In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBERijfls
In this paper, a new form of fuzzy number named as Hexadecagonal Fuzzy Number is introduced as it is not
possible to restrict the membership function to any specific form. The cut of Hexadecagonal fuzzy number is defined and basic arithmetic operations are performed using interval arithmetic of cut and illustrated with numerical examples.
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBERijfls
In this paper, a new form of fuzzy number named as Hexadecagonal Fuzzy Number is introduced as it is not
possible to restrict the membership function to any specific form. The cut of Hexadecagonal fuzzy
number is defined and basic arithmetic operations are performed using interval arithmetic of cut and
illustrated with numerical examples.
The paper deals with a generalized estimator of population mean which includes several estimators as its particular cases. Under certain conditions, the proposed estimator is more efficient than existing estimators. Results are supported by numerical illustration.
Hybrid Block Method for the Solution of First Order Initial Value Problems of...iosrjce
Method of collocation of the differential system and interpolation of the approximate solution which
is a combination of power series and exponential function at some selected grid and off-grid points to generate
a linear multistep method which is implemented in block method is considered in this paper. The basic
properties of the block method which include; consistency, convergence and stability interval is verified. The
method is tested on some numerical experiments and found to have better stability condition and better
approximation than the existing methods
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBERijfls
In this paper, a new form of fuzzy number named as Hexadecagonal Fuzzy Number is introduced as it is not
possible to restrict the membership function to any specific form. The cut of Hexadecagonal fuzzy number is defined and basic arithmetic operations are performed using interval arithmetic of cut and illustrated with numerical examples.
AN ARITHMETIC OPERATION ON HEXADECAGONAL FUZZY NUMBERijfls
In this paper, a new form of fuzzy number named as Hexadecagonal Fuzzy Number is introduced as it is not
possible to restrict the membership function to any specific form. The cut of Hexadecagonal fuzzy
number is defined and basic arithmetic operations are performed using interval arithmetic of cut and
illustrated with numerical examples.
The paper deals with a generalized estimator of population mean which includes several estimators as its particular cases. Under certain conditions, the proposed estimator is more efficient than existing estimators. Results are supported by numerical illustration.
Hybrid Block Method for the Solution of First Order Initial Value Problems of...iosrjce
Method of collocation of the differential system and interpolation of the approximate solution which
is a combination of power series and exponential function at some selected grid and off-grid points to generate
a linear multistep method which is implemented in block method is considered in this paper. The basic
properties of the block method which include; consistency, convergence and stability interval is verified. The
method is tested on some numerical experiments and found to have better stability condition and better
approximation than the existing methods
Expectation Maximization Algorithm with Combinatorial AssumptionLoc Nguyen
Expectation maximization (EM) algorithm is a popular and powerful mathematical method for parameter estimation in case that there exist both observed data and hidden data. The EM process depends on an implicit relationship between observed data and hidden data which is specified by a mapping function in traditional EM and a joint probability density function (PDF) in practical EM. However, the mapping function is vague and impractical whereas the joint PDF is not easy to be defined because of heterogeneity between observed data and hidden data. The research aims to improve competency of EM by making it more feasible and easier to be specified, which removes the vagueness. Therefore, the research proposes an assumption that observed data is the combination of hidden data which is realized as an analytic function where data points are numerical. In other words, observed points are supposedly calculated from hidden points via regression model. Mathematical computations and proofs indicate feasibility and clearness of the proposed method which can be considered as an extension of EM.
Correlation measure for intuitionistic fuzzy multi setseSAT Journals
Abstract In this paper, the Correlation measure of Intuitionistic Fuzzy Multi sets (IFMS) is proposed. The concept of this Correlation measure of IFMS is the extension of Correlation measure of IFS. Using the Correlation of IFMS measure, the application of medical diagnosis and pattern recognition are presented. The new method also shows that the correlation measure of any two IFMS equals one if and only if the two IFMS are the same. Keywords: Intuitionistic fuzzy set, Intuitionistic Fuzzy Multi sets, Correlation measure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Heuristic Algorithm for Finding Sensitivity Analysis in Interval Solid Transp...AM Publications
This paper develops a heuristic algorithm for finding the ranges of cost in the interval solid transportation
problem such that optimal basis is invariant. The procedure of the proposed approach is illustrated by numerical
example.
RESIDUALS AND INFLUENCE IN NONLINEAR REGRESSION FOR REPEATED MEASUREMENT DATAorajjournal
All observations don’t have equal significance in regression analysis. Diagnostics of observations is an important aspect of model building. In this paper, we use diagnostics method to detect residuals and influential points in nonlinear regression for repeated measurement data. Cook distance and Gauss newton method have been proposed to identify the outliers in nonlinear regression analysis and parameter estimation. Most of these techniques based on graphical representations of residuals, hat matrix and case deletion measures. The results
show us detection of single and multiple outliers cases in repeated measurement data. We use these techniques
to explore performance of residuals and influence in nonlinear regression model.
In this paper, we introduce intense subgraphs and feeble subgraphs based on their densities and discuss mild balanced IFG and equally balanced intuitionistic fuzzy subgraphs and their properties. The operations “sum” and “union” of subgraphs of Intuitionistic Fuzzy Graphs (IFG) are analyzed. As an application of equally balanced IF subgraphs, curriculum and syllabus formation in higher educational system is discussed. Mathematics Subject Classification: 05C72, 03E72, 03F55.
Isoparametric bilinear quadrilateral element _ ppt presentationFilipe Giesteira
The theoretical formulation of an isoparametric element, from the Lagrange family. In addition, the MATLAB code of the FEM from the bilinear element with four nodes was also implemented.
Assignment developed in the scope of the finite element method course, lectured at FEUP (Faculdade de Engenharia da Universidade do Porto).
Determination of Optimal Product Mix for Profit Maximization using Linear Pro...IJERA Editor
This paper demonstrates the use of liner programming methods in order to determine the optimal product mix for
profit maximization. There had been several papers written to demonstrate the use of linear programming in
finding the optimal product mix in various organization. This paper is aimed to show the generic approach to be
taken to find the optimal product mix.
In this paper, we introduced the modified differential transform which is a modified version of a two-dimensional differential transform method. First, the properties of the modified differential transform method (MDTM) are presented. After this, by using the idea modified differential transform method we will find an analytical-numerical solution of linear partial integro-differential equations (PIDE) with convolution kernel which occur naturally in various fields of science and engineering. In some cases, the exact solution may be achieved. The efficiency and reliability of this method are illustrated by some examples.
In this paper, an accurate numerical method is presented to find the numerical solution of the singularinitial value problems. The second-order singular initial value problem under consideration is transferredinto a first-order system of initial value problems, and then it can be solved by using the fifth-order RungeKutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methodsis confirmed by solving three model examples, and the obtained approximate solutions are compared withthe existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numericalmethod for solving the singular initial value problems.
ACCURATE NUMERICAL METHOD FOR SINGULAR INITIAL-VALUE PROBLEMSaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular
initial value problems. The second-order singular initial value problem under consideration is transferred
into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge
Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods
is confirmed by solving three model examples, and the obtained approximate solutions are compared with
the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical
method for solving the singular initial value problems.
ACCURATE NUMERICAL METHOD FOR SINGULAR INITIAL-VALUE PROBLEMSaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular
initial value problems. The second-order singular initial value problem under consideration is transferred
into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge
Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods
is confirmed by solving three model examples, and the obtained approximate solutions are compared with
the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical
method for solving the singular initial value problems.
Continuous models of economy adopted to either define evolutions of economic
systems or investigate economic dynamics, amongst its other areas of applications, are
known to be related to differential equations. The considered model in this article takes
the form of a second order non-linear ordinary differential equation (ODE) which is
conventional solved by reducing to the system of first order. This approach is
computationally tasking, unlike block methods which bypasses reduction by directly
solving the model. A new approach is introduced named Modified Taylor Series
Approach (MTSA). Hence, the resultant MTSA-derived block method is implemented to
solve the second order non-linear model of economy under consideration.
Expectation Maximization Algorithm with Combinatorial AssumptionLoc Nguyen
Expectation maximization (EM) algorithm is a popular and powerful mathematical method for parameter estimation in case that there exist both observed data and hidden data. The EM process depends on an implicit relationship between observed data and hidden data which is specified by a mapping function in traditional EM and a joint probability density function (PDF) in practical EM. However, the mapping function is vague and impractical whereas the joint PDF is not easy to be defined because of heterogeneity between observed data and hidden data. The research aims to improve competency of EM by making it more feasible and easier to be specified, which removes the vagueness. Therefore, the research proposes an assumption that observed data is the combination of hidden data which is realized as an analytic function where data points are numerical. In other words, observed points are supposedly calculated from hidden points via regression model. Mathematical computations and proofs indicate feasibility and clearness of the proposed method which can be considered as an extension of EM.
Correlation measure for intuitionistic fuzzy multi setseSAT Journals
Abstract In this paper, the Correlation measure of Intuitionistic Fuzzy Multi sets (IFMS) is proposed. The concept of this Correlation measure of IFMS is the extension of Correlation measure of IFS. Using the Correlation of IFMS measure, the application of medical diagnosis and pattern recognition are presented. The new method also shows that the correlation measure of any two IFMS equals one if and only if the two IFMS are the same. Keywords: Intuitionistic fuzzy set, Intuitionistic Fuzzy Multi sets, Correlation measure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Heuristic Algorithm for Finding Sensitivity Analysis in Interval Solid Transp...AM Publications
This paper develops a heuristic algorithm for finding the ranges of cost in the interval solid transportation
problem such that optimal basis is invariant. The procedure of the proposed approach is illustrated by numerical
example.
RESIDUALS AND INFLUENCE IN NONLINEAR REGRESSION FOR REPEATED MEASUREMENT DATAorajjournal
All observations don’t have equal significance in regression analysis. Diagnostics of observations is an important aspect of model building. In this paper, we use diagnostics method to detect residuals and influential points in nonlinear regression for repeated measurement data. Cook distance and Gauss newton method have been proposed to identify the outliers in nonlinear regression analysis and parameter estimation. Most of these techniques based on graphical representations of residuals, hat matrix and case deletion measures. The results
show us detection of single and multiple outliers cases in repeated measurement data. We use these techniques
to explore performance of residuals and influence in nonlinear regression model.
In this paper, we introduce intense subgraphs and feeble subgraphs based on their densities and discuss mild balanced IFG and equally balanced intuitionistic fuzzy subgraphs and their properties. The operations “sum” and “union” of subgraphs of Intuitionistic Fuzzy Graphs (IFG) are analyzed. As an application of equally balanced IF subgraphs, curriculum and syllabus formation in higher educational system is discussed. Mathematics Subject Classification: 05C72, 03E72, 03F55.
Isoparametric bilinear quadrilateral element _ ppt presentationFilipe Giesteira
The theoretical formulation of an isoparametric element, from the Lagrange family. In addition, the MATLAB code of the FEM from the bilinear element with four nodes was also implemented.
Assignment developed in the scope of the finite element method course, lectured at FEUP (Faculdade de Engenharia da Universidade do Porto).
Determination of Optimal Product Mix for Profit Maximization using Linear Pro...IJERA Editor
This paper demonstrates the use of liner programming methods in order to determine the optimal product mix for
profit maximization. There had been several papers written to demonstrate the use of linear programming in
finding the optimal product mix in various organization. This paper is aimed to show the generic approach to be
taken to find the optimal product mix.
In this paper, we introduced the modified differential transform which is a modified version of a two-dimensional differential transform method. First, the properties of the modified differential transform method (MDTM) are presented. After this, by using the idea modified differential transform method we will find an analytical-numerical solution of linear partial integro-differential equations (PIDE) with convolution kernel which occur naturally in various fields of science and engineering. In some cases, the exact solution may be achieved. The efficiency and reliability of this method are illustrated by some examples.
In this paper, an accurate numerical method is presented to find the numerical solution of the singularinitial value problems. The second-order singular initial value problem under consideration is transferredinto a first-order system of initial value problems, and then it can be solved by using the fifth-order RungeKutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methodsis confirmed by solving three model examples, and the obtained approximate solutions are compared withthe existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numericalmethod for solving the singular initial value problems.
ACCURATE NUMERICAL METHOD FOR SINGULAR INITIAL-VALUE PROBLEMSaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular
initial value problems. The second-order singular initial value problem under consideration is transferred
into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge
Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods
is confirmed by solving three model examples, and the obtained approximate solutions are compared with
the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical
method for solving the singular initial value problems.
ACCURATE NUMERICAL METHOD FOR SINGULAR INITIAL-VALUE PROBLEMSaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular
initial value problems. The second-order singular initial value problem under consideration is transferred
into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge
Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods
is confirmed by solving three model examples, and the obtained approximate solutions are compared with
the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical
method for solving the singular initial value problems.
Continuous models of economy adopted to either define evolutions of economic
systems or investigate economic dynamics, amongst its other areas of applications, are
known to be related to differential equations. The considered model in this article takes
the form of a second order non-linear ordinary differential equation (ODE) which is
conventional solved by reducing to the system of first order. This approach is
computationally tasking, unlike block methods which bypasses reduction by directly
solving the model. A new approach is introduced named Modified Taylor Series
Approach (MTSA). Hence, the resultant MTSA-derived block method is implemented to
solve the second order non-linear model of economy under consideration.
Symmetric quadratic tetration interpolation using forward and backward opera...IJECEIAES
The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.
Numerical solution of fuzzy differential equations by Milne’s predictor-corre...mathsjournal
The study of this paper suggests on dependency problem in fuzzy computational method by using the numerical solution of Fuzzy differential equations(FDEs) in Milne’s predictor-corrector method. This method is adopted to solve the dependency problem in fuzzy computation. We solve some fuzzy initial value problems to illustrate the theory.
Time Delay and Mean Square Stochastic Differential Equations in Impetuous Sta...ijtsrd
This paper specially exhibits about the time delay and mean square stochastic differential equations in impetuous stabilization is analyzed. By projecting a delay differential inequality and using the stochastic analysis technique, a few present stage for mean square exponential stabilization are survived. It is express that an unstable stochastic delay system can be achieved some stability by impetuous. This example is also argued to derived the efficiency of the obtained results. G. Pramila | S. Ramadevi"Time Delay and Mean Square Stochastic Differential Equations in Impetuous Stabilization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-3 , April 2018, URL: http://www.ijtsrd.com/papers/ijtsrd11062.pdf http://www.ijtsrd.com/humanities-and-the-arts/other/11062/time-delay-and-mean-square-stochastic-differential-equations-in-impetuous-stabilization/g-pramila
We present a strong convergence implicit Runge-Kutta method, with four stages, for solution of
initial value problem of ordinary differential equations. Collocation method is used to derive a continuous
scheme; and the continuous scheme evaluated at special points, the Gaussian points of fourth degree Legendre
polynomial, gives us four function evaluations and the Runge-Kutta method for the iteration of the solutions.
Convergent properties of the method are discussed. Experimental problems used to check the quality of the
scheme show that the method is highly efficient, A – stable, has simple structure, converges to exact solution
faster and better than some existing popular methods cited in this paper.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called 𝜏 and gave a way to compute the variant. Nevertheless, the way failed to determine every 𝜏 correctly.
In this paper, we will give a probabilistic algorithm to determine the variant 𝜏 correctly in most cases by adding a few steps instead of computing 𝑡(𝑥) when given 𝑓(𝑥) and𝑔(𝑥) ∈ ℤ[𝑥], where 𝑡(𝑥) satisfies that 𝑠(𝑥)𝑓(𝑥) + 𝑡(𝑥)𝑔(𝑥) = 𝑟(𝑥), here 𝑡(𝑥), 𝑠(𝑥) ∈ ℤ[𝑥]
Bibliometric analysis highlighting the role of women in addressing climate ch...IJECEIAES
Fossil fuel consumption increased quickly, contributing to climate change
that is evident in unusual flooding and draughts, and global warming. Over
the past ten years, women's involvement in society has grown dramatically,
and they succeeded in playing a noticeable role in reducing climate change.
A bibliometric analysis of data from the last ten years has been carried out to
examine the role of women in addressing the climate change. The analysis's
findings discussed the relevant to the sustainable development goals (SDGs),
particularly SDG 7 and SDG 13. The results considered contributions made
by women in the various sectors while taking geographic dispersion into
account. The bibliometric analysis delves into topics including women's
leadership in environmental groups, their involvement in policymaking, their
contributions to sustainable development projects, and the influence of
gender diversity on attempts to mitigate climate change. This study's results
highlight how women have influenced policies and actions related to climate
change, point out areas of research deficiency and recommendations on how
to increase role of the women in addressing the climate change and
achieving sustainability. To achieve more successful results, this initiative
aims to highlight the significance of gender equality and encourage
inclusivity in climate change decision-making processes.
Voltage and frequency control of microgrid in presence of micro-turbine inter...IJECEIAES
The active and reactive load changes have a significant impact on voltage
and frequency. In this paper, in order to stabilize the microgrid (MG) against
load variations in islanding mode, the active and reactive power of all
distributed generators (DGs), including energy storage (battery), diesel
generator, and micro-turbine, are controlled. The micro-turbine generator is
connected to MG through a three-phase to three-phase matrix converter, and
the droop control method is applied for controlling the voltage and
frequency of MG. In addition, a method is introduced for voltage and
frequency control of micro-turbines in the transition state from gridconnected mode to islanding mode. A novel switching strategy of the matrix
converter is used for converting the high-frequency output voltage of the
micro-turbine to the grid-side frequency of the utility system. Moreover,
using the switching strategy, the low-order harmonics in the output current
and voltage are not produced, and consequently, the size of the output filter
would be reduced. In fact, the suggested control strategy is load-independent
and has no frequency conversion restrictions. The proposed approach for
voltage and frequency regulation demonstrates exceptional performance and
favorable response across various load alteration scenarios. The suggested
strategy is examined in several scenarios in the MG test systems, and the
simulation results are addressed.
Enhancing battery system identification: nonlinear autoregressive modeling fo...IJECEIAES
Precisely characterizing Li-ion batteries is essential for optimizing their
performance, enhancing safety, and prolonging their lifespan across various
applications, such as electric vehicles and renewable energy systems. This
article introduces an innovative nonlinear methodology for system
identification of a Li-ion battery, employing a nonlinear autoregressive with
exogenous inputs (NARX) model. The proposed approach integrates the
benefits of nonlinear modeling with the adaptability of the NARX structure,
facilitating a more comprehensive representation of the intricate
electrochemical processes within the battery. Experimental data collected
from a Li-ion battery operating under diverse scenarios are employed to
validate the effectiveness of the proposed methodology. The identified
NARX model exhibits superior accuracy in predicting the battery's behavior
compared to traditional linear models. This study underscores the
importance of accounting for nonlinearities in battery modeling, providing
insights into the intricate relationships between state-of-charge, voltage, and
current under dynamic conditions.
Smart grid deployment: from a bibliometric analysis to a surveyIJECEIAES
Smart grids are one of the last decades' innovations in electrical energy.
They bring relevant advantages compared to the traditional grid and
significant interest from the research community. Assessing the field's
evolution is essential to propose guidelines for facing new and future smart
grid challenges. In addition, knowing the main technologies involved in the
deployment of smart grids (SGs) is important to highlight possible
shortcomings that can be mitigated by developing new tools. This paper
contributes to the research trends mentioned above by focusing on two
objectives. First, a bibliometric analysis is presented to give an overview of
the current research level about smart grid deployment. Second, a survey of
the main technological approaches used for smart grid implementation and
their contributions are highlighted. To that effect, we searched the Web of
Science (WoS), and the Scopus databases. We obtained 5,663 documents
from WoS and 7,215 from Scopus on smart grid implementation or
deployment. With the extraction limitation in the Scopus database, 5,872 of
the 7,215 documents were extracted using a multi-step process. These two
datasets have been analyzed using a bibliometric tool called bibliometrix.
The main outputs are presented with some recommendations for future
research.
Use of analytical hierarchy process for selecting and prioritizing islanding ...IJECEIAES
One of the problems that are associated to power systems is islanding
condition, which must be rapidly and properly detected to prevent any
negative consequences on the system's protection, stability, and security.
This paper offers a thorough overview of several islanding detection
strategies, which are divided into two categories: classic approaches,
including local and remote approaches, and modern techniques, including
techniques based on signal processing and computational intelligence.
Additionally, each approach is compared and assessed based on several
factors, including implementation costs, non-detected zones, declining
power quality, and response times using the analytical hierarchy process
(AHP). The multi-criteria decision-making analysis shows that the overall
weight of passive methods (24.7%), active methods (7.8%), hybrid methods
(5.6%), remote methods (14.5%), signal processing-based methods (26.6%),
and computational intelligent-based methods (20.8%) based on the
comparison of all criteria together. Thus, it can be seen from the total weight
that hybrid approaches are the least suitable to be chosen, while signal
processing-based methods are the most appropriate islanding detection
method to be selected and implemented in power system with respect to the
aforementioned factors. Using Expert Choice software, the proposed
hierarchy model is studied and examined.
Enhancing of single-stage grid-connected photovoltaic system using fuzzy logi...IJECEIAES
The power generated by photovoltaic (PV) systems is influenced by
environmental factors. This variability hampers the control and utilization of
solar cells' peak output. In this study, a single-stage grid-connected PV
system is designed to enhance power quality. Our approach employs fuzzy
logic in the direct power control (DPC) of a three-phase voltage source
inverter (VSI), enabling seamless integration of the PV connected to the
grid. Additionally, a fuzzy logic-based maximum power point tracking
(MPPT) controller is adopted, which outperforms traditional methods like
incremental conductance (INC) in enhancing solar cell efficiency and
minimizing the response time. Moreover, the inverter's real-time active and
reactive power is directly managed to achieve a unity power factor (UPF).
The system's performance is assessed through MATLAB/Simulink
implementation, showing marked improvement over conventional methods,
particularly in steady-state and varying weather conditions. For solar
irradiances of 500 and 1,000 W/m2
, the results show that the proposed
method reduces the total harmonic distortion (THD) of the injected current
to the grid by approximately 46% and 38% compared to conventional
methods, respectively. Furthermore, we compare the simulation results with
IEEE standards to evaluate the system's grid compatibility.
Enhancing photovoltaic system maximum power point tracking with fuzzy logic-b...IJECEIAES
Photovoltaic systems have emerged as a promising energy resource that
caters to the future needs of society, owing to their renewable, inexhaustible,
and cost-free nature. The power output of these systems relies on solar cell
radiation and temperature. In order to mitigate the dependence on
atmospheric conditions and enhance power tracking, a conventional
approach has been improved by integrating various methods. To optimize
the generation of electricity from solar systems, the maximum power point
tracking (MPPT) technique is employed. To overcome limitations such as
steady-state voltage oscillations and improve transient response, two
traditional MPPT methods, namely fuzzy logic controller (FLC) and perturb
and observe (P&O), have been modified. This research paper aims to
simulate and validate the step size of the proposed modified P&O and FLC
techniques within the MPPT algorithm using MATLAB/Simulink for
efficient power tracking in photovoltaic systems.
Adaptive synchronous sliding control for a robot manipulator based on neural ...IJECEIAES
Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for
robot hands is always an attractive topic in the research community. This is a
challenging problem because robot manipulators are complex nonlinear systems
and are often subject to fluctuations in loads and external disturbances. This
article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller
ensures that the positions of the joints track the desired trajectory, synchronize
the errors, and significantly reduces chattering. First, the synchronous tracking
errors and synchronous sliding surfaces are presented. Second, the synchronous
tracking error dynamics are determined. Third, a robust adaptive control law is
designed,the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy
logic. The built algorithm ensures that the tracking and approximation errors
are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results.
Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is
significantly reduced.
Remote field-programmable gate array laboratory for signal acquisition and de...IJECEIAES
A remote laboratory utilizing field-programmable gate array (FPGA) technologies enhances students’ learning experience anywhere and anytime in embedded system design. Existing remote laboratories prioritize hardware access and visual feedback for observing board behavior after programming, neglecting comprehensive debugging tools to resolve errors that require internal signal acquisition. This paper proposes a novel remote embeddedsystem design approach targeting FPGA technologies that are fully interactive via a web-based platform. Our solution provides FPGA board access and debugging capabilities beyond the visual feedback provided by existing remote laboratories. We implemented a lab module that allows users to seamlessly incorporate into their FPGA design. The module minimizes hardware resource utilization while enabling the acquisition of a large number of data samples from the signal during the experiments by adaptively compressing the signal prior to data transmission. The results demonstrate an average compression ratio of 2.90 across three benchmark signals, indicating efficient signal acquisition and effective debugging and analysis. This method allows users to acquire more data samples than conventional methods. The proposed lab allows students to remotely test and debug their designs, bridging the gap between theory and practice in embedded system design.
Detecting and resolving feature envy through automated machine learning and m...IJECEIAES
Efficiently identifying and resolving code smells enhances software project quality. This paper presents a novel solution, utilizing automated machine learning (AutoML) techniques, to detect code smells and apply move method refactoring. By evaluating code metrics before and after refactoring, we assessed its impact on coupling, complexity, and cohesion. Key contributions of this research include a unique dataset for code smell classification and the development of models using AutoGluon for optimal performance. Furthermore, the study identifies the top 20 influential features in classifying feature envy, a well-known code smell, stemming from excessive reliance on external classes. We also explored how move method refactoring addresses feature envy, revealing reduced coupling and complexity, and improved cohesion, ultimately enhancing code quality. In summary, this research offers an empirical, data-driven approach, integrating AutoML and move method refactoring to optimize software project quality. Insights gained shed light on the benefits of refactoring on code quality and the significance of specific features in detecting feature envy. Future research can expand to explore additional refactoring techniques and a broader range of code metrics, advancing software engineering practices and standards.
Smart monitoring technique for solar cell systems using internet of things ba...IJECEIAES
Rapidly and remotely monitoring and receiving the solar cell systems status parameters, solar irradiance, temperature, and humidity, are critical issues in enhancement their efficiency. Hence, in the present article an improved smart prototype of internet of things (IoT) technique based on embedded system through NodeMCU ESP8266 (ESP-12E) was carried out experimentally. Three different regions at Egypt; Luxor, Cairo, and El-Beheira cities were chosen to study their solar irradiance profile, temperature, and humidity by the proposed IoT system. The monitoring data of solar irradiance, temperature, and humidity were live visualized directly by Ubidots through hypertext transfer protocol (HTTP) protocol. The measured solar power radiation in Luxor, Cairo, and El-Beheira ranged between 216-1000, 245-958, and 187-692 W/m 2 respectively during the solar day. The accuracy and rapidity of obtaining monitoring results using the proposed IoT system made it a strong candidate for application in monitoring solar cell systems. On the other hand, the obtained solar power radiation results of the three considered regions strongly candidate Luxor and Cairo as suitable places to build up a solar cells system station rather than El-Beheira.
An efficient security framework for intrusion detection and prevention in int...IJECEIAES
Over the past few years, the internet of things (IoT) has advanced to connect billions of smart devices to improve quality of life. However, anomalies or malicious intrusions pose several security loopholes, leading to performance degradation and threat to data security in IoT operations. Thereby, IoT security systems must keep an eye on and restrict unwanted events from occurring in the IoT network. Recently, various technical solutions based on machine learning (ML) models have been derived towards identifying and restricting unwanted events in IoT. However, most ML-based approaches are prone to miss-classification due to inappropriate feature selection. Additionally, most ML approaches applied to intrusion detection and prevention consider supervised learning, which requires a large amount of labeled data to be trained. Consequently, such complex datasets are impossible to source in a large network like IoT. To address this problem, this proposed study introduces an efficient learning mechanism to strengthen the IoT security aspects. The proposed algorithm incorporates supervised and unsupervised approaches to improve the learning models for intrusion detection and mitigation. Compared with the related works, the experimental outcome shows that the model performs well in a benchmark dataset. It accomplishes an improved detection accuracy of approximately 99.21%.
Developing a smart system for infant incubators using the internet of things ...IJECEIAES
This research is developing an incubator system that integrates the internet of things and artificial intelligence to improve care for premature babies. The system workflow starts with sensors that collect data from the incubator. Then, the data is sent in real-time to the internet of things (IoT) broker eclipse mosquito using the message queue telemetry transport (MQTT) protocol version 5.0. After that, the data is stored in a database for analysis using the long short-term memory network (LSTM) method and displayed in a web application using an application programming interface (API) service. Furthermore, the experimental results produce as many as 2,880 rows of data stored in the database. The correlation coefficient between the target attribute and other attributes ranges from 0.23 to 0.48. Next, several experiments were conducted to evaluate the model-predicted value on the test data. The best results are obtained using a two-layer LSTM configuration model, each with 60 neurons and a lookback setting 6. This model produces an R 2 value of 0.934, with a root mean square error (RMSE) value of 0.015 and a mean absolute error (MAE) of 0.008. In addition, the R 2 value was also evaluated for each attribute used as input, with a result of values between 0.590 and 0.845.
A review on internet of things-based stingless bee's honey production with im...IJECEIAES
Honey is produced exclusively by honeybees and stingless bees which both are well adapted to tropical and subtropical regions such as Malaysia. Stingless bees are known for producing small amounts of honey and are known for having a unique flavor profile. Problem identified that many stingless bees collapsed due to weather, temperature and environment. It is critical to understand the relationship between the production of stingless bee honey and environmental conditions to improve honey production. Thus, this paper presents a review on stingless bee's honey production and prediction modeling. About 54 previous research has been analyzed and compared in identifying the research gaps. A framework on modeling the prediction of stingless bee honey is derived. The result presents the comparison and analysis on the internet of things (IoT) monitoring systems, honey production estimation, convolution neural networks (CNNs), and automatic identification methods on bee species. It is identified based on image detection method the top best three efficiency presents CNN is at 98.67%, densely connected convolutional networks with YOLO v3 is 97.7%, and DenseNet201 convolutional networks 99.81%. This study is significant to assist the researcher in developing a model for predicting stingless honey produced by bee's output, which is important for a stable economy and food security.
A trust based secure access control using authentication mechanism for intero...IJECEIAES
The internet of things (IoT) is a revolutionary innovation in many aspects of our society including interactions, financial activity, and global security such as the military and battlefield internet. Due to the limited energy and processing capacity of network devices, security, energy consumption, compatibility, and device heterogeneity are the long-term IoT problems. As a result, energy and security are critical for data transmission across edge and IoT networks. Existing IoT interoperability techniques need more computation time, have unreliable authentication mechanisms that break easily, lose data easily, and have low confidentiality. In this paper, a key agreement protocol-based authentication mechanism for IoT devices is offered as a solution to this issue. This system makes use of information exchange, which must be secured to prevent access by unauthorized users. Using a compact contiki/cooja simulator, the performance and design of the suggested framework are validated. The simulation findings are evaluated based on detection of malicious nodes after 60 minutes of simulation. The suggested trust method, which is based on privacy access control, reduced packet loss ratio to 0.32%, consumed 0.39% power, and had the greatest average residual energy of 0.99 mJoules at 10 nodes.
Fuzzy linear programming with the intuitionistic polygonal fuzzy numbersIJECEIAES
In real world applications, data are subject to ambiguity due to several factors; fuzzy sets and fuzzy numbers propose a great tool to model such ambiguity. In case of hesitation, the complement of a membership value in fuzzy numbers can be different from the non-membership value, in which case we can model using intuitionistic fuzzy numbers as they provide flexibility by defining both a membership and a non-membership functions. In this article, we consider the intuitionistic fuzzy linear programming problem with intuitionistic polygonal fuzzy numbers, which is a generalization of the previous polygonal fuzzy numbers found in the literature. We present a modification of the simplex method that can be used to solve any general intuitionistic fuzzy linear programming problem after approximating the problem by an intuitionistic polygonal fuzzy number with n edges. This method is given in a simple tableau formulation, and then applied on numerical examples for clarity.
The performance of artificial intelligence in prostate magnetic resonance im...IJECEIAES
Prostate cancer is the predominant form of cancer observed in men worldwide. The application of magnetic resonance imaging (MRI) as a guidance tool for conducting biopsies has been established as a reliable and well-established approach in the diagnosis of prostate cancer. The diagnostic performance of MRI-guided prostate cancer diagnosis exhibits significant heterogeneity due to the intricate and multi-step nature of the diagnostic pathway. The development of artificial intelligence (AI) models, specifically through the utilization of machine learning techniques such as deep learning, is assuming an increasingly significant role in the field of radiology. In the realm of prostate MRI, a considerable body of literature has been dedicated to the development of various AI algorithms. These algorithms have been specifically designed for tasks such as prostate segmentation, lesion identification, and classification. The overarching objective of these endeavors is to enhance diagnostic performance and foster greater agreement among different observers within MRI scans for the prostate. This review article aims to provide a concise overview of the application of AI in the field of radiology, with a specific focus on its utilization in prostate MRI.
Seizure stage detection of epileptic seizure using convolutional neural networksIJECEIAES
According to the World Health Organization (WHO), seventy million individuals worldwide suffer from epilepsy, a neurological disorder. While electroencephalography (EEG) is crucial for diagnosing epilepsy and monitoring the brain activity of epilepsy patients, it requires a specialist to examine all EEG recordings to find epileptic behavior. This procedure needs an experienced doctor, and a precise epilepsy diagnosis is crucial for appropriate treatment. To identify epileptic seizures, this study employed a convolutional neural network (CNN) based on raw scalp EEG signals to discriminate between preictal, ictal, postictal, and interictal segments. The possibility of these characteristics is explored by examining how well timedomain signals work in the detection of epileptic signals using intracranial Freiburg Hospital (FH), scalp Children's Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) databases, and Temple University Hospital (TUH) EEG. To test the viability of this approach, two types of experiments were carried out. Firstly, binary class classification (preictal, ictal, postictal each versus interictal) and four-class classification (interictal versus preictal versus ictal versus postictal). The average accuracy for stage detection using CHB-MIT database was 84.4%, while the Freiburg database's time-domain signals had an accuracy of 79.7% and the highest accuracy of 94.02% for classification in the TUH EEG database when comparing interictal stage to preictal stage.
Analysis of driving style using self-organizing maps to analyze driver behaviorIJECEIAES
Modern life is strongly associated with the use of cars, but the increase in acceleration speeds and their maneuverability leads to a dangerous driving style for some drivers. In these conditions, the development of a method that allows you to track the behavior of the driver is relevant. The article provides an overview of existing methods and models for assessing the functioning of motor vehicles and driver behavior. Based on this, a combined algorithm for recognizing driving style is proposed. To do this, a set of input data was formed, including 20 descriptive features: About the environment, the driver's behavior and the characteristics of the functioning of the car, collected using OBD II. The generated data set is sent to the Kohonen network, where clustering is performed according to driving style and degree of danger. Getting the driving characteristics into a particular cluster allows you to switch to the private indicators of an individual driver and considering individual driving characteristics. The application of the method allows you to identify potentially dangerous driving styles that can prevent accidents.
Hyperspectral object classification using hybrid spectral-spatial fusion and ...IJECEIAES
Because of its spectral-spatial and temporal resolution of greater areas, hyperspectral imaging (HSI) has found widespread application in the field of object classification. The HSI is typically used to accurately determine an object's physical characteristics as well as to locate related objects with appropriate spectral fingerprints. As a result, the HSI has been extensively applied to object identification in several fields, including surveillance, agricultural monitoring, environmental research, and precision agriculture. However, because of their enormous size, objects require a lot of time to classify; for this reason, both spectral and spatial feature fusion have been completed. The existing classification strategy leads to increased misclassification, and the feature fusion method is unable to preserve semantic object inherent features; This study addresses the research difficulties by introducing a hybrid spectral-spatial fusion (HSSF) technique to minimize feature size while maintaining object intrinsic qualities; Lastly, a soft-margins kernel is proposed for multi-layer deep support vector machine (MLDSVM) to reduce misclassification. The standard Indian pines dataset is used for the experiment, and the outcome demonstrates that the HSSF-MLDSVM model performs substantially better in terms of accuracy and Kappa coefficient.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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method [16]. Fuzzy DDE problem will model when the crisp model is not complete and its premasters or
conditions under fuzzy properties. FDDEs were solved by multiple researchers in recent years with an
approximate solution in [17, 18]. We will present in this article new plans for the approximate solution of
FDDEs by means of the curves of Bezier method in fuzzy domain and analyzed the fuzzy solutions in
different degree of approximations.
The outline of this paper will be as follows: FDDEs will be introduced in section 2. In section 3,
Problem of Fuzzy Delay System will be declared. Introduced proportional delay with FDDEs in section 4.
In sections 5 and 6 respectively degree elevation and Bezier curves and will be declared. Using Bezier
control points for Solving FDDE aforementioned method and suggested will be implemented on it in
section 7. In section 8 solved numerical problems, appeared the accuracy and adequacy of the method.
Lastly, the conclusion briefly will be given in section 9.
2. DESCRIPTION OF DELAY FUZZY DIFFERENTIAL EQUATIONS
Many DDEs are increasing, fundamentally optimistic in the models of epidemiology and population
dynamics. It is therefore worth noting that positive initial data lead to positive solutions [15]. Consider
the following FDDE:
𝐷𝑣̃(𝑥) = 𝑦̃(𝑥, 𝑣̃(𝑥), 𝑣̃(𝑥 – 𝑘)) (1)
where for all fuzzy level sets 𝑟 ∈ [0,1] we have the following defuzzifications:
- The fuzzy functions 𝑣̃(𝑥) [19] is denoted as 𝑣̃(𝑥; 𝑟) = [𝑣(𝑥; 𝑟), 𝑣(𝑥; 𝑟)],
- The fuzzy delay functions 𝑣̃(𝑥 − 𝑘) is denoted as 𝑣̃(𝑥 − 𝛼; 𝑟) = [𝑣(𝑥 − 𝛼; 𝑟), 𝑣(𝑥 − 𝛼; 𝑟)]
- The fuzzy first order H-derivative, see [19]
𝐷𝑣̃(𝑥; 𝑟) = [𝐷𝑣(𝑥; 𝑟), 𝐷𝑣(𝑥; 𝑟)],
Next, assume that the fuzzy function in (1) can be written as:
𝑦̃(𝑥, 𝑣̃(𝑥), 𝑣̃(𝑥 − 𝛼)) = 𝑦̃ (𝑥, 𝑉̃(𝑥)) such that
𝑦̃ (𝑡, 𝑉̃(𝑥)) = [𝑦 (𝑡, 𝑉̃(𝑥)) , 𝑦 (𝑡, 𝑉̃(𝑥))]
By using Zadeh extension principles [20], we have the following membership function
𝐹 (𝑥, 𝑉̃(𝑥; 𝑟)) = 𝑚𝑖𝑛{𝐷𝑣̃(𝑥; 𝑟): 𝜇|𝜇 ∈ [𝑉̃(𝑥)] 𝑟},
𝐺 (𝑥, 𝑉̃(𝑥; 𝑟)) = 𝑚𝑎𝑥{𝐷𝑣̃(𝑥; 𝑟): 𝜇|𝜇 ∈ [𝑉̃(𝑥)] 𝑟},
where
{
𝑦 (𝑥, 𝑉̃(𝑥; 𝑟)) = 𝐹 (𝑡, 𝑉(𝑥; 𝑟), 𝑉(𝑥; 𝑟)) = 𝐹 (𝑥, 𝑉̃(𝑥; 𝑟))
𝑦 (𝑥, 𝑉̃(𝑥; 𝑟)) = 𝐺 (𝑡, 𝑉(𝑥; 𝑟), 𝑉(𝑡; 𝑟)) = 𝐺 (𝑥, 𝑉̃(𝑥; 𝑟))
(2)
with a single delay 𝑘 > 0. For each 𝑟 ∈ [0,1], suppose that [𝑦̃(𝑥, 𝑉̃)] 𝑟 and[𝑦̃𝑣(𝑥, 𝑉̃)] 𝑟, are continuous on ℝ3
.
Let 𝜑: [𝑧 − 𝑘, 𝑧] → ℝ be continuous where 𝑧 ∈ ℝ be given. Require the solution 𝑣(𝑥) of (1) satisfying
𝑣̃(𝑥; 𝑟) = 𝜑̃(𝑥; 𝑟),𝑧 − 𝑘 ≤ 𝑥 ≤ 𝑧 (3)
and satisfying (1) on 𝑧 ≤ 𝑥 ≤ 𝑧 + 𝛼 for some 𝛼 > 0. Note: should be explain 𝐷𝑣̃(𝑥; 𝑟) as the right-hand
derivative at z. Now demonstrate a material system design problem that shows phenomenon of time delay.
The question picked in this section is exactly the right one in the test (1).
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3. PROBLEM OF TIME FUZZY DELAY SYSTEM
The existence of lags in economic systems is completely normal since a decision for the results of
article should be given a fixed period after. In one sample [21] of total economy and suppose 𝑈̃(𝑥) be
the proceeds which can divide into autonomous expenditure, consumption 𝐴̃(𝑥), and investment 𝐵̃(𝑥).
From section 2, we have:
𝑈̃(𝑥; 𝑟) = 𝐴̃(𝑥; 𝑟) + 𝐵̃(𝑥; 𝑟) + 𝐶̃(𝑥; 𝑟) (4)
𝐴̃(𝑥; 𝑟) = 𝑏̃ 𝑈̃(𝑥; 𝑟)
where 𝑏̃ is a consumption fuzzy coefficient following the properties of triangular fuzzy number [17].
From (4),
𝑈̃(𝑥; 𝑟) =
𝐵̃(𝑥;𝑟) + 𝐶̃(𝑥;𝑟)
1 − 𝑏̃
{
𝐵(𝑥;𝑟) + 𝐶(𝑥;𝑟)
1 − 𝑏(𝑟)
𝐵(𝑥;𝑟) + 𝐶(𝑥;𝑟)
1 − 𝑏(𝑟)
(5)
Assuming that, following a decision to run 𝐷̃(𝑥) there is limited time between the production and
ordering of capital instruments. In expression of the paper of capital savings 𝐽̃(𝑥), we have
𝐽̃′
(𝑥; 𝑟) = 𝐷̃(𝑥 − 𝑘; 𝑟) (6)
𝐵̃(𝑥; 𝑟) =
1
𝑘
∫ 𝐷̃(𝑇; 𝑟)𝑑𝑇
𝑥
𝑥−𝑘
(7)
For each fuzzy level set 𝑟 ∈ [0,1] in crisp domain the economic rationale suggests that 𝐷̃(𝑥; 𝑟) is
given by rate of saving proportionate to 𝑈̃(𝑥; 𝑟) and by the capital paper 𝐽̃(𝑥; 𝑟) such that
𝐷̃(𝑥; 𝑟) = 𝛾(1 − 𝑏̃) 𝑈̃(𝑥; 𝑟) − 𝛿 𝐽̃(𝑥; 𝑟) + 𝜌 (8)
where 𝛾 > 0, 𝛿 > 0 and 𝜌 is direction factor. Combining (6) and (7) to obtain the following
𝐵̃(𝑥; 𝑟) =
1
𝑘
[ 𝐽̃(𝑥 + 𝑘; 𝑟) − 𝐽̃(𝑥; 𝑟)] (9)
From (6) and (9), we get
𝑈̃(𝑥; 𝑟) =
1
𝑘(1− 𝑏̃)
[ 𝐽̃(𝑥 + 𝑘; 𝑟) − 𝐽̃(𝑥; 𝑟)] +
𝐶̃(𝑥;𝑟)
1− 𝑏̃
(10)
By combining (8)-(10), we can yield
𝐽̃̇(𝑥; 𝑟) =
𝛾
𝑘
𝐽̃′
(𝑥; 𝑟) − (𝛿 +
𝛾
𝑘
) 𝐽̃(𝑥 + 𝑘; 𝑟) + [𝛾𝐶̃(𝑥; 𝑟) + 𝜌] (11)
Express acceptance rate new appointment information. It is a delayed-type template operational FDDE.
4. FDDES WITH PROPORTIONAL DELAY
In this research, the Bezier control point method can finish off approximate analytical solutions with
a high level of reliability. Consider the following neutral functional FDEE with proportional delays [21, 22],
(𝑣̃(𝑥; 𝑟) + 𝑎̃(𝑥; 𝑟)𝑣̃(𝑝 𝑘 𝑥; 𝑟))
𝑛
= 𝛽̃ 𝑣̃(𝑥; 𝑟) + ∑ 𝑏̃ 𝑘(𝑥; 𝑟)𝑣̃(𝑘)
(𝑝 𝑘 𝑥; 𝑟) + 𝑦̃(𝑥; 𝑟)𝑛−1
𝑘=0 (12)
with the fuzzy initial conditions
∑ 𝑐̃𝑖𝑘 𝑣̃(𝑘)
(0; 𝑟) = 𝛿̃𝑖
𝑛−1
𝑘=0 (𝑟), (13)
𝑖 = 0, 1, … , 𝑛 − 1.
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Here, 𝑎̃(𝑥; 𝑟) and𝑏̃ 𝑘(𝑥; 𝑟) (𝑘 = 0, 1, … , 𝑛 − 1) k are given analytical fuzzy functions, and 𝛽̃, 𝑝̃ 𝑘, 𝑐̃𝑖𝑘,
and 𝛿̌𝑖 denote given fuzzy constants with 0 < 𝑝 𝑘 < 1, (𝑘 = 0, 1, … , 𝑛). The presence and singularity of
the multi pantograph equation analytical solution is demonstrated [21], the solution Dirichlet sequence is
constructed and the asymptotic stability of the analytical solution is sufficiently defined.. It is proved that
the θ-methods with a variable step size are asymptotically stable if
1
2
< 𝜃 ≤ 1. There are several examples
that show the properties of the θ-methods. In order to apply the Bezier control point method,
we rewrite (12) as
(𝑣̃(𝑥; 𝑟))
𝑛
= 𝛽𝑣̃(𝑥; 𝑟) − (𝑎(𝑥)𝑣(𝑝 𝑘 𝑥))
𝑛
+ ∑ 𝑏 𝑘(𝑥)𝑣(𝑘)
(𝑝 𝑘 𝑥) + 𝑦(𝑥)𝑛−1
𝑘=0 , 𝑥 ≥ 0.
A particular class of crisp DDE represents neutral functional DEEs with proportional delays. The mathematical
modeling of real-world phenomena takes such functioning DEEs on a significant role [12].
5. BEZIER CURVES IN FUZZY DOMAIN
From the definition of Bezier curve polynomial of 𝑚 degree [23] and according to sections 2-4,
we have the following fuzzy analysis
𝐵̃(𝑥; 𝑟) = ∑ 𝑃̃𝑗 𝐵̃𝑗
𝑚
(
𝑥−𝑏1
𝑏2−𝑏1
; 𝑟)𝑚
𝑗=0 , 𝑥 ∈ [𝑏1, 𝑏2]. (14)
𝐵̃𝑗
𝑚
(
𝑥−𝑏1
𝑏2−𝑏1
; 𝑟) =
𝑚!
𝑗!(𝑚−𝑗)!
(
𝑥−𝑏1
𝑏2−𝑏1
; 𝑟)
𝑗
(
𝑏2−𝑥
𝑏2−𝑏1
; 𝑟)
𝑚−𝑗
𝑃𝑗 is control points of Bezier coefficient and 𝐵̃𝑗
𝑚
are the polynomial of Bernstein on interval [a1, a2]
per each fuzzy level set 𝑟 ∈ [0,1], see Figure 1. In particular
𝐵̃(𝑥; 𝑟) = ∑ 𝑃𝑗 𝐵̃𝑗
𝑚
(𝑥; 𝑟)𝑚
𝑗=0 , 𝑥 ∈ [0,1]. (15)
𝐵̃𝑗
𝑚
(𝑥; 𝑟) =
𝑚!
𝑗!(𝑚−𝑗)!
(𝑥; 𝑟) 𝑗(1 − 𝑥; 𝑟) 𝑚−𝑗
(16)
where 𝐵̃(𝑥; 𝑟) is a fuzzy parametric Bezier curve when it’s polynomial of vector valued. Figure 1 shows
the comprise line segments with control polygon of a Bezier curve 𝐶𝑗 − 𝐶𝑗+1, j = 0, 1, … , m − 1. If 𝐵̃(𝑥; 𝑟)
polynomial of a scalar valued, the function is call 𝑦̃ = 𝐵̃(𝑥; 𝑟) then from [23, 24] an explicit Bezier curve
denoted by (𝑥, 𝐵̃(𝑥; 𝑟)).
Figure 1. Degree 5 bezier curve with control polygon
6. SOLUTION OF FDDE USING BEZIER CONTROL POINTS
Consider the following boundary value problem
𝐿(𝑣̃(𝑥; 𝑟), 𝑣̃(𝑝0 𝑥; 𝑟), … , 𝑣̃(𝑝 𝑛 𝑥; 𝑟))𝑣̃(𝑛)
(𝑥; 𝑟) − 𝛽𝑣̃(𝑥; 𝑟) + (𝑎(𝑥)𝑣̃(𝑝 𝑛 𝑥; 𝑟)(𝑛)
−
∑ 𝑏̃ 𝑘(𝑥; 𝑟)𝑣̃(𝑘)
(𝑝 𝑘 𝑥; 𝑟) + 𝑦̃(𝑥; 𝑟)𝑛−1
𝑘=0 , , 𝑥 ≥ 0 (17)
𝑑 𝑗 𝑣̃(0;𝑟)
𝑑𝑥 𝑗 = 𝑎𝑗,
𝑑 𝑗 𝑣̃(1;𝑟)
𝑑𝑥 𝑗 = 𝛽𝑗, 𝑗 = 0,1, … , 𝑛 − 1, (18)
P0
P1
P2 P3
P4
P5
5. Int J Elec & Comp Eng ISSN: 2088-8708
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where 𝐿 is differential operator with proportional delay, is 𝑦̃(𝑥; 𝑟) also a polynomial in x, 0 < 𝑝 𝑘 < 1 and
(k = 0, 1, ···, m) [24, 25]. We propose to represent the approximate solution of eq. (18) 𝑣̃(𝑥; 𝑟) in fuzzy
Bezier form. The preference between Bezier and B-Spline is that the Bezier form is easier to carry out
multiplication, contrast and degree elevation operations symbolically than B-Spline. We choose the sum of
squares of the Bezier control points of the residual to be the measure quantity. Minimizing this quantity gives
the approximate solution. Therefore, the obvious spotlight is in the following, if the minimizing of
the quantity is zero, so the residual function is zero, which implies that the solution is the exact solution.
We call this approach the control point based method. By following [25] detailed steps of the method are
as follows:
Step 1. Choose a degree n and symbolically express the solution 𝑣̃(𝑥; 𝑟)in the degree m (𝑚 ≥ 𝑛) Bezier form
𝑣̃ = 𝑣̃(𝑥; 𝑟) = ∑ 𝛼̃𝑗(𝑥; 𝑟)𝐵̃𝑗
𝑚
(𝑥; 𝑟)𝑚
𝑗=0 (19)
where the control points are 𝛼0, 𝛼1, … , 𝛼 𝑚 to be de-termined.
Step 2. Substituting the approximate solution 𝑣 = 𝑣(𝑥) into the (19), we obtain the residual function
𝑅̃(𝑥; 𝑟) = 𝐿(𝑣̃(𝑥; 𝑟), 𝑣̃(𝑝0 𝑥), 𝑣̃(𝑝1 𝑥; 𝑟), … , 𝑣̃(𝑝 𝑛 𝑥; 𝑟)) − 𝑦̃(𝑥; 𝑟).
This is a polynomial in 𝑥 with degree ≤ h, where
ℎ = max{𝑚 − 𝑛 + deg (𝛼̃(𝑥; 𝑟), 𝑚 + deg (𝑏̃0(𝑥; 𝑟)) , 𝑚 − 1 + deg (𝑏̃1(𝑥; 𝑟)) , … , 𝑚 − 𝑛 + 1 +
deg (𝑏̃ 𝑛−1(𝑥; 𝑟)) , deg(𝑦̃(𝑥; 𝑟))}.
So the residual function 𝑅̃(𝑥; 𝑟) can be expressed in fuzzy Bezier form as well,
𝑅̃ = 𝑅̃(𝑥; 𝑟) = ∑ 𝑏̃𝑗 𝐵̃𝑗
ℎ
(𝑥)ℎ
𝑗=0 (20)
where for each fuzzy level set 𝑟 ∈ [0,1]the control points 𝑏̃0, 𝑏̃1, … , 𝑏̃ℎ are linear functions in the unknowns
𝛼̃𝑗. These functions are derived using the operations of multiplication, degree elevation and differentiation for
Bezier form.
Step 3. Construct the objective function
𝐹̃(𝑥; 𝑟) = ∑ 𝑏̃𝑗
2
(𝑥; 𝑟)ℎ
𝑗=0 .
Then 𝐹̃(𝑥; 𝑟) is also a fuzzy function of 𝑎0, 𝑎1, … , 𝑎 𝑚.
Step 4. Solve the constrained optimization problem:
min 𝐹̃(𝑥; 𝑟) = ∑ 𝑏̃𝑗
2
(𝑎0, 𝑎1, … , 𝑎 𝑚; 𝑟)ℎ
𝑗=0 ,
𝑑 𝑗 𝑣̃(0;𝑟)
𝑑𝑥 𝑗 = 𝑎𝑗,
𝑑 𝑗 𝑣̃(1;𝑟)
𝑑𝑥 𝑗 = 𝛽̃𝑗,𝑗 = 0,1, … , 𝑛 − 1, (21)
by some optimization techniques, such as Lagrange multipliers method, we can be used to solve (21).
Step 5. Substituting the minimum solution back into (19) arrives at the approximate solution to
the differential equation.
7. NUMERICAL EXAMPLE
In this part, we used the mentioned control-point-based method on Bezier control points to solve
DDE’s and system of DDE’s. As a practical example, we consider Evens and Raslan [6] the following
pantograph delay equation in fuzzy form:
𝑢̃′(𝑥) =
1
2
exp (
𝑥
2
) 𝑢̃ (
𝑥
2
) +
1
2
𝑢̃(𝑥), 0 ≤ 𝑥 ≤ 1, (22)
𝑢̃(0) = [𝑟. 2 − 𝑟].
6. ISSN: 2088-8708
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The exact solution is given by .)2();(,);( xx
errxurerxu
According to [5] (21) can be written in defuzzfication form
{
𝑢′(𝑥; 𝑟) =
1
2
exp (
𝑥
2
; 𝑟) 𝑢 (
𝑥
2
; 𝑟) +
1
2
𝑢(𝑥; 𝑟),
𝑢(0; 𝑟) = 𝑟
𝑢
′
(𝑥; 𝑟) =
1
2
exp (
𝑥
2
; 𝑟) 𝑢 (
𝑥
2
; 𝑟) +
1
2
𝑢(𝑥; 𝑟),
𝑢(0; 𝑟) = 2 − 𝑟
(23)
For numerical implementation, we consider the approximate solution using Bezier curves of
degree 3 (m=3) and 8 (m=8) respectively as given in (15). In order to obtain the residual function, we also
approximate ex
in Taylor polynomial of order 6. The detail results are as follows.
7.1. Degree-3 Bezier curve
Let,
3
1
3
3
1
3
)();(
)();(
i
ii
i
ii
xBarxu
xBarxu
, (24)
where 10 x and 3...,,0,and iaa ii are the Bezier control points need to be determined. Substitute
into (23) and the residual functions can be obtained, i.e.
))(
))
2
()(;
2
exp(
2
1
))(();(
))(
))
2
()(;
2
exp(
2
1
))(();(
3
1
3
3
1
3
3
1
3
3
1
3
3
1
3
3
1
3
i
ii
i
ii
i
ii
i
ii
i
ii
i
ii
xBa
x
Bar
x
xBa
dx
d
rxR
xBa
x
Bar
x
xBa
dx
d
rxR
(25)
The right-hand side of (25) is a polynomial of degree 8 and therefore the residual function can be
represented in the form of (20) with ℎ = 8 as follows.
)();(
)();(
8
8
0
8
8
0
xBbrxR
xBbrxR
i
i
i
i
i
i
(26)
To obtain the Bezier control points in (24), we follow the step 3 to step 5 as stated in section 6.
The approximate solutions are available in Tables 1 and 2 and the comparsion of degree 3 bezier curve
solution with exact solution of equation (22) is illustrated in Figure 2 such that:
)]71821024.2
)1(4528665.5)1(0126515.4)1([);(
3
223
x
xxxxxrrxu
)])71821024.243642047.4(
)1)(4528665.5090573311.1(
)1)(0126516.4025303.8()1)(2();(
3
2
23
xr
xxr
xxrxrrxu
7. Int J Elec & Comp Eng ISSN: 2088-8708
On solving fuzzy delay differential equation using bezier curves (Ali F. Jameel)
6527
Table 1. Appoximate and exact values for lower solution,
);( rxu (degree 3 bezier curve)
r approx exact abs. error
0 0 0 0
0.2 0.5436420472 0.5436563657 1.4318499128x 10-5
0.4 1.0872840944 1.0873127314 2.8636998257x10-5
0.6 1.6309261416 1.6309690971 4.2955497386x 10-5
0.8 2.1745681888 2.1746254628 5.7273996514x 10-5
1.0 2.718210236 2.7182818285 7.1592495642x 10-5
Table 2. Approximate and exact values for upper solution,
);( rxu (degree 3 bezier curve)
r approx exact abs. error
0 5.436420472 5.4365636569 1.4318499128 x 10-4
0.2 4.892778425 4.8929072912 1.2886649216x 10-4
0.4 4.349136378 4.3492509255 1.1454799303 x 10-4
0.6 3.805494330 3.8055945598 1.002294939 x 10-4
0.8 3.261852283 3.2619381942 8.591099477 x 10-5
1.0 2 .71821024 2.7182818285 7.159249564 x 10-5
Figure 2. Approximate and exact solution of 𝑢(𝑡) at t = 1 (degree 3 bezier curves)
7.2. Degree-8 Bezier curve
Let,
8
0
3
8
0
8
)();(
)();(
i
ii
i
ii
xBarxu
xBarxu
, (27)
where 10 x and 8...,,0,and iaa ii are the Bezier control points need to be determined.
Substitute into (23) and the residual functions can be obtained, i.e.
0 1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
u(r;1)
r
FDDE using Bezier at t = 1
approximate
exact
8. ISSN: 2088-8708
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6528
))(
))
2
()(;
2
exp(
2
1
))(();(
))(
))
2
()(;
2
exp(
2
1
))(();(
8
0
8
8
0
8
8
0
8
8
0
8
8
0
8
8
0
3
i
ii
i
ii
i
ii
i
ii
i
ii
i
ii
xBa
x
Bar
x
xBa
dx
d
rxR
xBa
x
Bar
x
xBa
dx
d
rxR
(28)
The right-hand side of (25) is a polynomial of degree 13 and therefore the residual function can be
represented in the form of (20) with ℎ = 13 as follows.
)();(
)();(
13
13
0
13
13
0
xBbrxR
xBbrxR
i
i
i
i
i
i
(29)
To obtain the Bezier control points in (27), we also use the step 3 to step 5 as stated in section 6.
The approximate solutions are in Tables 3 and 4 and the comparsion of degree 8 bezier curve solution with
exact solution of equation (22) is illustrated n Figure 3 such that:
]7182791.2)1(0279716.19
)1(44305288.58
)1(84166368.102)1(3750016.113
)1(16666616.80)1(5000002.35
)1(9)1[();(
87
26
3544
5362
78
ttt
tt
tttt
tttt
tttrrxu
8
7
26
35
44
53
62
78
)7182791.24365582.5(
)1()0279716.190559432.38(
)1()4430588.588861176.116(
)1()84166368.10268332736.205(
)1()3750016.1137500039.226(
)1()16666616.8033333232.160(
)1()5000002.5.300000012.71(
)1()98.1()1)(2();(
tr
ttr
ttr
ttr
ttr
ttr
ttr
ttrtrrxu
Table 3. Approximate and exact values for lower solution,
);( rxu (degree 8 bezier curve)
r approx exact abs. error
0 0 0 0
0.2 0.543655820 0.5436563657 5.45269859x10-7
0.4 1.087311648 1.0873127314 1.090539719x 10-6
0.6 1.630967461 1.6309690971 1.635809578x 10-6
0.8 2.174623282 2.1746254628 2.181079437x 10-6
1.0 2.718279102 2.7182818285 2.726349297x 10-6
9. Int J Elec & Comp Eng ISSN: 2088-8708
On solving fuzzy delay differential equation using bezier curves (Ali F. Jameel)
6529
Table 4. Approximate and exact values for upper solution,
);( rxu (degree 8 bezier curve)
r approx exact abs. error
0 5.4365582042 5.4365636569 5.452698593 x10-6
0.2 4.8929023838 4.8929072912 4.907428734 x10-6
0.4 4.3492465634 4.3492509255 4.362158874 x10-6
0.6 3.8055907430 3.8055945598 3.816889015 x10-6
0.8 3.2619349225 3.2619381941 3.271619156 x10-6
1.0 2.7182791021 2.7182818284 2.726349297 x10-6
Figure 3. Approximate and exact solution of u(t) at t = 1 (degree 8 bezier curves)
8. CONCLUSION
This work has successfully implemented and applied Bezier control points to overcome linear and
fuzzy DDEs. A general method framework has been successfully developed and evaluated using fuzzy sets
properties to obtain rough solutions for fuzzy DDEs. Details have been provided regarding the BCP
convergence mechanism related to the approximate first-order fuzzy DDEs solution. Studies of first-order
linear fizzy DDEs by BCP have shown that the system is capable and reliable studies are obtained that match
the properties of the solution of the fizzy differential equation in the form of the triangle fuzzy numbers with
varying degrees of precision.
ACKNOWLEDGEMENTS
The authors are very grateful to the Ministry of Higher Education of Malaysia for providing us with
the Fundamental Research Grant Scheme (FRGS) S/O number 14188 to enable us to pursue this research.
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Int J Elec & Comp Eng, Vol. 10, No. 6, December 2020 : 6521 - 6530
6530
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