The purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous impulses. Specifically, the existence is derived through the Nehari manifold method, and the proof of multiplicity is based on Bonanno and Bisci’s critical point theorem, which does not require proof that the functional satisfies the Palais–Smale condition. Finally, to illustrate the obtained results, an example is provided.
{"title":"Solvability of a Class of Fractional Advection–Dispersion Coupled Systems","authors":"Yan Qiao, Tao Lu","doi":"10.3390/math12182873","DOIUrl":"https://doi.org/10.3390/math12182873","url":null,"abstract":"The purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous impulses. Specifically, the existence is derived through the Nehari manifold method, and the proof of multiplicity is based on Bonanno and Bisci’s critical point theorem, which does not require proof that the functional satisfies the Palais–Smale condition. Finally, to illustrate the obtained results, an example is provided.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"14 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249191","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}
In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.
{"title":"Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function","authors":"Feng Qi","doi":"10.3390/math12182859","DOIUrl":"https://doi.org/10.3390/math12182859","url":null,"abstract":"In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"51 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249148","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}
Haotian Yang, Pujie Jing, Zihan Wu, Lu Liu, Pengyan Liu
The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.
{"title":"SEAIS: Secure and Efficient Agricultural Image Storage Combining Blockchain and Satellite Networks","authors":"Haotian Yang, Pujie Jing, Zihan Wu, Lu Liu, Pengyan Liu","doi":"10.3390/math12182861","DOIUrl":"https://doi.org/10.3390/math12182861","url":null,"abstract":"The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"20 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249150","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}
A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step changes observed in banded-TRL approaches when multiple Line standards are used. By introducing a bespoke weighting function that assigns phase-dependent weights to each Line standard, smoother transitions and improved S-parameter measurements can be achieved. Experimental validation using measurements of both 3.5 mm and Type-N devices demonstrates the effectiveness of the weighted-TRL method in eliminating discontinuities and calibration artifacts across a wide range of frequencies. The results reveal the improved calibration of S-parameters this approach can yield compared to traditional TRL calibration methods. The developed weighted-TRL calibration technique offers a significant advancement in metrology-grade measurements, enabling more precise characterization of high-frequency devices across broad frequency bands. By mitigating a key limitation of the TRL calibration, this method provides a valuable tool for enhancing the accuracy and reliability of VNA measurements for precision metrology applications.
本文介绍了一种应用于直通反射线路（TRL）校准技术的加权算法，以提高宽频带矢量网络分析仪（VNA）测量的准确性和可靠性。该方法解决了传统 TRL 校准的固有局限性，特别是在使用多个线路标准时，在带状 TRL 方法中观察到的阶跃变化。通过引入一个定制的加权函数，为每个线路标准分配与相位相关的权重，可以实现更平滑的转换和更好的 S 参数测量。通过对 3.5 毫米和 N 型器件的测量进行实验验证，证明了加权-TRL 方法在消除各种频率范围内的不连续性和校准伪影方面的有效性。结果表明，与传统的 TRL 校准方法相比，这种方法可以改进 S 参数的校准。所开发的加权-TRL 校准技术在计量级测量方面取得了重大进展，可在宽频带范围内对高频器件进行更精确的表征。通过缓解 TRL 校准的一个关键限制，该方法为提高精密计量应用中 VNA 测量的准确性和可靠性提供了宝贵的工具。
{"title":"Application of Weighting Algorithm for Enhanced Broadband Vector Network Analyzer Measurements","authors":"Sang-hee Shin, James Skinner","doi":"10.3390/math12182871","DOIUrl":"https://doi.org/10.3390/math12182871","url":null,"abstract":"A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step changes observed in banded-TRL approaches when multiple Line standards are used. By introducing a bespoke weighting function that assigns phase-dependent weights to each Line standard, smoother transitions and improved S-parameter measurements can be achieved. Experimental validation using measurements of both 3.5 mm and Type-N devices demonstrates the effectiveness of the weighted-TRL method in eliminating discontinuities and calibration artifacts across a wide range of frequencies. The results reveal the improved calibration of S-parameters this approach can yield compared to traditional TRL calibration methods. The developed weighted-TRL calibration technique offers a significant advancement in metrology-grade measurements, enabling more precise characterization of high-frequency devices across broad frequency bands. By mitigating a key limitation of the TRL calibration, this method provides a valuable tool for enhancing the accuracy and reliability of VNA measurements for precision metrology applications.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"48 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249190","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}
In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous elements x,y∈R, then x2∈P or yn∈P, for some positive integer n. Many examples and properties of Gwsq-primary ideals are given. Among several results, we compare Gwsq-primary ideals and other classical graded ideals such as graded strongly quasi primary ideals, graded weakly primary ideals and graded weakly 2-prime ideals etc.
本文将介绍并研究有级弱强准原初理想的概念。如果对于一些同质元素 x,y∈R 而言，当 0≠xy∈P 时，那么对于一些正整数 n 而言，x2∈P 或 yn∈P 时，我们称 R 的一个适当的有级理想 P 为有级弱强准原初（简称为 Gwsq-原初）理想。在几个结果中，我们比较了 Gwsq-原初理想和其他经典有级理想，如有级强准原初理想、有级弱原初理想和有级弱 2-prime 理想等。
{"title":"Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings","authors":"Azzh Saad Alshehry, Rashid Abu-Dawwas, Basel Hawary","doi":"10.3390/math12182857","DOIUrl":"https://doi.org/10.3390/math12182857","url":null,"abstract":"In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous elements x,y∈R, then x2∈P or yn∈P, for some positive integer n. Many examples and properties of Gwsq-primary ideals are given. Among several results, we compare Gwsq-primary ideals and other classical graded ideals such as graded strongly quasi primary ideals, graded weakly primary ideals and graded weakly 2-prime ideals etc.","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":"142249146","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}
Pshtiwan Othman Mohammed, Ravi P. Agarwal, Majeed A. Yousif, Eman Al-Sarairah, Alina Alb Lupas, Mohamed Abdelwahed
This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.
{"title":"Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting","authors":"Pshtiwan Othman Mohammed, Ravi P. Agarwal, Majeed A. Yousif, Eman Al-Sarairah, Alina Alb Lupas, Mohamed Abdelwahed","doi":"10.3390/math12182864","DOIUrl":"https://doi.org/10.3390/math12182864","url":null,"abstract":"This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"24 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249182","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}
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}
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}
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}
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