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Mathematics, Volume 9, Issue 20 (October-2 2021) – 110 articles

Cover Story (view full-size image): The introduction of a fuzzy set concept by Lotfi A. Zadeh in 1965 did not suggest the extraordinary evolution that followed. Used in various branches of science and technique, the concept was also embedded by mathematicians. Geometric function theory used the notion of a fuzzy set introducing the concept of fuzzy differential subordination. Fuzzy differential subordinations are obtained in this paper, and their fuzzy best dominants facilitate stating sufficient conditions for univalence of a new hypergeometric integral operator defined here using confluent hypergeometric function, having as inspiration an operator studied by Miller, Mocanu, and Reade. Applications in real life or in other scientific domains of the theory of fuzzy differential subordination are subjects for future investigation. View this paper
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Article
On K-Means Clustering with IVIF Datasets for Post-COVID-19 Recovery Efforts
Mathematics 2021, 9(20), 2639; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202639 - 19 Oct 2021
Viewed by 432
Abstract
The recovery efforts of the tourism and hospitality sector are compromised by the emergence of COVID-19 variants that can escape vaccines. Thus, maintaining non-pharmaceutical measures amidst massive vaccine rollouts is still relevant. The previous works which categorize tourist sites and restaurants according to [...] Read more.
The recovery efforts of the tourism and hospitality sector are compromised by the emergence of COVID-19 variants that can escape vaccines. Thus, maintaining non-pharmaceutical measures amidst massive vaccine rollouts is still relevant. The previous works which categorize tourist sites and restaurants according to the perceived degree of tourists’ and customers’ exposure to COVID-19 are deemed relevant for sectoral recovery. Due to the subjectivity of predetermining categories, along with the failure of capturing vagueness and uncertainty in the evaluation process, this work explores the use k-means clustering with dataset values expressed as interval-valued intuitionistic fuzzy sets. In addition, the proposed method allows for the incorporation of criteria (or attribute) weights into the dataset, often not considered in traditional k-means clustering but relevant in clustering problems with attributes having varying priorities. Two previously reported case studies were analyzed to demonstrate the proposed approach, and comparative and sensitivity analyses were performed. Results show that the priorities of the criteria in evaluating tourist sites remain the same. However, in evaluating restaurants, customers put emphasis on the physical characteristics of the restaurants. The proposed approach assigns 12, 15, and eight sites to the “low exposure”, “moderate exposure”, and “high exposure” cluster, respectively, each with distinct characteristics. On the other hand, 16 restaurants are assigned “low exposure”, 16 to “moderate exposure”, and eight to “high exposure” clusters, also with distinct characteristics. The characteristics described in the clusters offer meaningful insights for sectoral recovery efforts. Findings also show that the proposed approach is robust to small parameter changes. Although idiosyncrasies exist in the results of both case studies, considering the characteristics of the resulting clusters, tourists or customers could evaluate any tourist site or restaurant according to their perceived exposure to COVID-19. Full article
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Article
The Proof of a Conjecture Related to Divisibility Properties of z(n)
Mathematics 2021, 9(20), 2638; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202638 - 19 Oct 2021
Cited by 1 | Viewed by 249
Abstract
The order of appearance of n (in the Fibonacci sequence) z(n) is defined as the smallest positive integer k for which n divides the k—the Fibonacci number Fk. Very recently, Trojovský proved that z(n) [...] Read more.
The order of appearance of n (in the Fibonacci sequence) z(n) is defined as the smallest positive integer k for which n divides the k—the Fibonacci number Fk. Very recently, Trojovský proved that z(n) is an even number for almost all positive integers n (in the natural density sense). Moreover, he conjectured that the same is valid for the set of integers n1 for which the integer 4 divides z(n). In this paper, among other things, we prove that for any k1, the number z(n) is divisible by 2k for almost all positive integers n (in particular, we confirm Trojovský’s conjecture). Full article
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics and Number Theory II)
Article
On Graded S-Primary Ideals
Mathematics 2021, 9(20), 2637; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202637 - 19 Oct 2021
Viewed by 241
Abstract
Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that PS=. In this article, we introduce the concept of [...] Read more.
Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that PS=. In this article, we introduce the concept of graded S-primary ideals which is a generalization of graded primary ideals. We say that P is a graded S-primary ideal of R if there exists sS such that for all x,yh(R), if xyP, then sxP or syGrad(P) (the graded radical of P). We investigate some basic properties of graded S-primary ideals. Full article
(This article belongs to the Section Algebra and Geometry)
Article
An Application of Neutrosophic Set to Relative Importance Assignment in AHP
Mathematics 2021, 9(20), 2636; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202636 - 19 Oct 2021
Viewed by 311
Abstract
The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a [...] Read more.
The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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Article
Extended Kung–Traub Methods for Solving Equations with Applications
Mathematics 2021, 9(20), 2635; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202635 - 19 Oct 2021
Viewed by 316
Abstract
Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of [...] Read more.
Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of it to functions that are at least five times differentiable, although the methods may converge. As far as we know, no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided difference, which appear in the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study. Full article
(This article belongs to the Special Issue Application of Iterative Methods for Solving Nonlinear Equations)
Review
Nature-Inspired Metaheuristic Techniques for Combinatorial Optimization Problems: Overview and Recent Advances
Mathematics 2021, 9(20), 2633; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202633 - 19 Oct 2021
Viewed by 490
Abstract
Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have [...] Read more.
Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have been evolved and modified with respect to the problem nature since it was recommended for the first time. As there is a growing interest in incorporating necessary methods to develop metaheuristics, there is a need to rediscover the recent advancement of metaheuristics in combinatorial optimization. From the authors’ point of view, there is still a lack of comprehensive surveys on current research directions. Therefore, a substantial part of this paper is devoted to analyzing and discussing the modern age metaheuristic algorithms that gained popular use in mostly cited combinatorial optimization problems such as vehicle routing problems, traveling salesman problems, and supply chain network design problems. A survey of seven different metaheuristic algorithms (which are proposed after 2000) for combinatorial optimization problems is carried out in this study, apart from conventional metaheuristics like simulated annealing, particle swarm optimization, and tabu search. These metaheuristics have been filtered through some key factors like easy parameter handling, the scope of hybridization as well as performance efficiency. In this study, a concise description of the framework of the selected algorithm is included. Finally, a technical analysis of the recent trends of implementation is discussed, along with the impacts of algorithm modification on performance, constraint handling strategy, the handling of multi-objective situations using hybridization, and future research opportunities. Full article
(This article belongs to the Special Issue Optimization for Decision Making III)
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Article
Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces
Mathematics 2021, 9(20), 2632; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202632 - 19 Oct 2021
Viewed by 250
Abstract
We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft [...] Read more.
We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addition, we give a decomposition of soft ωp-open sets in terms of soft open sets and soft ω-dense sets. Moreover, we study the correspondence between the soft topology soft ωp-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ωp-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ωp-continuity. Finally, we study several relationships related to soft ωp-continuity. Full article
(This article belongs to the Special Issue Fuzzy Topology)
Article
Predicting the Traffic Capacity of an Intersection Using Fuzzy Logic and Computer Vision
Mathematics 2021, 9(20), 2631; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202631 - 18 Oct 2021
Viewed by 322
Abstract
This paper presents the application of simulation to assess and predict the influence of random factors of pedestrian flow and its continuity on the traffic capacity of a signal-controlled intersection during a right turn. The data were collected from the surveillance cameras of [...] Read more.
This paper presents the application of simulation to assess and predict the influence of random factors of pedestrian flow and its continuity on the traffic capacity of a signal-controlled intersection during a right turn. The data were collected from the surveillance cameras of 25 signal-controlled intersections in the city of Chelyabinsk, Russia, and interpreted by a neural network. We considered the influence of both the intensity of the pedestrian flow and its continuity on the traffic capacity of a signal-controlled intersection in the stochastic approach, provided that the flow of vehicles is redundant. We used a reasonably minimized regression model as the basis for our intersection models. At the first stage, we obtained and tested a simulated continuous-stochastic intersection model that accounts for the dynamics of traffic flow. The second approach, due to the unpredictability of pedestrian flow, used a relevant method for analysing traffic flows based on the fuzzy logic theory. The second was also used as the foundation to build and graphically demonstrate a computer model in the fuzzy TECH suite for predictive visualization of the values of a traffic flow crossing a signal-controlled intersection. The results of this study can contribute to understanding the real conditions at a signal-controlled intersection and making grounded decisions on its focused control. Full article
(This article belongs to the Special Issue Intelligent Computing in Industry Applications)
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Article
Dynamic Influence Ranking Algorithm Based on Musicians’ Social and Personal Information Network
Mathematics 2021, 9(20), 2630; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202630 - 18 Oct 2021
Viewed by 258
Abstract
Social influence analysis is a very popular research direction. This article analyzes the social network of musicians and the many influencing factors when musicians create music to rank the influence of musicians. In order to achieve the practical purpose of the model making [...] Read more.
Social influence analysis is a very popular research direction. This article analyzes the social network of musicians and the many influencing factors when musicians create music to rank the influence of musicians. In order to achieve the practical purpose of the model making accurate predictions in the broad music market, the algorithm adopts a macromodel and considers the social network topology network. The article adds the time decay function and the weight of genre influence to the traditional PageRank algorithm, and thus, the MRGT (Musician Ranking based on Genre and Time) algorithm appears. Considering the timeliness of social networks and the continuous development of music, we realized the importance of evolving MRGT into a dynamic social network. Therefore, we adopted audio data analysis technology and used Gaussian distance to classify and study the evolution of music properties at different times and different genres and finally formed the dynamic influence ranking algorithm based on musicians’ social and personal information networks. As a macromodel heuristic algorithm, our model is explanatory, can handle batch data and can avoid unfavorable factors, so as to provide fast speed and improved accuracy. The network can obtain an era indicator DMI (Dynamic Music Influence) that measures the degree of music revolution. DMI is the indicator we provide for music companies to invest in musicians. Full article
(This article belongs to the Section Mathematics and Computer Science)
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Article
Chaos on Fuzzy Dynamical Systems
Mathematics 2021, 9(20), 2629; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202629 - 18 Oct 2021
Viewed by 298
Abstract
Given a continuous map f:XX on a metric space, it induces the maps f¯:K(X)K(X), on the hyperspace of nonempty compact subspaces of X, and [...] Read more.
Given a continuous map f:XX on a metric space, it induces the maps f¯:K(X)K(X), on the hyperspace of nonempty compact subspaces of X, and f^:F(X)F(X), on the space of normal fuzzy sets, consisting of the upper semicontinuous functions u:X[0,1] with compact support. Each of these spaces can be endowed with a respective metric. In this work, we studied the relationships among the dynamical systems (X,f), (K(X),f¯), and (F(X),f^). In particular, we considered several dynamical properties related to chaos: Devaney chaos, A-transitivity, Li–Yorke chaos, and distributional chaos, extending some results in work by Jardón, Sánchez and Sanchis (Mathematics 2020, 8, 1862) and work by Bernardes, Peris and Rodenas (Integr. Equ. Oper. Theory 2017, 88, 451–463). Especial attention is given to the dynamics of (continuous and linear) operators on metrizable topological vector spaces (linear dynamics). Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods)
Article
A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme
Mathematics 2021, 9(20), 2628; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202628 - 18 Oct 2021
Viewed by 262
Abstract
In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized [...] Read more.
In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons. Full article
(This article belongs to the Special Issue Spline Functions and Applications)
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Article
An Intelligent Metaheuristic Binary Pigeon Optimization-Based Feature Selection and Big Data Classification in a MapReduce Environment
Mathematics 2021, 9(20), 2627; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202627 - 18 Oct 2021
Viewed by 264
Abstract
Big Data are highly effective for systematically extracting and analyzing massive data. It can be useful to manage data proficiently over the conventional data handling approaches. Recently, several schemes have been developed for handling big datasets with several features. At the same time, [...] Read more.
Big Data are highly effective for systematically extracting and analyzing massive data. It can be useful to manage data proficiently over the conventional data handling approaches. Recently, several schemes have been developed for handling big datasets with several features. At the same time, feature selection (FS) methodologies intend to eliminate repetitive, noisy, and unwanted features that degrade the classifier results. Since conventional methods have failed to attain scalability under massive data, the design of new Big Data classification models is essential. In this aspect, this study focuses on the design of metaheuristic optimization based on big data classification in a MapReduce (MOBDC-MR) environment. The MOBDC-MR technique aims to choose optimal features and effectively classify big data. In addition, the MOBDC-MR technique involves the design of a binary pigeon optimization algorithm (BPOA)-based FS technique to reduce the complexity and increase the accuracy. Beetle antenna search (BAS) with long short-term memory (LSTM) model is employed for big data classification. The presented MOBDC-MR technique has been realized on Hadoop with the MapReduce programming model. The effective performance of the MOBDC-MR technique was validated using a benchmark dataset and the results were investigated under several measures. The MOBDC-MR technique demonstrated promising performance over the other existing techniques under different dimensions. Full article
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Article
A Hybrid Spherical Fuzzy MCDM Approach to Prioritize Governmental Intervention Strategies against the COVID-19 Pandemic: A Case Study from Vietnam
Mathematics 2021, 9(20), 2626; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202626 - 18 Oct 2021
Viewed by 380
Abstract
The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, [...] Read more.
The unprecedented coronavirus pandemic (COVID-19) is fluctuating worldwide. Since the COVID-19 epidemic has a negative impact on all countries and has become a significant threat, it is necessary to determine the most effective strategy for governments by considering a variety of criteria; however, few studies in the literature can assist governments in this topic. Selective governmental intervention during the COVID-19 outbreak is considered a Multi-Criteria Decision-Making (MCDM) problem under a vague and uncertain environment when governments and medical communities adjust their priorities in response to rising issues and the efficacy of interventions applied in various nations. In this study, a novel hybrid Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Fuzzy Weighted Aggregated Sum Product Assessment (WASPAS-F) model is proposed to help stakeholders such as governors and policymakers to prioritize governmental interventions for dealing with the COVID-19 outbreak. The SF-AHP is implemented to measure the significance of the criteria, while the WASPAS-F approach is deployed to rank intervention alternatives. An empirical case study is conducted in Vietnam. From the SF-AHP findings, the criteria of “effectiveness in preventing the spread of COVID-19”, “ease of implementation”, and “high acceptability to citizens” were recognized as the most important criteria. As for the ranking of strategies, “vaccinations”, “enhanced control of the country’s health resources”, “common health testing”, “formation of an emergency response team”, and “quarantining patients and those suspected of infection” are the top five strategies. Aside from that, the robustness of the approach was tested by performing a comparative analysis. The results illustrate that the applied methods reach the general best strategy rankings. The applied methodology and its analysis will provide insight to authorities for fighting against the severe pandemic in the long run. It may aid in solving many complicated challenges in government strategy selection and assessment. It is also a flexible design model for considering the evaluation criteria. Finally, this research provides valuable guidance for policymakers in other nations. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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Article
Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons
Mathematics 2021, 9(20), 2625; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202625 - 18 Oct 2021
Viewed by 173
Abstract
An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is [...] Read more.
An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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Article
Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems
Mathematics 2021, 9(20), 2624; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202624 - 18 Oct 2021
Viewed by 331
Abstract
The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during [...] Read more.
The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value. Full article
(This article belongs to the Special Issue Distributed Computer and Communication Networks)
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Article
Pricing and Channel Coordination in Online-to-Offline Supply Chain Considering Corporate Environmental Responsibility and Lateral Inventory Transshipment
Mathematics 2021, 9(20), 2623; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202623 - 18 Oct 2021
Viewed by 253
Abstract
In this study, we investigate pricing policy and coordination conditions in an online-to-offline supply chain considering corporate environmental responsibility and lateral inventory transshipment. First, we provide demand functions to capture effects of price, corporate environmental responsibility level, and preference degree of the consumer [...] Read more.
In this study, we investigate pricing policy and coordination conditions in an online-to-offline supply chain considering corporate environmental responsibility and lateral inventory transshipment. First, we provide demand functions to capture effects of price, corporate environmental responsibility level, and preference degree of the consumer to online channel. Then, we build profit functions and develop three joint pricing and corporate environmental responsibility-level decision models for centralized decision (Scenario CD), retailer Stackelberg game (Scenario RS), and manufacturer Stackelberg game (Scenario MS). Furthermore, we determine the optimal decision policies by solving developed models, and conduct sensitivity analysis of significant factors. Finally, we use a revenue-sharing contract to realize supply chain coordination and find coordination conditions for Scenario RS and MS, and further show the impacts of revenue-sharing rate and investment cost sensitivity on the conditions using numerical studies. We find that optimal joint decision policies can be affected by significant factors to a varying degree. In certain conditions, the revenue-sharing contract can coordinate online-to-offline supply chains considering corporate environmental responsibility and lateral inventory transshipment. Our study proposes a new decision problem, constructs new joint decision models, determines new optimal joint policies, conducts new coordination analysis, and thus contributes to the research on supply chain operations considering corporate environmental responsibility and lateral inventory transshipment. Full article
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Article
Comparable Studies of Financial Bankruptcy Prediction Using Advanced Hybrid Intelligent Classification Models to Provide Early Warning in the Electronics Industry
Mathematics 2021, 9(20), 2622; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202622 - 18 Oct 2021
Viewed by 299
Abstract
In recent years in Taiwan, scholars who study financial bankruptcy have mostly focused on individual listed and over-the-counter (OTC) industries or the entire industry, while few have studied the independent electronics industry. Thus, this study investigated the application of an advanced hybrid Z-score [...] Read more.
In recent years in Taiwan, scholars who study financial bankruptcy have mostly focused on individual listed and over-the-counter (OTC) industries or the entire industry, while few have studied the independent electronics industry. Thus, this study investigated the application of an advanced hybrid Z-score bankruptcy prediction model in selecting financial ratios of listed companies in eight related electronics industries (semiconductor, computer, and peripherals, photoelectric, communication network, electronic components, electronic channel, information service, and other electronics industries) using data from 2000 to 2019. Based on 22 financial ratios of condition attributes and one decision attribute recommended and selected by experts and in the literature, this study used five classifiers for binary logistic regression analysis and in the decision tree. The experimental results show that for the Z-score model, samples analyzed using the five classifiers in five groups (1:1–5:1) of different ratios of companies, the bagging classifier scores are worse (40.82%) than when no feature selection method is used, while the logistic regression classifier and decision tree classifier (J48) result in better scores. However, it is significant that the bagging classifier score improved to over 90% after using the feature selection technique. In conclusion, it was found that the feature selection method can be effectively applied to improve the prediction accuracy, and three financial ratios (the liquidity ratio, debt ratio, and fixed assets turnover ratio) are identified as being the most important determinants affecting the prediction of financial bankruptcy in providing a useful reference for interested parties to evaluate capital allocation to avoid high investment risks. Full article
(This article belongs to the Special Issue Data Analysis and Domain Knowledge)
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Article
A Self-Learning Based Preference Model for Portfolio Optimization
Mathematics 2021, 9(20), 2621; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202621 - 17 Oct 2021
Viewed by 397
Abstract
An investment in a portfolio can not only guarantee returns but can also effectively control risk factors. Portfolio optimization is a multi-objective optimization problem. In order to better assist a decision maker to obtain his/her preferred investment solution, an interactive multi-criterion decision making [...] Read more.
An investment in a portfolio can not only guarantee returns but can also effectively control risk factors. Portfolio optimization is a multi-objective optimization problem. In order to better assist a decision maker to obtain his/her preferred investment solution, an interactive multi-criterion decision making system (MV-IMCDM) is designed for the Mean-Variance (MV) model of the portfolio optimization problem. Considering the flexibility requirement of a preference model that provides a guiding role in MV-IMCDM, a self-learning based preference model DT-PM (decision tree-preference model) is constructed. Compared with the present function based preference model, the DT-PM fully considers a decision maker’s bounded rationality. It does not require an assumption that the decision maker’s preference structure and preference change are known a priori and can be automatically generated and completely updated by learning from the decision maker’s preference feedback. Experimental results of a comparison show that, in the case that the decision maker’s preference structure and preference change are unknown a priori, the performances of guidance and fitness of the DT-PM are remarkably superior to function based preference models; in the case that the decision maker’s preference structure is known a priori, the performances of guidance and fitness of the DT-PM is approximated to the predefined function based model. It can be concluded that the DT-PM can agree with the preference ambiguity and the variability of a decision maker with bounded rationality and be applied more widely in a real decision system. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making and Data Mining)
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Article
Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission
Mathematics 2021, 9(20), 2620; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202620 - 17 Oct 2021
Viewed by 341
Abstract
This paper proposes a code defined on a finite ring pM, where pM = 2m1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence [...] Read more.
This paper proposes a code defined on a finite ring pM, where pM = 2m1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,, ±2m1. The elements of E correspond to the weights of binary error patterns that can be corrected, with the bidirectional single-bit error being the representative that occurs the most. The splitting set splits the code-word into sub-words, which inspired the name splitting code. Each sub-word, provided with auxiliary control symbols that are a byproduct of the coding procedure, corrects a single symbol error. The code can be defined, with some constraints, for general Mersenne numbers as well, while the multiplier set can be adjusted for adjacent binary errors correction. The application proposed for this code is a hybrid three-stage incremental ARQ procedure that transmits the code-word in the first stage, auxiliary control symbols in the second stage, and retransmits the sub-words detected as incorrect in the third stage. At each stage, error correction can be turned on or off, keeping both the retransmission rate and residual error rate at a low level. Full article
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Article
A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems
Mathematics 2021, 9(20), 2619; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202619 - 17 Oct 2021
Viewed by 238
Abstract
In this paper, we introduce a new iterative method using an inertial technique for approximating a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space. The proposed method’s weak convergence theorem was established under some suitable conditions. Furthermore, [...] Read more.
In this paper, we introduce a new iterative method using an inertial technique for approximating a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space. The proposed method’s weak convergence theorem was established under some suitable conditions. Furthermore, we applied our main results to solve convex minimization problems and image restoration problems. Full article
(This article belongs to the Special Issue Functional Inequalities and Equations)
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Article
BVPs Codes for Solving Optimal Control Problems
Mathematics 2021, 9(20), 2618; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202618 - 17 Oct 2021
Viewed by 254
Abstract
Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Value Problems (BVPs). In this paper, we review [...] Read more.
Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Value Problems (BVPs). In this paper, we review some general-purpose codes for the solution of BVPs and we show their efficiency in solving some challenging optimal control problems. Full article
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Article
Solvability and Stability of the Inverse Problem for the Quadratic Differential Pencil
Mathematics 2021, 9(20), 2617; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202617 - 17 Oct 2021
Viewed by 384
Abstract
The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local solvability and stability. The problem is considered in the general [...] Read more.
The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local solvability and stability. The problem is considered in the general case of complex-valued pencil coefficients and arbitrary eigenvalue multiplicities. Studying local solvability and stability, we take the possible splitting of multiple eigenvalues under a small perturbation of the spectrum into account. Our approach is constructive. It is based on the reduction of the non-linear inverse problem to a linear equation in the Banach space of infinite sequences. The theoretical results are illustrated by numerical examples. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
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Article
Cancer Cell Profiling Using Image Moments and Neural Networks with Model Agnostic Explainability: A Case Study of Breast Cancer Histopathological (BreakHis) Database
Mathematics 2021, 9(20), 2616; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202616 - 17 Oct 2021
Viewed by 499
Abstract
With the evolution of modern digital pathology, examining cancer cell tissues has paved the way to quantify subtle symptoms, for example, by means of image staining procedures using Eosin and Hematoxylin. Cancer tissues in the case of breast and lung cancer are quite [...] Read more.
With the evolution of modern digital pathology, examining cancer cell tissues has paved the way to quantify subtle symptoms, for example, by means of image staining procedures using Eosin and Hematoxylin. Cancer tissues in the case of breast and lung cancer are quite challenging to examine by manual expert analysis of patients suffering from cancer. Merely relying on the observable characteristics by histopathologists for cell profiling may under-constrain the scale and diagnostic quality due to tedious repetition with constant concentration. Thus, automatic analysis of cancer cells has been proposed with algorithmic and soft-computing techniques to leverage speed and reliability. The paper’s novelty lies in the utility of Zernike image moments to extract complex features from cancer cell images and using simple neural networks for classification, followed by explainability on the test results using the Local Interpretable Model-Agnostic Explanations (LIME) technique and Explainable Artificial Intelligence (XAI). The general workflow of the proposed high throughput strategy involves acquiring the BreakHis public dataset, which consists of microscopic images, followed by the application of image processing and machine learning techniques. The recommended technique has been mathematically substantiated and compared with the state-of-the-art to justify the empirical basis in the pursuit of our algorithmic discovery. The proposed system is able to classify malignant and benign cancer cell images of 40× resolution with 100% recognition rate. XAI interprets and reasons the test results obtained from the machine learning model, making it reliable and transparent for analysis and parameter tuning. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Artificial Intelligence)
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Article
Multi-Criteria Analysis for Business Location Decisions
Mathematics 2021, 9(20), 2615; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202615 - 17 Oct 2021
Cited by 1 | Viewed by 404
Abstract
Choosing the physical place in which to locate a company or make investments is a strategic decision that managers must make when their business activities begin and as they expand. These decisions are key to firms’ survival. This study sought to shed light [...] Read more.
Choosing the physical place in which to locate a company or make investments is a strategic decision that managers must make when their business activities begin and as they expand. These decisions are key to firms’ survival. This study sought to shed light on this decision problem and assist managers in making these decisions. The first research objective was to examine the different dimensions that decision makers should consider regarding locations. The second objective was to test the efficacy of multi-criteria analysis methods regarding this decision problem. More specifically, this study applied a combination of the preference ranking organization method for enrichment of evaluations and the geometric analysis for interactive aid method, complemented by the analytical hierarchy process. The last objective was to rank major European cities on their suitability as business locations. The results include a preferential ranking of 66 European cities. London is the best positioned in all dimensions, followed by Paris and Barcelona. The findings’ originality comes from the inclusion of dimensions such as climate, security, and technology, which are given little weight in other similar indices, as well as the fresh approach to this decision problem from a business perspective and the combination of methodologies. Full article
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Article
The Impact of Electronic Money on Monetary Policy: Based on DSGE Model Simulations
Mathematics 2021, 9(20), 2614; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202614 - 17 Oct 2021
Viewed by 398
Abstract
Starting with the interactive relationship between electronic money and household consumption stimuli, this paper deeply analyzes the changes in the behavior of each monetary subject under the impact of electronic money, and establishes a DSGE model based on the three economic sectors of [...] Read more.
Starting with the interactive relationship between electronic money and household consumption stimuli, this paper deeply analyzes the changes in the behavior of each monetary subject under the impact of electronic money, and establishes a DSGE model based on the three economic sectors of family, commercial bank and central bank under the New Keynesian framework. On this basis, the impact of electronic money on savings, loans, output and the interest rate, and its impact on monetary policy, are described by numerical simulation. The simulation results show that: (1) electronic money has asymmetric effects on savings and loans, but an irrational deviation on households; (2) the influence of electronic money on the interest rate has a reverse effect, and the “inverse adjustment” of the interest rate increases the management difficulty of the micro subject to a certain extent, and affects the effectiveness of monetary policy; (3) the regulatory effect of price monetary policy is better than that of quantitative monetary policy, and electronic money has the effect of its risk restraining impact. Finally, based on the analysis, this paper gives policy recommendations. Full article
(This article belongs to the Special Issue Statistical Methods in Economics)
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Article
INF-GAN: Generative Adversarial Network for Illumination Normalization of Finger-Vein Images
Mathematics 2021, 9(20), 2613; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202613 - 17 Oct 2021
Viewed by 383
Abstract
When images are acquired for finger-vein recognition, images with nonuniformity of illumination are often acquired due to varying thickness of fingers or nonuniformity of illumination intensity elements. Accordingly, the recognition performance is significantly reduced as the features being recognized are deformed. To address [...] Read more.
When images are acquired for finger-vein recognition, images with nonuniformity of illumination are often acquired due to varying thickness of fingers or nonuniformity of illumination intensity elements. Accordingly, the recognition performance is significantly reduced as the features being recognized are deformed. To address this issue, previous studies have used image preprocessing methods, such as grayscale normalization or score-level fusion methods for multiple recognition models, which may improve performance in images with a low degree of nonuniformity of illumination. However, the performance cannot be improved drastically when certain parts of images are saturated due to a severe degree of nonuniformity of illumination. To overcome these drawbacks, this study newly proposes a generative adversarial network for the illumination normalization of finger-vein images (INF-GAN). In the INF-GAN, a one-channel image containing texture information is generated through a residual image generation block, and finger-vein texture information deformed by the severe nonuniformity of illumination is restored, thus improving the recognition performance. The proposed method using the INF-GAN exhibited a better performance compared with state-of-the-art methods when the experiment was conducted using two open databases, the Hong Kong Polytechnic University finger-image database version 1, and the Shandong University homologous multimodal traits finger-vein database. Full article
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Article
Compression of Neural Networks for Specialized Tasks via Value Locality
Mathematics 2021, 9(20), 2612; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202612 - 16 Oct 2021
Viewed by 499
Abstract
Convolutional Neural Networks (CNNs) are broadly used in numerous applications such as computer vision and image classification. Although CNN models deliver state-of-the-art accuracy, they require heavy computational resources that are not always affordable or available on every platform. Limited performance, system cost, and [...] Read more.
Convolutional Neural Networks (CNNs) are broadly used in numerous applications such as computer vision and image classification. Although CNN models deliver state-of-the-art accuracy, they require heavy computational resources that are not always affordable or available on every platform. Limited performance, system cost, and energy consumption, such as in edge devices, argue for the optimization of computations in neural networks. Toward this end, we propose herein the value-locality-based compression (VELCRO) algorithm for neural networks. VELCRO is a method to compress general-purpose neural networks that are deployed for a small subset of focused specialized tasks. Although this study focuses on CNNs, VELCRO can be used to compress any deep neural network. VELCRO relies on the property of value locality, which suggests that activation functions exhibit values in proximity through the inference process when the network is used for specialized tasks. VELCRO consists of two stages: a preprocessing stage that identifies output elements of the activation function with a high degree of value locality, and a compression stage that replaces these elements with their corresponding average arithmetic values. As a result, VELCRO not only saves the computation of the replaced activations but also avoids processing their corresponding output feature map elements. Unlike common neural network compression algorithms, which require computationally intensive training processes, VELCRO introduces significantly fewer computational requirements. An analysis of our experiments indicates that, when CNNs are used for specialized tasks, they introduce a high degree of value locality relative to the general-purpose case. In addition, the experimental results show that without any training process, VELCRO produces a compression-saving ratio in the range 13.5–30.0% with no degradation in accuracy. Finally, the experimental results indicate that, when VELCRO is used with a relatively low compression target, it significantly improves the accuracy by 2–20% for specialized CNN tasks. Full article
(This article belongs to the Special Issue Computational Optimizations for Machine Learning)
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Article
A Binary Machine Learning Cuckoo Search Algorithm Improved by a Local Search Operator for the Set-Union Knapsack Problem
Mathematics 2021, 9(20), 2611; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202611 - 16 Oct 2021
Cited by 1 | Viewed by 420
Abstract
Optimization techniques, specially metaheuristics, are constantly refined in order to decrease execution times, increase the quality of solutions, and address larger target cases. Hybridizing techniques are one of these strategies that are particularly noteworthy due to the breadth of applications. In this article, [...] Read more.
Optimization techniques, specially metaheuristics, are constantly refined in order to decrease execution times, increase the quality of solutions, and address larger target cases. Hybridizing techniques are one of these strategies that are particularly noteworthy due to the breadth of applications. In this article, a hybrid algorithm is proposed that integrates the k-means algorithm to generate a binary version of the cuckoo search technique, and this is strengthened by a local search operator. The binary cuckoo search algorithm is applied to the NP-hard Set-Union Knapsack Problem. This problem has recently attracted great attention from the operational research community due to the breadth of its applications and the difficulty it presents in solving medium and large instances. Numerical experiments were conducted to gain insight into the contribution of the final results of the k-means technique and the local search operator. Furthermore, a comparison to state-of-the-art algorithms is made. The results demonstrate that the hybrid algorithm consistently produces superior results in the majority of the analyzed medium instances, and its performance is competitive, but degrades in large instances. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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Article
A High Fidelity Authentication Scheme for AMBTC Compressed Image Using Reference Table Encoding
Mathematics 2021, 9(20), 2610; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202610 - 16 Oct 2021
Viewed by 301
Abstract
In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are [...] Read more.
In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are generated. In addition, these methods also suffer from their embedding technique, which limits the improvement of marked image quality. In our method, each block is classified as either a smooth block or a complex one based on its smoothness. To enhance the image quality, we toggle bits in bitmap of smooth block to generate a set of authentication codes. The pixel pair matching (PPM) technique is used to embed the code that causes the least error into the quantization values. To reduce the computation cost, we only use the original and flipped bitmaps to generate authentication codes for complex blocks, and select the one that causes the least error for embedment. The experimental results show that the proposed method not only obtains higher marked image quality but also achieves better detection performance compared with prior works. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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Article
Mixed Mesh Finite Volume Method for 1D Hyperbolic Systems with Application to Plug-Flow Heat Exchangers
Mathematics 2021, 9(20), 2609; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202609 - 16 Oct 2021
Viewed by 278
Abstract
We present a finite volume method formulated on a mixed Eulerian-Lagrangian mesh for highly advective 1D hyperbolic systems altogether with its application to plug-flow heat exchanger modeling/simulation. Advection of sharp moving fronts is an important problem in fluid dynamics, and even a simple [...] Read more.
We present a finite volume method formulated on a mixed Eulerian-Lagrangian mesh for highly advective 1D hyperbolic systems altogether with its application to plug-flow heat exchanger modeling/simulation. Advection of sharp moving fronts is an important problem in fluid dynamics, and even a simple transport equation cannot be solved precisely by having a finite number of nodes/elements/volumes. Finite volume methods are known to introduce numerical diffusion, and there exist a wide variety of schemes to minimize its occurrence; the most recent being adaptive grid methods such as moving mesh methods or adaptive mesh refinement methods. We present a solution method for a class of hyperbolic systems with one nonzero time-dependent characteristic velocity. This property allows us to rigorously define a finite volume method on a grid that is continuously moving by the characteristic velocity (Lagrangian grid) along a static Eulerian grid. The advective flux of the flowing field is, by this approach, removed from cell-to-cell interactions, and the ability to advect sharp fronts is therefore enhanced. The price to pay is a fixed velocity-dependent time sampling and a time delay in the solution. For these reasons, the method is best suited for systems with a dominating advection component. We illustrate the method’s properties on an illustrative advection-decay equation example and a 1D plug flow heat exchanger. Such heat exchanger model can then serve as a convection-accurate dynamic model in estimation and control algorithms for which it was developed. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
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