24,990 patients over a 10-year period at the hospitals, excluding those previously diagnosed with SLE. Patients were categorized into three groups: negative ANA, positive ANA with non-SLE, and positive ANA with SLE. Feature selection was conducted to identify key factors influencing SLE diagnosis, and machine learning algorithms were employed to develop the CDSS. Performance analysis of three machine learning algorithms—decision tree, random forest, and gradient boosting—based on feature sets of 10, 20, and all available features revealed accuracy rates of 70%, 88%, and 87%, respectively, for the 20-feature set. The proposed system, utilizing real-world medical data, demonstrated modest performance in SLE diagnosis, highlighting the potential of machine learning-based CDSS in real clinical settings.
系统性红斑狼疮（SLE）是一种病因复杂、症状多样的自身免疫性疾病。ANA（抗核抗体）检测是目前系统性红斑狼疮的主要诊断工具，但其灵敏度高而特异性低，常常导致诊断不准确。为了提高诊断的准确性，我们建议将机器学习算法与现有的临床分类指南相结合，以提高系统性红斑狼疮诊断的准确性，从而减少诊断错误和医疗成本。我们分析了各家医院 10 年间 24990 名患者的真实世界数据，其中不包括之前被诊断为系统性红斑狼疮的患者。患者被分为三组：ANA 阴性、非系统性红斑狼疮 ANA 阳性和系统性红斑狼疮 ANA 阳性。通过特征选择来确定影响系统性红斑狼疮诊断的关键因素，并采用机器学习算法来开发 CDSS。对基于 10、20 和所有可用特征集的三种机器学习算法（决策树、随机森林和梯度提升）进行的性能分析表明，20 个特征集的准确率分别为 70%、88% 和 87%。所提出的系统利用真实世界的医疗数据，在系统性红斑狼疮诊断中表现出了适度的性能，凸显了基于机器学习的 CDSS 在实际临床环境中的潜力。
{"title":"Improving the Diagnosis of Systemic Lupus Erythematosus with Machine Learning Algorithms Based on Real-World Data","authors":"Meeyoung Park","doi":"10.3390/math12182849","DOIUrl":"https://doi.org/10.3390/math12182849","url":null,"abstract":"This study addresses the diagnostic challenges of Systemic Lupus Erythematosus (SLE), an autoimmune disease with a complex etiology and varied symptoms. The ANA (antinuclear antibody) test, currently the primary diagnostic tool for SLE, exhibits high sensitivity but low specificity, often leading to inaccurate diagnoses. To enhance diagnostic precision, we propose integrating machine learning algorithms with existing clinical classification guidelines to improve SLE diagnosis accuracy, potentially reducing diagnostic errors and healthcare costs. We analyzed real-world data from a cohort of 24,990 patients over a 10-year period at the hospitals, excluding those previously diagnosed with SLE. Patients were categorized into three groups: negative ANA, positive ANA with non-SLE, and positive ANA with SLE. Feature selection was conducted to identify key factors influencing SLE diagnosis, and machine learning algorithms were employed to develop the CDSS. Performance analysis of three machine learning algorithms—decision tree, random forest, and gradient boosting—based on feature sets of 10, 20, and all available features revealed accuracy rates of 70%, 88%, and 87%, respectively, for the 20-feature set. The proposed system, utilizing real-world medical data, demonstrated modest performance in SLE diagnosis, highlighting the potential of machine learning-based CDSS in real clinical settings.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"151 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177052","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}
Aleksandar Senić, Momčilo Dobrodolac, Zoran Stojadinović
Road infrastructure plays a crucial role in the development of countries, significantly influencing economic growth, social progress, and environmental sustainability. Major infrastructure projects are frequently challenged by substantial risks and uncertainties, leading to delays, budget overruns, and compromised quality. These issues can undermine the economic viability and efficiency of projects, making effective risk management essential for minimizing negative impacts and ensuring project success. For these reasons, a study was conducted using a Sugeno fuzzy logic system applied to completed projects. The resulting model is based on 10 project characteristics and provides highly accurate predictions for Extension of Time (EoT) and Increasing Contract Price (ICP). By utilizing this model, project management can be significantly improved through more accurate forecasting of potential delays and cost overruns. The high precision of the Sugeno fuzzy logic system enables better risk assessment and proactive decision-making, allowing project managers to implement targeted strategies to mitigate risks and optimize project outcomes.
{"title":"Predicting Extension of Time and Increasing Contract Price in Road Infrastructure Projects Using a Sugeno Fuzzy Logic Model","authors":"Aleksandar Senić, Momčilo Dobrodolac, Zoran Stojadinović","doi":"10.3390/math12182852","DOIUrl":"https://doi.org/10.3390/math12182852","url":null,"abstract":"Road infrastructure plays a crucial role in the development of countries, significantly influencing economic growth, social progress, and environmental sustainability. Major infrastructure projects are frequently challenged by substantial risks and uncertainties, leading to delays, budget overruns, and compromised quality. These issues can undermine the economic viability and efficiency of projects, making effective risk management essential for minimizing negative impacts and ensuring project success. For these reasons, a study was conducted using a Sugeno fuzzy logic system applied to completed projects. The resulting model is based on 10 project characteristics and provides highly accurate predictions for Extension of Time (EoT) and Increasing Contract Price (ICP). By utilizing this model, project management can be significantly improved through more accurate forecasting of potential delays and cost overruns. The high precision of the Sugeno fuzzy logic system enables better risk assessment and proactive decision-making, allowing project managers to implement targeted strategies to mitigate risks and optimize project outcomes.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"78 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177056","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}
Malihe Niksirat, Mohsen Saffarian, Javad Tayyebi, Adrian Marius Deaconu, Delia Elena Spridon
This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method.
{"title":"Fuzzy Multi-Objective, Multi-Period Integrated Routing–Scheduling Problem to Distribute Relief to Disaster Areas: A Hybrid Ant Colony Optimization Approach","authors":"Malihe Niksirat, Mohsen Saffarian, Javad Tayyebi, Adrian Marius Deaconu, Delia Elena Spridon","doi":"10.3390/math12182844","DOIUrl":"https://doi.org/10.3390/math12182844","url":null,"abstract":"This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"88 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177047","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}
We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality.
{"title":"Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem","authors":"Alessio Troiani","doi":"10.3390/math12182850","DOIUrl":"https://doi.org/10.3390/math12182850","url":null,"abstract":"We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"46 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177053","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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