When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker’s preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method.
{"title":"Fermatean Hesitant Fuzzy Multi-Attribute Decision-Making Method with Probabilistic Information and Its Application","authors":"Chuanyang Ruan, Xiangjing Chen, Lin Yan","doi":"10.3390/axioms13070456","DOIUrl":"https://doi.org/10.3390/axioms13070456","url":null,"abstract":"When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker’s preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141677137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fashion apparel industry is facing an increasingly growing demand, compounded by the short sales lifecycle and strong seasonality of clothing, posing significant challenges to inventory management in the retail sector. Despite some retailers like Uniqlo and Zara implementing inventory management and dynamic pricing strategies, challenges persist due to the dynamic nature of fashion trends and the stochastic factors affecting inventory. To address these issues, we construct a mathematical model based on the mathematical expression of the deterministic fashion level function, where the geometric Brownian motion, widely applied in finance, is initially utilized in the stochastic fashion level function. Drawing on research findings from deteriorating inventory management and stochastic optimization, we investigate the fluctuation of inventory levels, optimal dynamic pricing, optimal production rates, and profits—four crucial indicators—via Pontryagin’s maximum principle. Analytical solutions are derived, and the numerical simulation is provided to verify and compare the proposed model with deterministic fashion level function models. The model emphasizes the importance of considering stochastic factors in decision-making processes and provides insights to enhance profitability, inventory management, and sustainable consumption in the fashion product industry.
时尚服装业正面临着日益增长的需求，再加上服装销售周期短、季节性强，给零售业的库存管理带来了巨大挑战。尽管优衣库和 Zara 等一些零售商实施了库存管理和动态定价策略，但由于时尚趋势的动态性和影响库存的随机因素，挑战依然存在。为了解决这些问题，我们在确定性时尚水平函数数学表达式的基础上构建了一个数学模型，在随机时尚水平函数中初步采用了广泛应用于金融领域的几何布朗运动。借鉴恶化库存管理和随机优化的研究成果，我们通过庞特里亚金最大原则研究了库存水平波动、最优动态定价、最优生产率和利润这四个关键指标。我们推导出了分析解，并提供了数值模拟来验证和比较所提出的模型与确定性时尚水平函数模型。该模型强调了在决策过程中考虑随机因素的重要性，并为提高时装产品行业的盈利能力、库存管理和可持续消费提供了启示。
{"title":"Dynamic Pricing and Inventory Strategies for Fashion Products Using Stochastic Fashion Level Function","authors":"Wenhan Lu, Litan Yan","doi":"10.3390/axioms13070453","DOIUrl":"https://doi.org/10.3390/axioms13070453","url":null,"abstract":"The fashion apparel industry is facing an increasingly growing demand, compounded by the short sales lifecycle and strong seasonality of clothing, posing significant challenges to inventory management in the retail sector. Despite some retailers like Uniqlo and Zara implementing inventory management and dynamic pricing strategies, challenges persist due to the dynamic nature of fashion trends and the stochastic factors affecting inventory. To address these issues, we construct a mathematical model based on the mathematical expression of the deterministic fashion level function, where the geometric Brownian motion, widely applied in finance, is initially utilized in the stochastic fashion level function. Drawing on research findings from deteriorating inventory management and stochastic optimization, we investigate the fluctuation of inventory levels, optimal dynamic pricing, optimal production rates, and profits—four crucial indicators—via Pontryagin’s maximum principle. Analytical solutions are derived, and the numerical simulation is provided to verify and compare the proposed model with deterministic fashion level function models. The model emphasizes the importance of considering stochastic factors in decision-making processes and provides insights to enhance profitability, inventory management, and sustainable consumption in the fashion product industry.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 30","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141678755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yanlin Li, Mohd Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, Khalid Masood
This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-depth analysis of its equality case. More precisely, if the mean curvature vector at a point vanishes, then the equality case of this inequality is achieved by a unit tangent vector at the point if and only if the vector belongs to the normal space. Finally, we have shown that when a point is a totally geodesic point or is totally umbilical with n=2, the equality case of this inequality holds true for all unit tangent vectors at the point, and conversely.
{"title":"Analyzing the Ricci Tensor for Slant Submanifolds in Locally Metallic Product Space Forms with a Semi-Symmetric Metric Connection","authors":"Yanlin Li, Mohd Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, Khalid Masood","doi":"10.3390/axioms13070454","DOIUrl":"https://doi.org/10.3390/axioms13070454","url":null,"abstract":"This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-depth analysis of its equality case. More precisely, if the mean curvature vector at a point vanishes, then the equality case of this inequality is achieved by a unit tangent vector at the point if and only if the vector belongs to the normal space. Finally, we have shown that when a point is a totally geodesic point or is totally umbilical with n=2, the equality case of this inequality holds true for all unit tangent vectors at the point, and conversely.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141678889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Alshehry, L. Ciurdariu, Yaser Saber, Amal F. Soliman
This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F·V·Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities.
{"title":"Some New Estimations of Ostrowski-Type Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and Hypergeometric Functions","authors":"A. Alshehry, L. Ciurdariu, Yaser Saber, Amal F. Soliman","doi":"10.3390/axioms13070455","DOIUrl":"https://doi.org/10.3390/axioms13070455","url":null,"abstract":"This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F·V·Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"71 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The performance degradation of initiating explosive devices is influenced by various internal and external factors, leading to uncertainties in their reliability and lifetime predictions. This paper proposes an uncertain degradation model based on uncertain differential equations, utilizing the Liu process to characterize the volatility in degradation rates. The ignition delay time is selected as the primary performance parameter, and the uncertain distributions, expected values and confidence intervals are derived for the model. Moment estimation techniques are employed to estimate the unknown parameters within the model. A real data analysis of ignition delay times under accelerated storage conditions demonstrates the practical applicability of the proposed method.
{"title":"Uncertainty Degradation Model for Initiating Explosive Devices Based on Uncertain Differential Equations","authors":"Changli Ma, Li Jia, Meilin Wen","doi":"10.3390/axioms13070449","DOIUrl":"https://doi.org/10.3390/axioms13070449","url":null,"abstract":"The performance degradation of initiating explosive devices is influenced by various internal and external factors, leading to uncertainties in their reliability and lifetime predictions. This paper proposes an uncertain degradation model based on uncertain differential equations, utilizing the Liu process to characterize the volatility in degradation rates. The ignition delay time is selected as the primary performance parameter, and the uncertain distributions, expected values and confidence intervals are derived for the model. Moment estimation techniques are employed to estimate the unknown parameters within the model. A real data analysis of ignition delay times under accelerated storage conditions demonstrates the practical applicability of the proposed method.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141680386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A class of semi-linear elliptic equations with the critical Hardy–Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory, and statistical mechanics, as well as in gravity balance problems in galaxies. The PSc sequence of energy functional was investigated, and then the mountain pass lemma was used to prove the existence of at least one nontrivial solution. Also a multiplicity result was obtained. Some known results were generalized.
{"title":"Existence and Multiplicity of Nontrivial Solutions for Semilinear Elliptic Equations Involving Hardy–Sobolev Critical Exponents","authors":"Yonghong Fan, Wenheng Sun, Linlin Wang","doi":"10.3390/axioms13070450","DOIUrl":"https://doi.org/10.3390/axioms13070450","url":null,"abstract":"A class of semi-linear elliptic equations with the critical Hardy–Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory, and statistical mechanics, as well as in gravity balance problems in galaxies. The PSc sequence of energy functional was investigated, and then the mountain pass lemma was used to prove the existence of at least one nontrivial solution. Also a multiplicity result was obtained. Some known results were generalized.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"77 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Muratbekov, A. Suleimbekova, Mukhtar Baizhumanov
In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation numbers is proven. Here, we note that finding estimates of approximation numbers, as well as extremal subspaces, for a set of solutions to the equation is a task that is certainly important from both a theoretical and a practical point of view. The paper also obtained an upper bound for the eigenvalues. Note that, in this paper, estimates of eigenvalues and approximation numbers for the degenerate third-order partial differential operators are obtained for the first time.
{"title":"Estimates of Eigenvalues and Approximation Numbers for a Class of Degenerate Third-Order Partial Differential Operators","authors":"M. Muratbekov, A. Suleimbekova, Mukhtar Baizhumanov","doi":"10.3390/axioms13070451","DOIUrl":"https://doi.org/10.3390/axioms13070451","url":null,"abstract":"In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation numbers is proven. Here, we note that finding estimates of approximation numbers, as well as extremal subspaces, for a set of solutions to the equation is a task that is certainly important from both a theoretical and a practical point of view. The paper also obtained an upper bound for the eigenvalues. Note that, in this paper, estimates of eigenvalues and approximation numbers for the degenerate third-order partial differential operators are obtained for the first time.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"74 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce center-like subsets Z∘*(A,d),Z∘**(A,d), where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for the center-like subsets existing in the literature and establish the relations between these sets. In addition to these new sets, the theorems are generalized as multiplicative derivations instead of the derivations found in previous studies. Additionally, different proofs are provided for different center-like sets. Finally, we enrich this article with examples demonstrating that the hypotheses we use are necessary.
我们引入类中心子集 Z∘*(A,d),Z∘**(A,d)，其中 A 是环，d 是乘法衍生。下面，我们将对文献中已有的类中心子集进行新的推导，并建立这些集合之间的关系。除了这些新集合，定理也被概括为乘法推导，而不是以往研究中的推导。此外，我们还为不同的类中心集合提供了不同的证明。最后，我们用实例丰富了这篇文章，证明我们使用的假设是必要的。
{"title":"Center-like Subsets in Semiprime Rings with Multiplicative Derivations","authors":"Sarah Aljohani, E. K. Sögütcü, N. Rehman","doi":"10.3390/axioms13070448","DOIUrl":"https://doi.org/10.3390/axioms13070448","url":null,"abstract":"We introduce center-like subsets Z∘*(A,d),Z∘**(A,d), where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for the center-like subsets existing in the literature and establish the relations between these sets. In addition to these new sets, the theorems are generalized as multiplicative derivations instead of the derivations found in previous studies. Additionally, different proofs are provided for different center-like sets. Finally, we enrich this article with examples demonstrating that the hypotheses we use are necessary.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"8 30","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141684589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras. In this paper, the quantization of the rank two Heisenberg–Virasoro algebra by Drinfel’d twists is presented, Lie bialgebra structures of which have been investigated by the authors recently.
{"title":"Quantization of the Rank Two Heisenberg–Virasoro Algebra","authors":"Xuekun Chen","doi":"10.3390/axioms13070446","DOIUrl":"https://doi.org/10.3390/axioms13070446","url":null,"abstract":"Quantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras. In this paper, the quantization of the rank two Heisenberg–Virasoro algebra by Drinfel’d twists is presented, Lie bialgebra structures of which have been investigated by the authors recently.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"2018 40","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141706651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given using the ∇-Mittag-Leffler function, Laplace transform method, operational method and operational decomposition method. In addition, we also provide some results about a solution to a new class of fractional-order sequential differential equations with convolutional-type variable coefficients using the Laplace transform method.
{"title":"Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales","authors":"Cheng-Cheng Zhu, Jiang Zhu","doi":"10.3390/axioms13070447","DOIUrl":"https://doi.org/10.3390/axioms13070447","url":null,"abstract":"In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given using the ∇-Mittag-Leffler function, Laplace transform method, operational method and operational decomposition method. In addition, we also provide some results about a solution to a new class of fractional-order sequential differential equations with convolutional-type variable coefficients using the Laplace transform method.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"17 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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