Mathematics

25 pages, 18293 KiB

Open AccessArticle

Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method

by Feiyun Pei, Guojiang Wu and Yong Guo

Mathematics 2023, 11(6), 1560; https://doi.org/10.3390/math11061560 - 22 Mar 2023

Cited by 2 | Viewed by 2484

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of [...] Read more.

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of studying these topics, it is very important to obtain the exact solutions of the KPI equation. In this paper, a general Riccati equation is treated as an auxiliary equation, which is solved to obtain many new types of solutions through several different function transformations. We solve the KPI equation using this general Riccati equation, and construct ten sets of the infinite series exact solitary wave solution of the KPI equation. The results show that this method is simple and effective for the construction of infinite series solutions of nonlinear evolution models. Full article

(This article belongs to the Special Issue Advances in Nonlinear Dynamics and Chaos: Theory and Application)

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19 pages, 1851 KiB

Open AccessArticle

A New Approach to Artificial Intelligent Based Three-Way Decision Making and Analyzing S-Box Image Encryption Using TOPSIS Method

by Saleem Abdullah, Alaa O. Almagrabi and Ihsan Ullah

Mathematics 2023, 11(6), 1559; https://doi.org/10.3390/math11061559 - 22 Mar 2023

Cited by 9 | Viewed by 2088

Abstract

In fuzzy artificial intelligent decision support systems, three-way intelligent-decision making (TWIDM) has played a very important role in ranking objects under the double hierarchy linguistic variable (DHLV). The 8 × 8 S-boxes are very important for image encryption in secure communication. Therefore, the [...] Read more.

In fuzzy artificial intelligent decision support systems, three-way intelligent-decision making (TWIDM) has played a very important role in ranking objects under the double hierarchy linguistic variable (DHLV). The 8 × 8 S-boxes are very important for image encryption in secure communication. Therefore, the aim of the present study is to develop a new approach to artificial intelligent three-way decision making via DHLV and apply it to S-box image encryption. Artificial intelligent based three-way decision-making problems with double hierarchy hesitant linguistic terms are developed. The first and second hierarchy hesitant linguistic term sets make up the double hierarchy hesitant linguistic term set, which allows for more flexible expressions of doubt and fuzziness. First, we define the Einstein operational laws, score function, and Einstein aggregation operators; i.e., double hierarchy hesitant linguistic Einstein weighted averaging and weighted geometric operators. First, the unknown weight vector for decision experts is determined by using aggregation operators and entropy measures for DHLV. Then, we find the weight vector for our criteria by using the distance measure. In TWIDM, conditional probability is determined by using the extended TOPSIS method for evaluating the S-boxes for image encryption. The expected losses are then computed by aggregating the loss functions with the help of Einstein-weighted averaging aggregation operators. Finally, we apply the minimum-loss decision rules for the selection of S-box to image encryption. The proposed decision technique has been compared with existing three-way decisions and the result of proposed three-way decision making for analyzing and ranking the S-box is very good and reliable for decision making. Full article

(This article belongs to the Special Issue Fuzzy Decision Making and Applications)

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31 pages, 4006 KiB

Open AccessArticle

Do Innovation Metrics Reflect Sustainable Policy Making in Europe? A Comparative Study Case on the Carpathian and Alpine Mountain Regions

by Andrei Coca, Manuela Rozalia Gabor and Irina Olimpia Susanu

Mathematics 2023, 11(6), 1558; https://doi.org/10.3390/math11061558 - 22 Mar 2023

Cited by 1 | Viewed by 2161

Abstract

This paper questions the evaluation of innovation systems and innovation measurements and the effectiveness of innovation policies applied at the territorial level by assessing whether the existing European regional scoreboard is effective in providing accurate inputs for decision-makers in mountainous regions. The aim [...] Read more.

This paper questions the evaluation of innovation systems and innovation measurements and the effectiveness of innovation policies applied at the territorial level by assessing whether the existing European regional scoreboard is effective in providing accurate inputs for decision-makers in mountainous regions. The aim of the research is to provide, through comparative analysis by using statistical multi-methods of two mountainous macro-regions (the Alps and the Carpathians), a possible and available path to develop novel perspectives and alternative views on innovation systems’ performance for informed and territorial-based policy making by using the indicators of the Regional Innovation Scoreboard. The methodology used includes descriptive statistics, chi-square bivariate test, Student’s t test, one-way ANOVA with Bonferroni post hoc multiple comparisons, multilinear regression analysis, and decision tree with CRT (classification and regression trees) algorithm. Our results emphasize the similarities and differences between the Alpine and Carpathian mountain regions, find the best predictors for each mountain region, and provide a scientific basis for the development of a holistic approach linking measurement theory, innovation systems, innovation policies, and their territorial approach toward sustainable development of mountain areas. The paper’s contribution is relevant in the context of remote, rural, and mountain areas, which are usually left behind in terms of innovation chances and in the context of the COVID-19 aftermath with budget constraints. The present results are pertinent for designing effective smart specialization strategies in these regions due to the difficulties that most remote areas and less developed regions are facing in developing innovation policies. Full article

(This article belongs to the Special Issue Mathematical and Statistical Methods for Fostering Innovations in Small and Medium-Sized Enterprises)

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22 pages, 7011 KiB

Open AccessArticle

Multi-Objective Discrete Brainstorming Optimizer to Solve the Stochastic Multiple-Product Robotic Disassembly Line Balancing Problem Subject to Disassembly Failures

by Gongdan Xu, Zhiwei Zhang, Zhiwu Li, Xiwang Guo, Liang Qi and Xianzhao Liu

Mathematics 2023, 11(6), 1557; https://doi.org/10.3390/math11061557 - 22 Mar 2023

Cited by 10 | Viewed by 1633

Abstract

Robots are now widely used in product disassembly lines, which significantly improves end-of-life (EOL) product disassembly efficiency. Most of the current research on disassembly line balancing problems focuses on decomposing one product. More than one product can be disassembled concurrently, which can further [...] Read more.

Robots are now widely used in product disassembly lines, which significantly improves end-of-life (EOL) product disassembly efficiency. Most of the current research on disassembly line balancing problems focuses on decomposing one product. More than one product can be disassembled concurrently, which can further improve the efficiency. Moreover, uncertainty such as the depreciation of EOL products, may result in disassembly failure. In this research, a stochastic multi-product robotic disassembly line balancing model is established using an AND/OR graph. It takes the precedence relationship, cycle constraint, and disassembly failure into consideration to maximize the profit and minimize the energy consumption for disassembling multiple products. A Pareto-improved multi-objective brainstorming optimization algorithm combined with stochastic simulation is proposed to solve the problem. Furthermore, by conducting experiments on some real cases and comparing with four state-of-the-art multi-objective optimization algorithms, i.e., the multi-objective discrete gray wolf optimizer, artificial bee colony algorithm, nondominated sorting genetic algorithm II, and multi-objective evolutionary algorithm based on decomposition, this paper validates its excellent performance in solving the concerned problem. Full article

(This article belongs to the Section Engineering Mathematics)

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24 pages, 7332 KiB

Open AccessArticle

Reinforcement Learning-Based Lane Change Decision for CAVs in Mixed Traffic Flow under Low Visibility Conditions

by Bowen Gong, Zhipeng Xu, Ruixin Wei, Tao Wang, Ciyun Lin and Peng Gao

Mathematics 2023, 11(6), 1556; https://doi.org/10.3390/math11061556 - 22 Mar 2023

Cited by 1 | Viewed by 2321

Abstract

As an important stage in the development of autonomous driving, mixed traffic conditions, consisting of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), have attracted more and more attention. In fact, the randomness of human-driven vehicles (HDV) is the largest challenge for connected [...] Read more.

As an important stage in the development of autonomous driving, mixed traffic conditions, consisting of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), have attracted more and more attention. In fact, the randomness of human-driven vehicles (HDV) is the largest challenge for connected autonomous vehicles (CAV) to make reasonable decisions, especially in lane change scenarios. In this paper, we propose the problem of lane change decisions for CAV in low visibility and mixed traffic conditions for the first time. First, we consider the randomness of HDV in this environment and construct a finite state machine (FSM) model. Then, this study develops a partially observed Markov decision process (POMDP) for describing the problem of lane change. In addition, we use the modified deep deterministic policy gradient (DDPG) to solve the problem and get the optimal lane change decision in this environment. The reward designing takes the comfort, safety and efficiency of the vehicle into account, and the introduction of transfer learning accelerates the adaptation of CAV to the randomness of HDV. Finally, numerical experiments are conducted. The results show that, compared with the original DDPG, the modified DDPG has a faster convergence velocity. The strategy learned by the modified DDPG can complete the lane change in most of the scenarios. The comparison between the modified DDPG and the rule-based decisions indicates that the modified DDPG has a stronger adaptability to this special environment and can grasp more lane change opportunities. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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16 pages, 455 KiB

Open AccessArticle

An Inventory Model with Advertisement- and Customer-Relationship-Management-Sensitive Demand for a Product’s Life Cycle

by Mei-Chuan Cheng, Chun-Tao Chang and Tsu-Pang Hsieh

Mathematics 2023, 11(6), 1555; https://doi.org/10.3390/math11061555 - 22 Mar 2023

Cited by 2 | Viewed by 1799

Abstract

Advertisements play an important role in communicating with target customers. A higher advertisement frequency increases costs but may increase the chances of acquiring new customers. Moreover, faced with a wide-ranging array of products that might fit specific needs, customers usually buy according to [...] Read more.

Advertisements play an important role in communicating with target customers. A higher advertisement frequency increases costs but may increase the chances of acquiring new customers. Moreover, faced with a wide-ranging array of products that might fit specific needs, customers usually buy according to expectations about value and satisfaction. When customers are satisfied with a purchasing experience, they are more likely to buy again and share their experiences with others. Hence, companies are concerned about increasing customer value and service satisfaction to develop and manage customer relationships. This maintains a company’s competitive edge and can improve its market share. In this article, we incorporate the frequency of advertisements and the cost of customer relationship management (CRM) into the demand function under a product life cycle (PLC). Customers can return products in the appreciation period offered by a retailer. A profit-maximizing model is developed to analyze the joint marketing and ordering policy of each stage of a product’s life cycle with a product return guarantee. We construct an algorithm to identify the optimal decisions. Finally, numerical examples are presented to illustrate the proposed model, and managerial insights are obtained from a sensitivity analysis, followed by conclusions and future research. Full article

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16 pages, 2533 KiB

Open AccessFeature PaperArticle

Experimental Design for Progressive Type I Interval Censoring on the Lifetime Performance Index of Chen Lifetime Distribution

by Shu-Fei Wu and Meng-Zong Song

Mathematics 2023, 11(6), 1554; https://doi.org/10.3390/math11061554 - 22 Mar 2023

Cited by 5 | Viewed by 1434

Abstract

The lifetime performance index is commonly utilized to assess the lifetime performance of products. Based on the testing procedure for the lifetime of products following Chen distribution, an experimental design for progressive type I interval censoring is determined to achieve the desired power [...] Read more.

The lifetime performance index is commonly utilized to assess the lifetime performance of products. Based on the testing procedure for the lifetime of products following Chen distribution, an experimental design for progressive type I interval censoring is determined to achieve the desired power level while minimizing total experimental cost. For fixed inspection interval lengths and an unfixed number of inspection intervals, the required number of inspection intervals and sample sizes to achieve the minimum experimental costs are computed and presented in a table format. For unfixed termination times, the required number of inspection intervals, minimum sample sizes, and equal interval lengths are obtained and presented in a table format, while the minimum experimental costs are achieved. Finally, a practical example is presented to demonstrate the utilization of this experimental design for collecting samples and conducting a testing procedure to evaluate the lifetime performance of products. Full article

(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications)

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26 pages, 7955 KiB

Open AccessArticle

Class of Crosscap Two Graphs Arising from Lattices–I

by T. Asir, K. Mano, Jehan A. Al-Bar and Wafaa M. Fakieh

Mathematics 2023, 11(6), 1553; https://doi.org/10.3390/math11061553 - 22 Mar 2023

Cited by 1 | Viewed by 1276

Abstract

Let

L

be a lattice. The annihilating-ideal graph of

L

is a simple graph whose vertex set is the set of all nontrivial ideals of

L

and whose two distinct vertices I and J are adjacent if and only if [...] Read more.

Let

L

be a lattice. The annihilating-ideal graph of

L

is a simple graph whose vertex set is the set of all nontrivial ideals of

L

and whose two distinct vertices I and J are adjacent if and only if

I \land J = 0

. In this paper, crosscap two annihilating-ideal graphs of lattices with at most four atoms are characterized. These characterizations provide the classes of multipartite graphs, which are embedded in the Klein bottle. Full article

(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)

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16 pages, 343 KiB

Open AccessArticle

On AP–Henstock–Kurzweil Integrals and Non-Atomic Radon Measure

by Hemanta Kalita, Bipan Hazarika and Tomás Pérez Becerra

Mathematics 2023, 11(6), 1552; https://doi.org/10.3390/math11061552 - 22 Mar 2023

Cited by 1 | Viewed by 1174

Abstract

The AP–Henstock–Kurzweil-type integral is defined on

X,

where

X

is a complete measure metric space. We present some properties of the integral, continuing the study’s use of a Radon measure

μ .

Finally, using locally finite measures, we extend the AP–Henstock–Kurzweil integral [...] Read more.

The AP–Henstock–Kurzweil-type integral is defined on

X,

where

X

is a complete measure metric space. We present some properties of the integral, continuing the study’s use of a Radon measure

μ .

Finally, using locally finite measures, we extend the AP–Henstock–Kurzweil integral theory to second countable Hausdorff spaces that are locally compact. A Saks–Henstock-type Lemma is proved here. Full article

12 pages, 303 KiB

Open AccessArticle

On Hybrid Numbers with Gaussian Leonardo Coefficients

by Nagihan Kara and Fatih Yilmaz

Mathematics 2023, 11(6), 1551; https://doi.org/10.3390/math11061551 - 22 Mar 2023

Cited by 6 | Viewed by 1819

Abstract

We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid Gaussian Leonardo numbers and obtain some of their particular [...] Read more.

We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid Gaussian Leonardo numbers and obtain some of their particular properties. Furthermore, we define

n n

Hessenberg matrices whose permanents yield the Leonardo and Gaussian Leonardo sequences. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

17 pages, 371 KiB

Open AccessArticle

Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk

by Wei Wang, Qianyan Li, Quan Li and Song Xu

Mathematics 2023, 11(6), 1550; https://doi.org/10.3390/math11061550 - 22 Mar 2023

Cited by 1 | Viewed by 1667

Abstract

The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations [...] Read more.

The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations are first obtained through the robust stochastic optimal control theory. Then, we discuss the optimal investment problems before and after default, and the value functions and optimal investment strategies are obtained. Finally, we find that the optimal investment strategies of pre-default are affected by the intensity of default and the credit spread, and the investors cannot hold defaultable bonds in the post-default case. Numerical results also show that the exchange rate risk, default risk and ambiguity aversion have a great effect on the optimal investment strategies. Full article

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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27 pages, 418 KiB

Open AccessArticle

Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications

by Song-Nan Liu, Min-Qian Liu and Jin-Yu Yang

Mathematics 2023, 11(6), 1549; https://doi.org/10.3390/math11061549 - 22 Mar 2023

Cited by 3 | Viewed by 1401

Abstract

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special [...] Read more.

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on

s^{2} \times s

or

s \times s^{2}

grids, and most column pairs satisfy stratifications on

s^{2} \times s^{2}

grids. Moreover, many column pairs can achieve stratifications on

s^{4} \times s^{2}

and

s^{2} \times s^{4}

grids. Furthermore, the obtained space-filling ODs can have

s^{6}

levels,

s^{4}

levels, and mixed levels, as required for different needs. Full article

(This article belongs to the Special Issue Distribution Theory and Application)

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16 pages, 1187 KiB

Open AccessArticle

PGA: A New Hybrid PSO and GA Method for Task Scheduling with Deadline Constraints in Distributed Computing

by Kaili Shao, Ying Song and Bo Wang

Mathematics 2023, 11(6), 1548; https://doi.org/10.3390/math11061548 - 22 Mar 2023

Cited by 13 | Viewed by 2283

Abstract

Distributed computing, e.g., cluster and cloud computing, has been applied in almost all areas for data processing, while high resource efficiency and user satisfaction are still the ambition of distributed computing. Task scheduling is indispensable for achieving the goal. As the task scheduling [...] Read more.

Distributed computing, e.g., cluster and cloud computing, has been applied in almost all areas for data processing, while high resource efficiency and user satisfaction are still the ambition of distributed computing. Task scheduling is indispensable for achieving the goal. As the task scheduling problem is NP-hard, heuristics and meta-heuristics are frequently applied. Every method has its own advantages and limitations. Thus, in this paper, we designed a hybrid heuristic task scheduling problem by exploiting the high global search ability of the Genetic Algorithm (GA) and the fast convergence of Particle Swarm Optimization (PSO). Different from existing hybrid heuristic approaches that simply sequentially perform two or more algorithms, the PGA applies the evolutionary method of a GA and integrates self- and social cognitions into the evolution. We conduct extensive simulated environments for the performance evaluation, where simulation parameters are set referring to some recent related works. Experimental results show that the PGA has 27.9–65.4% and 33.8–69.6% better performance than several recent works, on average, in user satisfaction and resource efficiency, respectively. Full article

(This article belongs to the Topic Theory and Applications of High Performance Computing)

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15 pages, 315 KiB

Open AccessArticle

Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis

by Mohamed Kayid and Mansour Shrahili

Mathematics 2023, 11(6), 1547; https://doi.org/10.3390/math11061547 - 22 Mar 2023

Viewed by 1225

Abstract

In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for [...] Read more.

In this article, using the scaled (weighted) residual life variable, some scaled measures, the scaled mean residual life and the scaled hazard rate, are introduced. Several scales are considered as examples of the derivation of the scaled measures. The measures are developed for the case of a weighted residual life at a random time, and it is shown that the measures are scale-free in these cases. This property proves useful in situations where a relative comparison of the lifetime distribution is studied. Some characterization properties are derived in terms of scaled measures evaluated at some sequences of random time points that follow a typical distribution. Examples are used to illustrate, examine, and satisfy the obtained characterizations. Full article

(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)

17 pages, 608 KiB

Open AccessArticle

Privacy-Preserving Public Route Planning Based on Passenger Capacity

by Xin Zhang, Hua Zhang, Kaixuan Li and Qiaoyan Wen

Mathematics 2023, 11(6), 1546; https://doi.org/10.3390/math11061546 - 22 Mar 2023

Viewed by 1240

Abstract

Precise route planning needs huge amounts of trajectory data recorded in multimedia devices. The data, including each user’s location privacy, are stored as cipher text. The ability to plan routes on an encrypted trajectory database is an urgent necessity. In this paper, in [...] Read more.

Precise route planning needs huge amounts of trajectory data recorded in multimedia devices. The data, including each user’s location privacy, are stored as cipher text. The ability to plan routes on an encrypted trajectory database is an urgent necessity. In this paper, in order to plan a public route while protecting privacy, we design a hybrid encrypted random bloom filter (RBF) tree on encrypted databases, named the encrypted random bloom filter (eRBF) tree, which supports pruning and a secure, fast k nearest neighbor search. Based on the encrypted random bloom filter tree and secure computation of distance, we first propose a reverse k nearest neighbor trajectory search on encrypted databases (RkNNToE). It returns all transitions, in which each takes the query trajectory as one of its k nearest neighbor trajectories on the encrypted database. The results can be the indicator of a new route’s capacity in route planning. The security of the trajectory and query is proven via the simulation proof technique. When the number of points in the trajectory database and transition database are 1174 and 18,670, respectively, the time cost of an R2NNToE is about 1200 s. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods in Intelligent Multimedia: Security and Applications)

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25 pages, 2227 KiB

Open AccessArticle

Structural Analysis of Projected Networks of Shareholders and Stocks Based on the Data of Large Shareholders’ Shareholding in China’s Stocks

by Ruijie Liu and Yajing Huang

Mathematics 2023, 11(6), 1545; https://doi.org/10.3390/math11061545 - 22 Mar 2023

Cited by 2 | Viewed by 1449

Abstract

This paper establishes a shareholder-stock bipartite network based on the data of large shareholders’ shareholding in the Shanghai A-share market of China in 2021. Based on the shareholder-stock bipartite network, the statistically validated network model is applied to establish a shareholder projected network [...] Read more.

This paper establishes a shareholder-stock bipartite network based on the data of large shareholders’ shareholding in the Shanghai A-share market of China in 2021. Based on the shareholder-stock bipartite network, the statistically validated network model is applied to establish a shareholder projected network and a stock projected network, whose structural characteristics can intuitively reveal the overlapping portfolios among different shareholders, as well as shareholder allocation structures among different stocks. The degree of nodes in the shareholder projected network obeys the power law distribution, the network aggregation coefficient is large, while the degree of most nodes in the stock projected network is small and the network aggregation coefficient is low. Furthermore, the two projected networks’ community structures are analyzed, respectively. Most of the communities in the shareholder projected network and stock projected network are small-scaled, indicating that the majority of large shareholders hold different shares from each other, and the investment portfolios of large shareholders in different stocks are also significantly different. Finally, by comparing the stock projected sub-network obtained from the shareholder-stock bipartite sub-network in which the degree of shareholder nodes is 2 and the original stock projected network, the effectiveness of the statistically validated network model, and the community division method on the research of the shareholder-stock bipartite network are further verified. These results have important implications for understanding the investment behavior of large shareholders in the stock market and contribute to developing investment strategies and risk management practices. Full article

(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications)

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20 pages, 1070 KiB

Open AccessArticle

Fuzzy Method Based on the Removal Effects of Criteria (MEREC) for Determining Objective Weights in Multi-Criteria Decision-Making Problems

by Mohamad Shahiir Saidin, Lai Soon Lee, Siti Mahani Marjugi, Muhammad Zaini Ahmad and Hsin-Vonn Seow

Mathematics 2023, 11(6), 1544; https://doi.org/10.3390/math11061544 - 22 Mar 2023

Cited by 12 | Viewed by 2698

Abstract

In multi-criteria decision-making (MCDM) research, the criteria weights are crucial components that significantly impact the results. Many researchers have proposed numerous methods to establish the weights of the criterion. This paper provides a modified technique, the fuzzy method based on the removal effects [...] Read more.

In multi-criteria decision-making (MCDM) research, the criteria weights are crucial components that significantly impact the results. Many researchers have proposed numerous methods to establish the weights of the criterion. This paper provides a modified technique, the fuzzy method based on the removal effects of criteria (MEREC) by modifying the normalization technique and enhancing the logarithm function used to assess the entire performance of alternatives in the weighting process. Since MCDM problems intrinsically are ambiguous or complex, fuzzy theory is used to interpret the linguistic phrases into triangular fuzzy numbers. The comparative analyses were conducted through the case study of staff performance appraisal at a Malaysian academic institution and the simulation-based study is used to validate the effectiveness and stability of the presented method. The results of the fuzzy MEREC are compared with those from a few different objective weighting techniques based on the correlation coefficients, outlier tests and central processing unit (CPU) time. The results of the comparative analyses demonstrate that fuzzy MEREC weights are verified as the correlation coefficient values are consistent throughout the study. Furthermore, the simulation-based study demonstrates that even in the presence of outliers in the collection of alternatives, fuzzy MEREC is able to offer consistent weights for the criterion. The fuzzy MEREC also requires less CPU time compared to the existing MEREC techniques. Hence, the modified method is a suitable alternative and efficient for computing the objective criteria weights in the MCDM problems. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Making Methods and Their Applications)

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20 pages, 4208 KiB

Open AccessArticle

Research on Location Selection for Urban Networks of Less-than-Truckload Express Enterprises Based on Improved Immune Optimization Algorithm

by Kangye Tan, Fang Xu, Xiaozhao Fang and Chunsheng Li

Mathematics 2023, 11(6), 1543; https://doi.org/10.3390/math11061543 - 22 Mar 2023

Cited by 4 | Viewed by 2931

Abstract

With the transformation and upgrading of the world economy entering a new normal, changes in the fields of industry and consumption have brought new business opportunities, and there is a large space for the less-than-truckload (LTL) express market. Considering the urban network resource [...] Read more.

With the transformation and upgrading of the world economy entering a new normal, changes in the fields of industry and consumption have brought new business opportunities, and there is a large space for the less-than-truckload (LTL) express market. Considering the urban network resource operation status, this study aims to solve the optimization problem of urban location selection for LTL express under the common delivery model. To minimize the total cost of logistics and distribution, we established an integer programming model with constraints such as radiation range and service-capacity limitations. A model with a fixed reality-node strategy, an expanded initial antibody group strategy, improved traditional elite individual retention strategy and a node-clustering strategy was introduced. An improved immune optimization algorithm was further designed to obtain globally optimal solutions. With the comparison of existing algorithms, the results verified the practicability of the proposed model to solve the urban location-selection problems for LTL express. We then conducted an empirical analysis of a real-world enterprise’s reasonable urban network location selection in a central-south city of China. The simulation results further verified the effectiveness of our proposed algorithm. This study provides new solutions and methods for resource utilization and urban network optimization of LTL-express enterprises. Full article

(This article belongs to the Special Issue Uncertain System Optimization and Games)

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20 pages, 4456 KiB

Open AccessArticle

Optimized Cooperative Control of Error Port-Controlled Hamiltonian and Adaptive Backstepping Sliding Mode for a Multi-Joint Industrial Robot

by Xiaoyu Yang and Haisheng Yu

Mathematics 2023, 11(6), 1542; https://doi.org/10.3390/math11061542 - 22 Mar 2023

Cited by 2 | Viewed by 1388

Abstract

Robot joints driven by permanent magnet synchronous motors (PMSM) often cannot have both superior accuracy and rapidity when they track target signals. The robot joints have fine dynamic characteristics and poor steady-state characteristics when the signal controller is used, or they have fine [...] Read more.

Robot joints driven by permanent magnet synchronous motors (PMSM) often cannot have both superior accuracy and rapidity when they track target signals. The robot joints have fine dynamic characteristics and poor steady-state characteristics when the signal controller is used, or they have fine steady-state characteristics and poor dynamic characteristics when the energy controller is used. It is hard to make robot joints that have both superior dynamic and steady-state characteristics at once using a single control method. In order to solve this problem, the strategy of optimized cooperative control is proposed. First, an error port-controlled Hamiltonian (EPCH) energy controller and an adaptive backstepping sliding mode (ABSM) signal controller are designed. Second, an optimized cooperative control coefficient based on the position error of a robot joint is designed; this enables the system to switch smoothly between the EPCH energy controller and ABSM signal controller. Next, the strategy of optimized cooperative control is designed. In this way, robot systems can combine the advantages of the EPCH energy controller and the ABSM signal controller. Finally, simulation results demonstrate that using the strategy of optimized cooperative control gives robot joints outstanding control performance in terms of tracking accuracy and response rapidity. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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10 pages, 949 KiB

Open AccessArticle

Stability Analysis for a Class of Stochastic Differential Equations with Impulses

by Mingli Xia, Linna Liu, Jianyin Fang and Yicheng Zhang

Mathematics 2023, 11(6), 1541; https://doi.org/10.3390/math11061541 - 22 Mar 2023

Cited by 47 | Viewed by 2940

Abstract

This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via Lyapunov stability theory, bounded difference condition and martingale [...] Read more.

This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results show that the impulses can facilitate the stability of the stochastic differential equations when the original system is not stable. Finally, the feasibility of our results is confirmed by two numerical examples and their simulations. Full article

(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)

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19 pages, 2774 KiB

Open AccessArticle

Cooperative Control for Signalized Intersections in Intelligent Connected Vehicle Environments

by Anton Agafonov, Alexander Yumaganov and Vladislav Myasnikov

Mathematics 2023, 11(6), 1540; https://doi.org/10.3390/math11061540 - 22 Mar 2023

Cited by 6 | Viewed by 2194

Abstract

Cooperative control of vehicle trajectories and traffic signal phases is a promising approach to improving the efficiency and safety of transportation systems. This type of traffic flow control refers to the coordination and optimization of vehicle trajectories and traffic signal phases to reduce [...] Read more.

Cooperative control of vehicle trajectories and traffic signal phases is a promising approach to improving the efficiency and safety of transportation systems. This type of traffic flow control refers to the coordination and optimization of vehicle trajectories and traffic signal phases to reduce congestion, travel time, and fuel consumption. In this paper, we propose a cooperative control method that combines a model predictive control algorithm for adaptive traffic signal control and a trajectory construction algorithm. For traffic signal phase selection, the proposed modification of the adaptive traffic signal control algorithm combines the travel time obtained using either the vehicle trajectory or a deep neural network model and stop delays. The vehicle trajectory construction algorithm takes into account the predicted traffic signal phase to achieve cooperative control. To evaluate the method performance, numerical experiments have been conducted for three real-world scenarios in the SUMO simulation package. The experimental results show that the proposed cooperative control method can reduce the average fuel consumption by 1% to 4.2%, the average travel time by 1% to 5.3%, and the average stop delays to 27% for different simulation scenarios compared to the baseline methods. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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29 pages, 8015 KiB

Open AccessArticle

Station Layout Optimization and Route Selection of Urban Rail Transit Planning: A Case Study of Shanghai Pudong International Airport

by Pei Yin and Miaojuan Peng

Mathematics 2023, 11(6), 1539; https://doi.org/10.3390/math11061539 - 22 Mar 2023

Cited by 3 | Viewed by 2323

Abstract

In this paper, a cost-oriented optimization model of station spacing is presented to analyze the influencing factors of station spacing and layout near Shanghai Pudong International Airport. The Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm is used to cluster and [...] Read more.

In this paper, a cost-oriented optimization model of station spacing is presented to analyze the influencing factors of station spacing and layout near Shanghai Pudong International Airport. The Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm is used to cluster and analyze the high population density, and optimize the station layout in the southwest of Pudong International Airport. A spatial analysis of the land use and geological conditions in Pudong New Area is given. Combining the optimal station spacing, ideal location and spatial analysis, five routing schemes to Pudong International Airport are proposed. The DBSCAN and K-means algorithms are used to analyze the “PDIA-SL” dataset. The results show that the space complexity of the HDBSCAN is O(825), and the silhouette coefficient is 0.6043, which has obvious advantages over the results of DBSCAN and K-means. This paper combines urban rail transit planning with the HDBSCAN algorithm to present some suggestions and specific route plans for local governments to scientifically plan rail transit lines. Meanwhile, the research method of station layout, which integrates station spacing, ideal location and spatial analysis optimization, is pioneering and can provide a reference for developing rail transit in metropolises. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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17 pages, 1412 KiB

Open AccessArticle

Analysis and Recognition of Human Gait Activity Based on Multimodal Sensors

by Diego Teran-Pineda, Karl Thurnhofer-Hemsi and Enrique Dominguez

Mathematics 2023, 11(6), 1538; https://doi.org/10.3390/math11061538 - 22 Mar 2023

Cited by 5 | Viewed by 2565

Abstract

Remote health monitoring plays a significant role in research areas related to medicine, neurology, rehabilitation, and robotic systems. These applications include Human Activity Recognition (HAR) using wearable sensors, signal processing, mathematical methods, and machine learning to improve the accuracy of remote health monitoring [...] Read more.

Remote health monitoring plays a significant role in research areas related to medicine, neurology, rehabilitation, and robotic systems. These applications include Human Activity Recognition (HAR) using wearable sensors, signal processing, mathematical methods, and machine learning to improve the accuracy of remote health monitoring systems. To improve the detection and accuracy of human activity recognition, we create a novel method to reduce the complexities of extracting features using the HuGaDB dataset. Our model extracts power spectra; due to the high dimensionality of features, sliding windows techniques are used to determine frequency bandwidth automatically, where an improved QRS algorithm selects the first dominant spectrum amplitude. In addition, the bandwidth algorithm has been used to reduce the dimensionality of data, remove redundant dimensions, and improve feature extraction. In this work, we have considered widely used machine learning classifiers. Our proposed method was evaluated using the accelerometer angles spectrum installed in six parts of the body and then reducing the bandwidth to know the evolution. Our approach attains an accuracy rate of 95.1% in the HuGaDB dataset with 70% of bandwidth, outperforming others in the human activity recognition accuracy. Full article

(This article belongs to the Special Issue Mathematical Methods and Applications for Artificial Intelligence and Computer Vision)

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14 pages, 330 KiB

Open AccessArticle

An Adapted Multi-Objective Genetic Algorithm for Healthcare Supplier Selection Decision

by Marwa F. Mohamed, Mohamed Meselhy Eltoukhy, Khalil Al Ruqeishi and Ahmad Salah

Mathematics 2023, 11(6), 1537; https://doi.org/10.3390/math11061537 - 22 Mar 2023

Cited by 5 | Viewed by 1644

Abstract

With the advancement of information technology and economic globalization, the problem of supplier selection is gaining in popularity. The impact of supplier selection decisions made were quick and noteworthy on the healthcare profitability and total cost of medical equipment. Thus, there is an [...] Read more.

With the advancement of information technology and economic globalization, the problem of supplier selection is gaining in popularity. The impact of supplier selection decisions made were quick and noteworthy on the healthcare profitability and total cost of medical equipment. Thus, there is an urgent need for decision support systems that address the optimal healthcare supplier selection problem, as this problem is addressed by a limited number of studies. Those studies addressed this problem mathematically or by using meta-heuristics methods. The focus of this work is to advance the meta-heuristics methods by considering more objectives rather than the utilized objectives. In this context, the optimal supplier selection problem for healthcare equipment was formulated as a mathematical model to expose the required objectives and constraints for the sake of searching for the optimal suppliers. Subsequently, the problem is realized as a multi-objective problem, with the help of this proposed model. The model has three minimization objectives: (1) transportation cost; (2) delivery time; and (3) the number of damaged items. The proposed system includes realistic constraints such as device quality, usability, and service quality. The model also takes into account capacity limits for each supplier. Next, it is proposed to adapt the well-known non-dominated sorting genetic algorithm (NSGA)-III algorithm to choose the optimal suppliers. The results of the adapted NSGA-III have been compared with several heuristic algorithms and two meta-heuristic algorithms (i.e., particle swarm optimization and NSGA-II). The obtained results show that the adapted NSGA-III outperformed the methods of comparison. Full article

(This article belongs to the Section Mathematics and Computer Science)

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18 pages, 1326 KiB

Open AccessEditor’s ChoiceArticle

Facilitating Conditions as the Biggest Factor Influencing Elementary School Teachers’ Usage Behavior of Dynamic Mathematics Software in China

by Zhiqiang Yuan, Jing Liu, Xi Deng, Tianzi Ding and Tommy Tanu Wijaya

Mathematics 2023, 11(6), 1536; https://doi.org/10.3390/math11061536 - 22 Mar 2023

Cited by 12 | Viewed by 3251

Abstract

Dynamic mathematics software, such as GeoGebra, is one of the most important teaching and learning media. This kind of software can help teachers teach mathematics, especially geometry, at the elementary school level. However, the use of dynamic mathematics software of elementary school teachers [...] Read more.

Dynamic mathematics software, such as GeoGebra, is one of the most important teaching and learning media. This kind of software can help teachers teach mathematics, especially geometry, at the elementary school level. However, the use of dynamic mathematics software of elementary school teachers is still very limited so far. This study analyzed the factors influencing elementary school teachers’ usage behavior of dynamic mathematics software. Four independent variables, namely performance expectancy (PE), effort expectancy (EE), social influence (SI), and facilitating conditions (FC) from the united theory of acceptance and use of technology (UTAUT), were used to understand elementary school teachers’ usage behavior of dynamic mathematics software. A questionnaire survey was conducted in the Hunan and Guangdong provinces of China. Two hundred and sixty-six elementary school mathematics teachers provided valid questionnaire data. The partial least squares structural equation modeling (PLS-SEM) approach was used to analyze the data. The results showed that facilitating conditions and effort expectancy significantly affect elementary school teachers’ usage behavior of dynamic mathematics software, and facilitating conditions were the biggest factor that affected user behavior. The moderating effects of gender, major, and training on all relationships in the dynamic mathematics software usage conceptual model were not significant. This study contributes by developing a model and providing new knowledge to elementary school principals and the government about factors that can increase the adoption of dynamic mathematics software. Full article

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8 pages, 486 KiB

Open AccessArticle

Solving SIVPs of Lane–Emden–Fowler Type Using a Pair of Optimized Nyström Methods with a Variable Step Size

by Mufutau Ajani Rufai and Higinio Ramos

Mathematics 2023, 11(6), 1535; https://doi.org/10.3390/math11061535 - 22 Mar 2023

Cited by 5 | Viewed by 1557

Abstract

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair of hybrid block methods with a variable step-size mode. The method pairs an optimized Nyström technique with a set of formulas applied [...] Read more.

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair of hybrid block methods with a variable step-size mode. The method pairs an optimized Nyström technique with a set of formulas applied at the initial step to circumvent the singularity at the beginning of the interval. The variable step-size formulation is implemented using an embedded-type approach, resulting in an efficient technique that outperforms its counterpart methods that used fixed step-size implementation. The numerical simulations confirm the better performance of the variable step-size implementation. Full article

(This article belongs to the Special Issue Numerical Methods for Solving Differential Problems-II)

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7 pages, 219 KiB

Open AccessArticle

Approximate Solutions of a Fixed-Point Problem with an Algorithm Based on Unions of Nonexpansive Mappings

by Alexander J. Zaslavski

Mathematics 2023, 11(6), 1534; https://doi.org/10.3390/math11061534 - 22 Mar 2023

Cited by 1 | Viewed by 1199

Abstract

In this paper, we study a fixed-point problem with a set-valued mapping by using an algorithm based on unions of nonexpansive mappings. We show that an approximate solution is reached after a finite number of iterations in the presence of computational errors. This [...] Read more.

In this paper, we study a fixed-point problem with a set-valued mapping by using an algorithm based on unions of nonexpansive mappings. We show that an approximate solution is reached after a finite number of iterations in the presence of computational errors. This result is an extension of the results known in the literature. Full article

9 pages, 252 KiB

Open AccessArticle

Geodesics and Translation Curves in

{Sol}_{0}^{4}

by Zlatko Erjavec

Mathematics 2023, 11(6), 1533; https://doi.org/10.3390/math11061533 - 22 Mar 2023

Cited by 2 | Viewed by 1243

Abstract

A translation curve in a Thurston space is a curve such that for given unit vector at the origin, the translation of this vector is tangent to the curve in every point of the curve. In most Thurston spaces, translation curves coincide with [...] Read more.

A translation curve in a Thurston space is a curve such that for given unit vector at the origin, the translation of this vector is tangent to the curve in every point of the curve. In most Thurston spaces, translation curves coincide with geodesic lines. However, this does not hold for Thurston spaces equipped with twisted product. In these spaces, translation curves seem more intuitive and simpler than geodesics. In this paper, geodesics and translation curves in

{Sol}_{0}^{4}

space are classified and the curvature properties of translation curves are investigated. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

13 pages, 270 KiB

Open AccessArticle

On a Conjecture of Cai–Zhang–Shen for Figurate Primes

by Junli Zhang and Pengcheng Niu

Mathematics 2023, 11(6), 1532; https://doi.org/10.3390/math11061532 - 22 Mar 2023

Cited by 3 | Viewed by 955

Abstract

A conjecture of Cai–Zhang–Shen for figurate primes says that every integer

k > 1

is the sum of two figurate primes. In this paper, we give an equivalent proposition to the conjecture. By considering extreme value problems with constraints about the conjecture in [...] Read more.

A conjecture of Cai–Zhang–Shen for figurate primes says that every integer

k > 1

is the sum of two figurate primes. In this paper, we give an equivalent proposition to the conjecture. By considering extreme value problems with constraints about the conjecture in the cases of odd and even integers and using the method of Lagrange multipliers, the Cardano formula for cubic equations, and the contradiction, we prove the conjecture. Full article

24 pages, 786 KiB

Open AccessArticle

Estimation of Fixed Effects Partially Linear Varying Coefficient Panel Data Regression Model with Nonseparable Space-Time Filters

by Bogui Li, Jianbao Chen and Shuangshuang Li

Mathematics 2023, 11(6), 1531; https://doi.org/10.3390/math11061531 - 21 Mar 2023

Cited by 3 | Viewed by 1722

Abstract

Space-time panel data widely exist in many research fields such as economics, management, geography and environmental science. It is of interest to study the relationship between response variable and regressors which come from above fields by establishing regression models. This paper introduces a [...] Read more.

Space-time panel data widely exist in many research fields such as economics, management, geography and environmental science. It is of interest to study the relationship between response variable and regressors which come from above fields by establishing regression models. This paper introduces a new fixed effects partially linear varying coefficient panel data regression model with nonseparable space-time filters. On the basis of approximating the varying coefficient functions with a powerful B-spline method, the profile quasi-maximum likelihood estimators of parameters and varying coefficient functions are constructed. Under some regular conditions, we derive their consistency and asymptotic normality. Monte Carlo simulation shows that our estimates have good finite performance and ignoring spatial and serial correlations may lead to inefficiency of estimates. Finally, the driving forces of Chinese resident consumption rate are studied using our estimation method. Full article

(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)

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Mathematics, Volume 11, Issue 6 (March-2 2023) – 284 articles

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