2017
9
2
0
0
A New Method for Comparing Fuzzy Quantities Based on Scaler Value and MiddlePoint of Fuzzy Numbers
2
2
The importance as well as the difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middlepoint and the spread of each $gamma$cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each $gamma$cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions.
1

99
104


Rahim
Saneifard
Department of Applied Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of Applied Mathematics, Urmia
Iran
srsaneeifard@yahoo.com


Rasoul
Saneifard
Department of Engineering Technology, Texas Southern University, Houston, Texas, USA.
Department of Engineering Technology,
Iran
Ranking
Fuzzy number
Defuzzification
Signal/noise ratios
On End and Coupled Endpoints of $theta$$F$Contractive SetValued Mappings
2
2
In this paper, we introduce a new concept in setvalued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive setvalued mappings, recently has been introduced by AminiHarandi [Fixed and coupled fixed points of a new type contractive setvalued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that this mapping have a unique end point. Then, we state and prove a result about existence of coupled fixed point of this type of contractive setvalued mappings defined on $M times M$, where $M$ is a complete metric space (Recently, Amini Harandi proved existence of coupled fixed point only for self mappings). Finally, we introduce one another new concept, which we have called condition $(UHS)^*$. Then, adding this condition we state and prove existence of coupled endpoint for such contractive setvalued mappings. Some examples are given to illustrate the results.
1

105
110


B.
Mohammadi
Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.
Department of Mathematics, Marand Branch,
Iran
bmohammadi@marandiau.ac.ir


A.
Alizadeh
Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.
Department of Mathematics, Marand Branch,
Iran
Endpoint
Coupled fixed point
Coupled endpoint
$theta$$F$Contractive
Setvalued mappings.
Approximate Solution of Fuzzy Fractional Differential Equations
2
2
In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative examples.
1

111
118


A.
Panahi
Department of Mathematics, Saveh Branch, Islamic Azad University, Saveh, Iran.
Department of Mathematics, Saveh Branch,
Iran
panahi53@gmail.com
Fuzzy Differential Equations
Fractional derivative
Fuzzy variational iteration method
Fuzzy derivative
Comparison of Neural Network Models, Vector Auto Regression (VAR), Bayesian VectorAutoregressive (BVAR), Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) Process and Time Series in Forecasting Inflation in Iran
2
2
This paper has two aims. The first is forecasting inflation in Iran using Macroeconomic variables data in Iran (Inflation rate, liquidity, GDP, prices of imported goods and exchange rates) , and the second is comparing the performance of forecasting vector auto regression (VAR), Bayesian VectorAutoregressive (BVAR), GARCH, time series and neural network models by which Iran's inflation is forecasted. The comparison of performance of forecasting models used to forecast Iran's inflation has been done based on the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) of the models. Due to the annual values of Inflation, liquidity, GDP, prices of imported goods and exchange rates at free market to estimate different models in this paper and compare root mean square error and Mean Absolute Percentage Error of models by which inflation has been forecasted, neural network model had better performance than others models in forecasting Iran's inflation. Indeed root mean square error and Mean Absolute Percentage Error of neural network model have less value rather than root mean square error and Mean Absolute Percentage Error of other forecasting models.
1

119
128


M.
Pendar
Department of Agriculture Economy, University of Tehran, Tehran, Iran.
Department of Agriculture Economy, University
Iran


M.
Haji
Department of Accounting, Ghiyamdasht Branch, Islamic Azad University, Ghiyamdasht, Iran.
Department of Accounting,
Iran
haji.majid@gmail.com
Inflation
Forecast
Neural Network
Vector auto regression
Bayesian VectorAutoregressive
GARCH
Time series.
New Artificial Intelligence Modeling for the Photocatalytic Removal of C.I. Acid Yellow 23 in Wastwater
2
2
This paper proposes two methods to predict the efficiency of photochemical removal of AY23 by UV/AgTiO$_{2}$ process. In this work the potential of the particle swarm optimization (PSO) and imperialist competitive algorithm (ICA) modeling approaches are presented to forecast the photocatalytic removal of AY23 in the presence of AgTiO$_{2}$ nanoparticles prepared under desired conditions. To validate the techniques, a total of 100 data are used that randomly splitted in two parts, 80 samples for the training the models and 20 for testing of the models. Experimental results on datasets show that ICA approach is better than PSO approach. Remarkable analysis results reveal that AY23 initial concentration is the most significant factors that influence on the AY23 removal efficiency.
1

129
137


F.
Ganbary
Department of Chemistry, Mahabad Branch, Islamic Azad University, Mahabad, Iran.
Department of Chemistry, Mahabad Branch,
Iran
ghanbary83@yahoo.com
Nanoparticles
AgTiO_2
C. I. Acid Yellow 23
Particle swarm optimization
Imperialist competitive algorithm
Dynamical Control of Computations Using the Family of Optimal Twopoint Methods to Solve Nonlinear Equations
2
2
One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal twopoint methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in the given iterative solution and obtain the optimal solution with its accuracy. For this purpose, a theorem is proved to illustrate the accuracy of the iterative method and the CESTAC$^1$footnote{$^1$Controle et Estimation Stochastique des Arrondis de Calculs} method and CADNA$^2$footnote{$^2$Control of Accuracy and Debugging for Numerical Application} library are applied which allows us to estimate the roundoff error effect on any computed result. The classical criterion to terminate the iterative procedure is replaced by a criterion independent of the given accuracy ($epsilon$) such that the best solution is evaluated numerically, which is able to stop the process as soon as a satisfactory informatical solution is obtained. Some numerical examples are given to validate the results and show the efficiency and importance of using the stochastic arithmetic in place of the floatingpoint arithmetic.
1

139
147


M. A.
Fariborzi Araghi
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Central Tehran
Iran
fariborzi.araghi@gmail.com


E.
Zarei
Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
Department of Mathematics, Hamedan Branch,
Iran
Stochastic arithmetic
CESTAC method
CADNA library
Twopoint methods
Nonlinear equations
Entropy Generation In an Unsteady MHD Channel Flow With Navier Slip and Asymmetric Convective Cooling
2
2
The combined effects of magnetic field, Navier slip and convective heating on the entropy generation in a flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel plates under a constant pressure gradient have been examined. Both the lower and upper plates of the channel are subjected to asymmetric convective heat exchange with the ambient fluid. The governing nonlinear governing partial differential equations are solved using the MATLAB PDE solver. The entropy generation number and the Bejan number are also obtained. The influences of the pertinent flow parameters on velocity, temperature, entropy generation and Bejan number are discussed graphically. It is observed that the plate surfaces act as a strong source of entropy generation and heat transfer irreversibility. Also, the entropy generation number decreases for increasing values of the magnetic parameter. The slip parameters are found to control the entropy generation. By using asymmetric cooling of the plates, it is possible to operate the system with reduced entropy generation rate.
1

149
160


S.
Das
Department of Mathematics, University of Gour Banga, Malda, India.
Department of Mathematics, University of
Iran
tutusanasd@yahoo.co.in


R. N.
Jana
Department of Applied Mathematics, Vidyasagar University, Midnapore, India.
Department of Applied Mathematics, Vidyasagar
Iran


A. J.
Chamkha
Mechanical Engineering Department, Prince Mohammad Bin Fahd University, AlKhobar 31952, Saudi Arabia.
Mechanical Engineering Department, Prince
Iran
MHD channel flow
Navier slip
Convective cooling
Entropy generation number
Bejan number
Use of Fuzzy Numbers for Assessing Problem Solving Skills
2
2
The importance of Problem Solving (PS) has been realized for such a long time that in a direct or indirect way affects our daily lives in many ways. Assessment cases appear frequently for PS skills which involve a degree of uncertainty and (or) ambiguity. Fuzzy logic, due to its nature of characterizing such cases with multiple values, offers rich resources for dealing with them. On the other hand, Fuzzy Numbers (FNs) play a fundamental role in fuzzy mathematics, analogous to the role played by the ordinary numbers in classical mathematics. In the present paper we utilize the two simplest forms of them, i.e. the Triangular and Trapezoidal FNs, together with the Centre of Gravity (COG) defuzzification technique as assessment tools for PS skills. Our results are illustrated by three examples in which the assessment outcomes of FNs are validated through their comparison with the corresponding outcomes of assessment methods of the bivalued and fuzzy logic already tested in author's earlier works.
1

161
171


Michael Gr.
Voskoglou
Department of Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece.
Department of Mathematical Sciences,
Iran
mvosk@hol.gr


S. N.
Mishra
Department of Mathematics, National Institute of Technology Durgapur, West Bengal, India.
Department of Mathematics, National
Iran
Problem Solving Assessment
Fuzzy Logic (FL)
Fuzzy Numbers (FNs)
Triangular (TFNs) and Trapezoidal (TpFNs) Fuzzy Numbers
Centre of Gravity (COG) Defuzzification Technique.
Convergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations
2
2
In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear delay Volterra integral equations is considered by two methods. The methods are developed by means of the sinc approximation with the single exponential (SE) and double exponential (DE) transformations. These numerical methods combine a sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. The existence and uniqueness of numerical solutions for these equations are provided. Also an error analysis for the methods is given. So far approximate solutions with polynomial convergence have been reported for this equation. These methods improve conventional results and achieve exponential convergence. Numerical results are included to confirm the efficiency and accuracy of the methods.
1

173
181


M.
Zarebnia
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics, University of
Iran
zarebnia@uma.ac.ir


L.
Shiri
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics, University of
Iran
Nonlinear Volterra integral equations
General delays
Sinccollocation
Convergence analysis.