The ability to make decisions is crucial for achieving success in any field, particularly in areas that involve managing extensive information and knowledge. The process of decision-making in real-world scenarios often involves considering numerous factors and aspects. It can be challenging to make decisions in such complex environments. In this paper, we present a new technique that solves multicriteria decision-making (MCDM) problems by considering opportunity losses-based polar coordinate distance (OPLO-POCOD). MCDM is a subdiscipline of operations research in which some alternatives are evaluated concerning some criteria to choose the most optimal alternative(s). Opportunity loss is a fundamental concept in economics and management, which can be used as a basis for determining the value associated with information. The authors emphasize that the technique incorporates the concept of opportunity losses and uses distance vectors in polar coordinates, making it a compelling approach. By considering opportunity losses, decision-makers gain a better understanding of the trade-offs involved in selecting alternatives, enabling them to make more informed decisions. Finally, the proposed method is exhibited through the use of numerical an example to illustrate its process. Additionally, a comparative sensitivity analysis is conducted to evaluate the outcomes of OPLO-POCOD and compare them with existing MCDM methods. The OPLO-POCOD method is found to have high reliability compared to other methods, as indicated by Spearman’s correlation coefficient, which is greater than 0.9. The method shows a correlation of over 98.5% with TOPSIS, COPRAS, ARAS, and MCRAT methods, demonstrating its robustness and effectiveness. These analyses show the efficiency of the proposed method and highlight the stability of the results.
{"title":"A Novel Opportunity Losses-Based Polar Coordinate Distance (OPLO-POCOD) Approach to Multiple Criteria Decision-Making","authors":"Reza Sheikh, Soheila Senfi","doi":"10.1155/2024/8845886","DOIUrl":"https://doi.org/10.1155/2024/8845886","url":null,"abstract":"The ability to make decisions is crucial for achieving success in any field, particularly in areas that involve managing extensive information and knowledge. The process of decision-making in real-world scenarios often involves considering numerous factors and aspects. It can be challenging to make decisions in such complex environments. In this paper, we present a new technique that solves multicriteria decision-making (MCDM) problems by considering opportunity losses-based polar coordinate distance (OPLO-POCOD). MCDM is a subdiscipline of operations research in which some alternatives are evaluated concerning some criteria to choose the most optimal alternative(s). Opportunity loss is a fundamental concept in economics and management, which can be used as a basis for determining the value associated with information. The authors emphasize that the technique incorporates the concept of opportunity losses and uses distance vectors in polar coordinates, making it a compelling approach. By considering opportunity losses, decision-makers gain a better understanding of the trade-offs involved in selecting alternatives, enabling them to make more informed decisions. Finally, the proposed method is exhibited through the use of numerical an example to illustrate its process. Additionally, a comparative sensitivity analysis is conducted to evaluate the outcomes of OPLO-POCOD and compare them with existing MCDM methods. The OPLO-POCOD method is found to have high reliability compared to other methods, as indicated by Spearman’s correlation coefficient, which is greater than 0.9. The method shows a correlation of over 98.5% with TOPSIS, COPRAS, ARAS, and MCRAT methods, demonstrating its robustness and effectiveness. These analyses show the efficiency of the proposed method and highlight the stability of the results.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current study explores the space and time-fractional Black–Scholes European option pricing model that primarily occurs in the financial market. To tackle the complexities associated with solving models in a fractional environment, the Aboodh transform is hybridized with He’s algorithm. This facilitates in improving the efficiency and applicability of the classical homotopy perturbation method (HPM) by ensuring the rapid convergence of the series form solution. Three cases that are time-fractional scenario, space-fractional scenario, and time-space-fractional scenario are observed through graphs and tables. 2D graphical analysis is performed to depict the behaviour of a given option pricing model for varying time, stock price, and fractional parameters. Solutions of the European option pricing model at various fractional orders are also presented as 3D plots. The results obtained through these graphs unfold the interchange between time- and space-fractional derivatives, presenting a comprehensive study of option pricing under fractional dynamics. The competency of the proposed scheme is illustrated via solutions and errors throughout the fractional domain in tabular form. The validity of the He-Aboodh results is exhibited by comparison with existing errors. Analysis shows that the proposed methodology (He-Aboodh algorithm) is a valuable scheme for solving time-space-fractional models arising in business and economics.
本研究探讨了主要出现在金融市场上的空间和时间分式布莱克-斯科尔斯欧式期权定价模型。为了解决在分数环境中求解模型的复杂性，Aboodh 变换与 He 算法进行了混合。这有助于提高经典同调扰动法（HPM）的效率和适用性，确保序列形式解的快速收敛。通过图形和表格观察了三种情况，即时间-分数情况、空间-分数情况和时间-空间-分数情况。通过二维图形分析，描述了给定期权定价模型在不同时间、股票价格和分数参数下的行为。欧式期权定价模型在不同分数阶数下的解决方案也以三维图的形式呈现。通过这些图表获得的结果展现了时间和空间分数导数之间的相互关系，从而对分数动态下的期权定价进行了全面研究。建议方案的能力通过整个分数域的解和误差以表格形式加以说明。通过与现有误差的比较，展示了 He-Aboodh 结果的有效性。分析表明，所提出的方法（He-Aboodh 算法）是解决商业和经济学中出现的时空分数模型的重要方案。
{"title":"New Solutions of Time- and Space-Fractional Black–Scholes European Option Pricing Model via Fractional Extension of He-Aboodh Algorithm","authors":"Mubashir Qayyum, Efaza Ahmad","doi":"10.1155/2024/6623636","DOIUrl":"https://doi.org/10.1155/2024/6623636","url":null,"abstract":"The current study explores the space and time-fractional Black–Scholes European option pricing model that primarily occurs in the financial market. To tackle the complexities associated with solving models in a fractional environment, the Aboodh transform is hybridized with He’s algorithm. This facilitates in improving the efficiency and applicability of the classical homotopy perturbation method (HPM) by ensuring the rapid convergence of the series form solution. Three cases that are time-fractional scenario, space-fractional scenario, and time-space-fractional scenario are observed through graphs and tables. 2D graphical analysis is performed to depict the behaviour of a given option pricing model for varying time, stock price, and fractional parameters. Solutions of the European option pricing model at various fractional orders are also presented as 3D plots. The results obtained through these graphs unfold the interchange between time- and space-fractional derivatives, presenting a comprehensive study of option pricing under fractional dynamics. The competency of the proposed scheme is illustrated via solutions and errors throughout the fractional domain in tabular form. The validity of the He-Aboodh results is exhibited by comparison with existing errors. Analysis shows that the proposed methodology (He-Aboodh algorithm) is a valuable scheme for solving time-space-fractional models arising in business and economics.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"284 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the mixed convection boundary-layer flow of Casson nanofluid with an internal heat source on an exponentially stretched sheet. The Buongiorno model, incorporating thermophoresis and Brownian motion, describes fluid temperature. The modeled system is solved numerically using bvp4c routine to analyze the impact of different fluid parameters on velocity, temperature, and concentration profiles. The analysis reveals that the suction effect, magnetic field, and Casson parameter reduce momentum boundary layer thickness and hence slow fluid motion. Conversely, buoyancy forces increase mass boundary layer thickness which results in accelerating fluid motion. Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.
{"title":"Radiative Mixed Convection Flow of Casson Nanofluid through Exponentially Permeable Stretching Sheet with Internal Heat Generation","authors":"Mazhar Hussain, Shereen Fatima, Mubashir Qayyum","doi":"10.1155/2024/9038635","DOIUrl":"https://doi.org/10.1155/2024/9038635","url":null,"abstract":"This paper investigates the mixed convection boundary-layer flow of Casson nanofluid with an internal heat source on an exponentially stretched sheet. The Buongiorno model, incorporating thermophoresis and Brownian motion, describes fluid temperature. The modeled system is solved numerically using bvp4c routine to analyze the impact of different fluid parameters on velocity, temperature, and concentration profiles. The analysis reveals that the suction effect, magnetic field, and Casson parameter reduce momentum boundary layer thickness and hence slow fluid motion. Conversely, buoyancy forces increase mass boundary layer thickness which results in accelerating fluid motion. Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"242 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The growth of world population has fueled environmental, legal, and social concerns, making governments and companies attempt to mitigate the environmental and social implications stemming from supply chain operations. The state-run Environmental Protection Agency has initially offered financial incentives (subsidies) meant to encourage supply chain managers to use cleaner technologies in order to minimize pollution. In today’s competitive markets, using green technologies remains vital. In the present project, we have examined a class of closed-loop supply chain competitive facility location-routing problems. According to the framework of the competition, one of the players, called the Leader, opens its facilities first. The second player, called the Follower, makes its decision when Leader’s location is known. Afterwards, each customer chooses an open facility based on some preference huff rules before returning the benefits to one of the two companies. The follower, under the influence of the leader’s decisions, performs the best reaction in order to obtain the maximum capture of the market. So, a bilevel mixed-integer linear programming model is formulated. The objective function at both levels includes market capture profit, fixed and operating costs, and financial incentives. A metaheuristic quantum binary particle swarm optimization (PSO) is developed via Benders decomposition algorithm to solve the proposed model. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.
{"title":"A Competitive Bilevel Programming Model for Green, CLSCs in Light of Government Incentives","authors":"Arsalan Rahmani, Meysam Hosseini, Amir Sahami","doi":"10.1155/2024/4866890","DOIUrl":"https://doi.org/10.1155/2024/4866890","url":null,"abstract":"The growth of world population has fueled environmental, legal, and social concerns, making governments and companies attempt to mitigate the environmental and social implications stemming from supply chain operations. The state-run Environmental Protection Agency has initially offered financial incentives (subsidies) meant to encourage supply chain managers to use cleaner technologies in order to minimize pollution. In today’s competitive markets, using green technologies remains vital. In the present project, we have examined a class of closed-loop supply chain competitive facility location-routing problems. According to the framework of the competition, one of the players, called the Leader, opens its facilities first. The second player, called the Follower, makes its decision when Leader’s location is known. Afterwards, each customer chooses an open facility based on some preference huff rules before returning the benefits to one of the two companies. The follower, under the influence of the leader’s decisions, performs the best reaction in order to obtain the maximum capture of the market. So, a bilevel mixed-integer linear programming model is formulated. The objective function at both levels includes market capture profit, fixed and operating costs, and financial incentives. A metaheuristic quantum binary particle swarm optimization (PSO) is developed via Benders decomposition algorithm to solve the proposed model. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"96 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139951308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca, Hugo Cruz-Suárez
The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the -cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model.
{"title":"Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities","authors":"R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca, Hugo Cruz-Suárez","doi":"10.1155/2024/6885051","DOIUrl":"https://doi.org/10.1155/2024/6885051","url":null,"abstract":"The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.51131 6.1673\" width=\"7.51131pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"138 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139911302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper aims to introduce an iterative algorithm based on an inertial technique that uses the minimum number of projections onto a nonempty, closed, and convex set. We show that the algorithm generates a sequence that converges strongly to the common solution of a variational inequality involving inverse strongly monotone mapping and fixed point problems for a countable family of nonexpansive mappings in the setting of real Hilbert space. Numerical experiments are also presented to discuss the advantages of using our algorithm over earlier established algorithms. Moreover, we solve a real-life signal recovery problem via a minimization problem to demonstrate our algorithm’s practicality.
{"title":"A Modified Form of Inertial Viscosity Projection Methods for Variational Inequality and Fixed Point Problems","authors":"Watanjeet Singh, Sumit Chandok","doi":"10.1155/2024/9509788","DOIUrl":"https://doi.org/10.1155/2024/9509788","url":null,"abstract":"This paper aims to introduce an iterative algorithm based on an inertial technique that uses the minimum number of projections onto a nonempty, closed, and convex set. We show that the algorithm generates a sequence that converges strongly to the common solution of a variational inequality involving inverse strongly monotone mapping and fixed point problems for a countable family of nonexpansive mappings in the setting of real Hilbert space. Numerical experiments are also presented to discuss the advantages of using our algorithm over earlier established algorithms. Moreover, we solve a real-life signal recovery problem via a minimization problem to demonstrate our algorithm’s practicality.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"50 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chemical graph theory, a branch of computational and applied mathematics, covers a very wide range of topics. As a result, the world of applied sciences heavily relies on graph theory. The concept of partition dimension has significant importance in the field of chemical graph theory. Although certain graphs have bounded partition dimensions, a graph’s partition dimension may be constant. In this study, we look at two alternative chemical structures made of an octagonal grid: nanosheets and nanotubes. We determined the partition dimension of an octagonal grid-generated nanosheet to be 3, and the partition dimension of a nanotube to be limited from 4.
{"title":"Partition Resolvability of Nanosheet and Nanotube Derived from Octagonal Grid","authors":"Ali Al Khabyah, Ali N. A. Koam, Ali Ahmad","doi":"10.1155/2024/6222086","DOIUrl":"https://doi.org/10.1155/2024/6222086","url":null,"abstract":"Chemical graph theory, a branch of computational and applied mathematics, covers a very wide range of topics. As a result, the world of applied sciences heavily relies on graph theory. The concept of partition dimension has significant importance in the field of chemical graph theory. Although certain graphs have bounded partition dimensions, a graph’s partition dimension may be constant. In this study, we look at two alternative chemical structures made of an octagonal grid: nanosheets and nanotubes. We determined the partition dimension of an octagonal grid-generated nanosheet to be 3, and the partition dimension of a nanotube to be limited from 4.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"70 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed M. Al-Gharabli, Shadi Al-Omari, Adel M. Al-Mahdi
In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations.
{"title":"Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type","authors":"Mohammed M. Al-Gharabli, Shadi Al-Omari, Adel M. Al-Mahdi","doi":"10.1155/2024/1615178","DOIUrl":"https://doi.org/10.1155/2024/1615178","url":null,"abstract":"In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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