rss_2.0Foundations of Computing and Decision Sciences FeedSciendo RSS Feed for Foundations of Computing and Decision Sciences of Computing and Decision Sciences 's Cover Matrix Method for Legendre Curve in Sasakian 3-Manifold<abstract> <title style='display:none'>Abstract</title> <p>In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00Some Generalized Estimating Equations Models Based on Causality Tests for Investigation of The Economic Growth of The Country Groups<abstract> <title style='display:none'>Abstract</title> <p>In this study, investigation of the economic growth of the Organization for Economic Cooperation and Development (OECD) countries and the countries in different income groups in the World Data Bank is conducted by using causality analyses and Generalized Estimating Equations (GEEs) which is an extension of Generalized Linear Models (GLMs). Eight different macro-economic, energy and environmental variables such as the gross domestic product (GDP) (current US$), CO<sub>2</sub> emission (metric tons per capita), electric power consumption (kWh per capita), energy use (kg of oil equivalent per capita), imports of goods and services (% of GDP), exports of goods and services (% of GDP), foreign direct investment (FDI) and population growth rate (annual %) have been used. These countries have been categorized according to their OECD memberships and income groups. The causes of the economic growth of these countries belonging to their OECD memberships and income groups have been determined by using the Toda-Yamamoto causality test. Furthermore, various GEE models have been established for the economic growth of these countries belonging to their OECD membership and income groups in the aspect of the above variables. These various GEE models for the investigation of the economic growth of these countries have been compared to examine the contribution of the causality analyses to the statistical model establishment. As a result of this study, the highlight is found as the use of causally-related variables in the causality-based GEE models is much more appropriate than in the non-causality based GEE models for determining the economic growth profiles of these countries.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations<abstract> <title style='display:none'>Abstract</title> <p>In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00An Introduction to the Special Issue on Numerical Techniques Meet with OR - Part II<abstract> <title style='display:none'>Abstract</title> <p>The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00A Soft Interval Based Decision Making Method and Its Computer Application<abstract> <title style='display:none'>Abstract</title> <p>In today’s society, decision making is becoming more important and complicated with increasing and complex data. Decision making by using soft set theory, herein, we firstly report the comparison of soft intervals (SI) as the generalization of interval soft sets (ISS). The results showed that SIs are more effective and more general than the ISSs, for solving decision making problems due to allowing the ranking of parameters. Tabular form of SIs were used to construct a mathematical algorithm to make a decision for problems that involves uncertainties. Since these kinds of problems have huge data, constructing new and effective methods solving these problems and transforming them into the machine learning methods is very important. An important advance of our presented method is being a more general method than the Decision-Making methods based on special situations of soft set theory. The presented method in this study can be used for all of them, while the others can only work in special cases. The structures obtained from the results of soft intervals were subjected to test with examples. The designed algorithm was written in recently used functional programing language <italic>C</italic># and applied to the problems that have been published in earlier studies. This is a pioneering study, where this type of mathematical algorithm was converted into a code and applied successfully.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space<abstract> <title style='display:none'>Abstract</title> <p>A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00New Numerical Approach for Solving Abel’s Integral Equations<abstract> <title style='display:none'>Abstract</title> <p>In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.</p> </abstract>ARTICLE2021-09-17T00:00:00.000+00:00Applying Data Envelopment Analysis Principle in Ordinal Multi Criteria Decision Analysis<abstract> <title style='display:none'>Abstract</title> <p>We consider a multicriteria decision analysis (MCDA) problem where importance of criteria, and evaluations of alternatives with respect to the criteria, are expressed on a qualitative ordinal scale. Using the extreme-point principle of Data Envelopment Analysis (DEA), we develop a two-parameter method for obtaining overall ratings of the alternatives when preferences and evaluations are made on an ordinal scale. We assume no parametric setup other than the two parameters that reflect minimum intensities of discriminating among rank positions: one parameter for the alternatives’ ranking and one for the criteria ranking. These parameters are bounded by the ordinal input data, and they imply a universal tie among the alternatives when both parameters are selected to be zero. We describe the model, discuss its theoretical underpinning, and demonstrate its application.</p> </abstract>ARTICLE2021-06-17T00:00:00.000+00:00Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces<abstract> <title style='display:none'>Abstract</title> <p>A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coefficients at the squared variable.</p> </abstract>ARTICLE2021-06-17T00:00:00.000+00:00A Statistical Evaluation of The Depth of Inheritance Tree Metric for Open-Source Applications Developed in Java<abstract> <title style='display:none'>Abstract</title> <p>The Depth of Inheritance Tree (DIT) metric, along with other ones, is used for estimating some quality indicators of software systems, including open-source applications (apps). In cases involving multiple inheritances, at a class level, the DIT metric is the maximum length from the node to the root of the tree. At an application (app) level, this metric defines the corresponding average length per class. It is known, at a class level, a DIT value between 2 and 5 is good. At an app level, similar recommended values for the DIT metric are not known. To find the recommended values for the DIT mean of an app we have proposed to use the confidence and prediction intervals. A DIT mean value of an app from the confidence interval is good since this interval indicates how reliable the estimate is for the DIT mean values of all apps used for estimating the interval. A DIT mean value higher than an upper bound of prediction interval may indicate that some classes have a large number of the inheritance levels from the object hierarchy top. What constitutes greater app design complexity as more classes are involved. We have estimated the confidence and prediction intervals of the DIT mean using normalizing transformations for the data sample from 101 open-source apps developed in Java hosted on GitHub for the 0.05 significance level.</p> </abstract>ARTICLE2021-06-17T00:00:00.000+00:00Effect or Program Constructs on Code Readability and Predicting Code Readability Using Statistical Modeling<abstract> <title style='display:none'>Abstract</title> <p>In software, code is the only part that remains up to date, which shows how important code is. Code readability is the capability of the code that makes it readable and understandable for professionals. The readability of code has been a great concern for programmers and other technical people in development team because it can have a great influence on software maintenance. A lot of research has been done to measure the influence of program constructs on the code readability but none has placed the highly influential constructs together to predict the readability of a code snippet. In this article, we propose a novel framework using statistical modeling that extracts important features from the code that can help in estimating its readability. Besides that using multiple correlation analysis, our proposed approach can measure dependencies among di erent program constructs. In addition, a multiple regression equation is proposed to predict the code readability. We have automated the proposals in a tool that can do the aforementioned estimations on the input code. Using those tools we have conducted various experiments. The results show that the calculated estimations match with the original values that show the effectiveness of our proposed work. Finally, the results of the experiments are analyzed through statistical analysis in SPSS tool to show their significance.</p> </abstract>ARTICLE2021-06-17T00:00:00.000+00:00An Integration of Neural Network and Shuffled Frog-Leaping Algorithm for CNC Machining Monitoring<abstract> <title style='display:none'>Abstract</title> <p>This paper addresses Acoustic Emission (AE) from Computer Numerical Control (CNC) machining operations. Experimental measurements are performed on the CNC lathe sensors to provide the power consumption data. To this end, a hybrid methodology based on the integration of an Artificial Neural Network (ANN) and a Shuffled Frog-Leaping Algorithm (SFLA) is applied to the data resulting from these measurements for data fusion from the sensors which is called SFLA-ANN. The initial weights of ANN are selected using SFLA. The goal is to assess the potency of the signal periodic component among these sensors. The efficiency of the proposed SFLA-ANN method is analyzed compared to hybrid methodologies of Simulated Annealing (SA) algorithm and ANN (SA-ANN) and Genetic Algorithm (GA) and ANN (GA-ANN).</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Editorial – Preface to the Special Issue on Numerical Techniques Meet with OR<abstract> <title style='display:none'>Abstract</title> <p>This special issue of the Foundations of Computing and Decision Sciences, titled <italic>”Numerical Techniques Meet with OR”</italic>, is devoted to the numerical techniques and their applications in real-world phenomena. The special issue and its editorial present numerical algorithms as they meet with different research topics such as, e.g., from operational research, supply chain management, geometrical structures and Covid-19 effects on financial applications. Besides, the special issue covers instructional information about numerical techniques which are useful for OR research problems and real-world applications on such issues.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Revealed Comparative Advantage Method for Solving Multicriteria Decision-making Problems<abstract> <title style='display:none'>Abstract</title> <p>This study proposes and analyzes a new method for the post-Pareto analysis of multicriteria decision-making (MCDM) problems: the revealed comparative advantage (RCA) assessment method. An interesting feature of the suggested method is that it uses the solution to a special eigenvalue problem and can be considered an analog/modification in the MCDM context of well-known ranking methods including the authority-hub method, PageRank method, and so on, which have been successfully applied to such fields as economics, bibliometrics, web search design, and so on. For illustrative purposes, this study discusses a particular MCDM problem to demonstrate the practicality of the method. The theoretical considerations and conducted calculations reveal that the RCA assessment method is self-consistent and easily implementable. Moreover, comparisons with well-known tools of an MCDM analysis shows that the results obtained using this method are appropriate and competitive. An important particularity of the RCA assessment method is that it can be useful for decision-makers in the case in which no decision-making authority is available or when the relative importance of various criteria has not been preliminarily evaluated.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Understanding the Impact of COVID–19 on Global Financial Network Using Graph Based Algorithm: Minimum Spanning Tree Approach<abstract> <title style='display:none'>Abstract</title> <p>In this paper effects of COVID–19 pandemic on stock market network are analyzed by an application of operational research with a mathematical approach. For this purpose two minimum spanning trees for each time period namely before and during COVID–19 pandemic are constructed. Dynamic time warping algorithm is used to measure the similarity between each time series of the investigated stock markets. Then, clusters of investigated stock markets are constructed. Numerical values of the topology evaluation for each cluster and time period is computed.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00An Algorithm for Choosing, Ordering a New Criteria of a Bi-Objective Flow Problem<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our new idea, which is &lt;&lt; the gain cycles &gt;&gt;, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel<abstract> <title style='display:none'>Abstract</title> <p>Smoking is the most lethal social poisoning event. The World Health Organization defines smoking as the most important preventable cause of disease. Around 4.9 million people worldwide die from smoking every year. In order to analysis this matter, we aim to investigate an e-cigarette smoking model with Atangana-Baleanu fractional derivative. We obtain the existence conditions of the solution for this fractional model utilizing fixed-point theory. After giving existence conditions, the uniqueness of the solution is proved. Finally, to show the effect of the Atangana-Baleanu fractional derivative on the model, we give some numerical results supported by illustrative graphics.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width<abstract> <title style='display:none'>Abstract</title> <p>The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach.The geometric properties of this curve type are examined with the help of these solutions.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Using TeX Markup Language for 3D and 2D Geological Plotting<abstract> <title style='display:none'>Abstract</title> <p>The paper presents technical application of TeX high-level, descriptive markup language for processing geological dataset from soil laboratory. Geotechnical measurements included equivalent soil cohesion, absolute and absolute deformation index, soil compressibility coefficient by time of immersion depth, exposure time to compressive strength to samples and physical and mechanical properties (humidity, density). Dataset was received from laboratory based experimental tests of the physical and mechanical properties of soils. Data were converted to csv table and processed by LaTeX. Methodology is based on LaTeX packages: {tikz}, {tikz-3dplot}, {tikzpicture}, {pgfplot}, {filecontetns}, {spy} for 3D plotting showing correlation in variables and descriptive statistical analysis based on the data array processing. Results demonstrated LaTeX scripts and graphics: 2D and 3D scatterplots, ternaries, bar charts, boxplots, zooming techniques detailing fragment of the plot, flowchart. Research novelty consists in technical approach of TeX language application for geo- logical data processing and graphical visualization. Engineering graphics by TeX was demonstrated with screenshots of the codes used for plotting.</p> </abstract>ARTICLE2021-03-01T00:00:00.000+00:00Integrating imperfection of information into the promethee multicriteria decision aid methods: a general framework<abstract><title style='display:none'>Abstract.</title><p>Multicriteria decision aid methods are used to analyze decision problems including a series of alternative decisions evaluated on several criteria. They most often assume that perfect information is available with respect to the evaluation of the alternative decisions. However, in practice, imprecision, uncertainty or indetermination are often present at least for some criteria. This is a limit of most multicriteria methods. In particular the PROMETHEE methods do not allow directly for taking into account this kind of imperfection of information. We show how a general framework can be adapted to PROMETHEE and can be used in order to integrate different imperfect information models such as a.o. probabilities, fuzzy logic or possibility theory. An important characteristic of the proposed approach is that it makes it possible to use different models for different criteria in the same decision problem.</p></abstract>ARTICLE2012-10-24T00:00:00.000+00:00en-us-1