2016
8
3
3
0
Set a biobjective redundancy allocation model to optimize the reliability and cost of the Seriesparallel systems using NSGA II problem
2
2
With the huge global and wide range of attention placed upon quality, promoting and optimize the reliability of the products during the design process has turned out to be a high priority. In this study, the researcher have adopted one of the existing models in the reliability science and propose a biobjective model for redundancy allocation in the seriesparallel systems in accordance with the redundancy policy given that failure rate depends on the number of the active elements. The objective behind the proposed model is to maximize the reliability and to minimize the total cost of the system. Internal connection cost, which is the most common parameter in electronic systems, put in this model in order to simulate the realworld conditions. As the proposed model is an NPHard one(for getting results), the researcher adopted a Nondominated Sorting Genetic Algorithm (NSGA II) after optimizing its operatorsâ€™ rate by using Response Surface Methodology (RSM).
1

171
176


M. R.
Shahriari
Faculty of Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.
Faculty of Management, South Tehran
Iran
shahriari.mr@gmail.com
Reliability
Series
Parallel System
Redundancy Allocation Problem
Nondominated Sorting Genetic Algorithm
Response Surface Methodology
A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method
2
2
In this article, a new method is introduced to give approximate solution to Van der Pol equation. The proposed method is based on the combination of two different methods, the spectral Adomian decomposition method (SADM) and piecewise method, called the piecewise Adomian decomposition method (PSADM). The numerical results obtained from the proposed method show that this method is an effective, accurate and powerful tool for solving Van der Pol equation and, the comparison show that the proposed technique is in good agreement with the numerical results obtained using RungeKutta method. The advantage of piecewise spectral Adomian decomposition method over piecewise Adomian decomposition method is that it does not need to calculate complex integrals. Another merit of this method is that, unlike the spectral method, it does not require the solution of any linear or nonlinear system of equations. Furthermore, the proposed method is easy to implement and computationally very attractive.
1

177
184


S. GH
Hosseini
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran
ghasem602@yahoo.com


E.
Babolian
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran


S.
Abbasbandy
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran
Van der Pol equation
Spectral Adomian decomposition method
Piecewise method
RungeKutta method
A Study on Intuitionistic Fuzzy and Normal Fuzzy MSubgroup, MHomomorphism and Isomorphism
2
2
In this paper, we introduce some properties of an intuitionistic normal fuzzy msubgroup of m group with mhomomorphism and isomorphism. We study he image, the preimage and the inverse mapping of the intuitionistic normal fuzzy msubgroups.
1

185
188


M.
Oqla Massa'deh
Department of Applied Science, Ajloun College, AlBalqa'Applied University, Jordan.
Department of Applied Science, Ajloun College
Iran
moradoqla2000@yahoo.com
Intuitionistic Fuzzy Sets
MGroups
Intuitionistic Fuzzy MSubgroups
Intuitionistic Normal Fuzzy MSubgroups
MHomomorphism
Estimation of portfolio efficient frontier by different measures of risk via DEA
2
2
In this paper, linear Data Envelopment Analysis models are used to estimate Markowitz efficient frontier. Conventional DEA models assume nonnegative values for inputs and outputs. however, variance is the only variable in these models that takes nonnegative values. Therefore, negative data models which the risk of the assets had been used as an input and expected return was the output are utilized . At the beginning variance was considered as a risk measure. However, both theories and practices indicate that variance is not a good measure of risk. Then value at risk is introduced as new risk measure. In this paper,we should prove that with increasing sample size, the frontiers of the linear models with both variance and value at risk , as risk measure, gradually approximate the frontiers of the meanvariance and meanvalue at risk models and nonlinear model with negative data. Finally, we present a numerical example with variance and value at risk that obtained via historical simulation and variancecovariance method as risk measures to demonstrate the usefulness and effectiveness of our claim.
1

189
200


M.
Sanei
Department of Applied Mathematics, Islamic Azad University of Central Tehran Branch, Tehran, Iran.
Department of Applied Mathematics, Islamic
Iran


S.
Banihashemi
Department of Mathematics, Faculty of Mathematics and Computer Science, Allameh Tabataba'i University, Tehran Iran.
Department of Mathematics, Faculty of Mathematics
Iran
shbanihashemi@atu.ac.ir


M.
Kaveh
Department of Applied Mathematics, Islamic Azad University of Central Tehran Branch, Tehran, Iran.
Department of Applied Mathematics, Islamic
Iran
Portfolio
Data Envelopment Analysis (DEA)
Value at Risk (VaR)
Negative data
Bernoulli operational matrix method for system of linear Volterra integral equations
2
2
In this paper, the numerical technique based on hybrid Bernoulli and BlockPulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasistatic viscoelasticity and magnetoelectroelastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and BlockPulse functions which are orthonormal and have compact support on $[0, 1]$. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and efficiency of the proposed method.
1

201
207


E.
Hashemizadeh
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj Branch,
Iran
hashemizadeh@kiau.ac.ir


M.
Mohsenyzadeh
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj Branch,
Iran
System of Volterra integral equations
Bernoulli polynomials
Hybrid functions
Operational matrix
A new network simplex algorithm to reduce consecutive degenerate pivots and prevent stalling
2
2
It is well known that in operations research, degeneracy can cause a cycle in a network simplex algorithm which can be prevented by maintaining strong feasible bases in each pivot. Also, in a network consists of n arcs and m nodes, not considering any new conditions on the entering variable, the upper bound of consecutive degenerate pivots is equal $left( begin{array}{c} nm+k \ k \ end{array} right)$ where $k$ is the number of degenerate arcs in the basis. As well as, the network simplex algorithm may stall if it goes through some long consecutive degenerate pivot. Through conditions such as (LRC) and (LRS) upon entering variable rules, this upper bound can be reduced to $mn$ and $m^2$ respectively. In this current paper we first suggest a new algorithm for antistalling in which a new condition is provided to the entering variable and then show that through this algorithm there are at most $k$ consecutive degenerate pivots.
1

209
214


Z.
Aghababazadeh
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran


M.
RostamyMalkhalifeh
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran
mohsen_rostamy@yahoo.com
Network flow problem
Network simplex algorithm
Degeneracy
Strong feasible basis
Stalling
The spectral iterative method for Solving FractionalOrder Logistic Equation
2
2
In this paper, a new spectraliterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. The solutions obtained are compared with Adomian decomposition method and iterative method used in cite{35} and Adams method cite{36}.
1

215
223


A.
Shoja
Department of Mathematics, Science and Research Branches, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran
shoja@riau.ac.ir


E.
Babolian
Department of Mathematics, Science and Research Branches, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran


A. R.
Vahidi
Department of Mathematics, Science and Research Branches, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science
Iran
Adomian decomposition method (ADM)
Iterative method (IM)
Spectral method
Fractional logistic equation
Collocation method
A new iterative with memory class for solving nonlinear equations
2
2
In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also presented.
1

225
229


P.
Bassiri
Department of Mathematics, Payame Noor University (PNU), P. O. Box, 193953697, Tehran, Iran.
Department of Mathematics, Payame Noor University
Iran


P.
Bakhtiari
Young Researchers and Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
Young Researchers and Elite Club, Hamedan
Iran
bakhtiaripr@yahoo.com


S.
Abbasbandy
Department of Mathematics, Imam Khomeini International University, Ghazvin, 3414916818, Iran.
Department of Mathematics, Imam Khomeini
Iran
Multistep methods
Nonlinear equations
Optimal order
Methods with memory
KungTraub's conjecture.
Solving robot selection problem by a new intervalvalued hesitant fuzzy multiattributes group decision method
2
2
Selecting the most suitable robot among their wide range of specifications and capabilities is an important issue to perform the hazardous and repetitive jobs. Companies should take into consideration powerful group decisionmaking (GDM) methods to evaluate the candidates or potential robots versus the selected attributes (criteria). In this study, a new GDM method is proposed by utilizing the complex proportional assessment method under intervalvalued hesitant fuzzy (IVHF)environment. In the proposed method, a group of experts is established to evaluate the candidates or alternatives among the conflicted attributes. In addition, experts assign their preferences and judgments about the rating of alternatives and the relative importance of each attribute by linguistic terms which are converted to intervalvalued hesitant fuzzy elements (IVHFEs). Also, the attributesâ€™ weights and expertsâ€™ weights are applied in procedure of the proposed intervalvalued hesitant fuzzy group decisionmaking (IVHFGDM) method. Hence, the expertsâ€™ opinions about the relative importance of each attribute are considered in determination of attributesâ€™ weights. Thus, we propose a hybrid maximizing deviation method under uncertainty. Finally, an illustrative example is presented to show the feasibility of the proposed IVHFGDM method and also the obtained ranking results are compared with a recent method from the literature.
1

231
240


S. M.
Mousavi
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran.
Department of Industrial Engineering,
Iran


B.
Vahdani
Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
Faculty of Industrial and Mechanical Engineering&l
Iran
b.vahdani@gmail.com


H.
Gitinavard
Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran.
Young Researchers and Elite Club, South
Iran


H.
Hashemi
Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran
Young Researchers and Elite Club, South
Iran
Robot selection problem
Group decision making analysis
Intervalvalued hesitant fuzzy sets
Determining Malmquist Productivity Index in DEA and DEAR based on Value Efficiency
2
2
Malmquist Productivity Index (MPI) is a numeric index that is of great importance in measuring productivity and its changes. In recent years, tools like DEA have been utilized for determining MPI. In the present paper, some models are recommended for calculating MPI when there are just ratio data available. Then, using DEA and DEAR, some models are proposed under the constant returns to scale (CRS) technology and based on value efficiency (VE) in order to calculate MPI when there is just a ratio of the output to the input data (and vice versa). Finally, in an applied study on 30 welfare service companies under CRS technology, the progress and/or regression of companies are determined in DEA and DEAR.
1

241
254


M. R.
Mozaffari
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Department of Mathematics, Shiraz Branch,
Iran
mozaffari854@yahoo.com
Malmquist
Value Efficiency
DEA
DEAR
A Multisupplier Inventory Model with Permissible Delay in Payment and Discount
2
2
This paper proposes a multisupplier multiproduct inventory model in which the suppliers have unlimited production capacity, allow delayed payment, and offer either an allunit or incremental discount. The retailer can delay payment until after they have sold all the units of the purchased product. The retailerâ€™s warehouse is limited, but the surplus can be stored in a rented warehouse at a higher holding cost. The demand over a finite planning horizon is known. This model aims to choose the best set of suppliers and also seeks to determine the economic order quantity allocated to each supplier. The model will be formulated as a mixed integer and nonlinear programming model which is NPhard and will be solved by using genetic algorithm (GA), simulated annealing (SA) algorithm, and vibration damping optimization (VDO) algorithm. Finally, the performance of the algorithms will be compared.
1

255
268


M.
Farhangi
Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
Faculty of Industrial and Mechanical Engineering,
Iran


E.
Mehdizadeh
Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
Faculty of Industrial and Mechanical Engineering,
Iran
emehdi@qiau.ac.ir
Economic order quantity
Genetic algorithm
Simulated annealing
Vibration damping optimization
Flexibility of Variations in Radial and NonRadial Data Envelopment Analysis Models
2
2
One of the major problems in Data Envelopment Analysis (DEA) is to determine the projection of inefficient Decision Making Units (DMUs) into the efficient frontier. In conventional DEA models, inputs and outputs of inefficient DMUs alter arbitrarily for reaching to the efficient frontier. Nevertheless, sometimes the ability of DMUs is defined and restricted. Moreover, there are situations in the real world applications that limited resources exist. Therefore, in these cases inputs and outputs cannot vary irrationally. Actually, there are prespecified alteration levels of inputs and outputs. For this purpose, the current study proposes DEAbased models, radial and nonradial models, to evaluate the relative efficiency of DMUs with restricted input and output variables. Furthermore, nonradial superefficiency models are extended for ranking efficient DMUs. An example from the banking sector is used to illustrate the proposed approach.
1

269
278


S.
Kordrostami
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
Department of Mathematics, Lahijan Branch,
Iran
kordrostami@liau.ac.ir


A.
Amirteimoori
Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
Department of Applied Mathematics, Rasht
Iran


M.
Jahani Sayyad Noveiri
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Department of Mathematics, Lahijan Branch,
Iran
Data Envelopment Analysis (DEA)
Efficiency
Input/Output
Variations
Twophase Boundary Layer Flow, Heat and Mass Transfer of a Dusty Liquid past a Stretching Sheet with Thermal Radiation
2
2
The problem of twophase MHD boundary layer flow, heat and mass transfer over a stretching sheet with fluidparticle suspension and thermal radiation has been studied. The effect of mass transfer in dusty fluid over a stretching sheet is considered for the first time. The governing equations are reduced to a set of nonlinear ordinary differential equations under suitable similarity transformations. The transformed equations are then solved numerically. The influence of various physical parameters such as magnetic parameter, fluidparticle interaction parameters, Prandtl number, Eckert number and thermal radiation parameter on velocity, temperature and concentration of both fluid and particle phase is analyzed. The numerical results of the present investigation were compared with previously published results and found to be an excellent agreement. It is found that, the momentum, thermal and solute boundary layer thickness of both fluid and dust phase are reduced for higher values of mass concentration of suspended dust particles.
1

279
292


K. L.
Krupa Lakshmi
Department of Studies and Research in Mathematics, Kuvempu University, Shimoga577 451, Karnataka, INDIA.
Department of Studies and Research in Mathematics,
Iran


B. J.
Gireesha
Department of Studies and Research in Mathematics, Kuvempu University, Shimoga577 451, Karnataka, INDIA.
Department of Studies and Research in Mathematics,
Iran
bjgireesu@rediffmail.com


Rama
S R Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OHIO, USA.
Department of Mechanical Engineering, Cleveland
Iran


B.
Mahanthesh
Department of Mathematics and Statistics, Christ University, Bangalore560027, Karnataka, INDIA.
Department of Mathematics and Statistics,
Iran
Boundary layer flow
heat and mass transfer
Stretching sheet
Thermal radiation
Fluidparticle suspension
Numerical solution.
Generalized Hdifferentiability for solving second order linear fuzzy differential equations
2
2
In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized Hdifferentiability is presented. Solving first order fuzzy differential equations by extending 1cut solution of the original problem and solving fuzzy integrodifferential equations has been investigated by some authors (see for example cite{darabi1,TS}), but these methods have been done for fuzzy problems with triangular fuzzy initial value. Therefore by extending the rcut solutions of the original problem we will obviate this deficiency. The presented idea is based on: if a second order fuzzy differential equation satisfy the Lipschitz condition then the initial value problem has a unique solution on a specific interval, therefore our main purpose is to present a method to find an interval on which the solution is valid.
1

293
301


P.
Darabi
Department of Mathematics, Farhangian University, Tehran, Iran.
Department of Mathematics, Farhangian University,
Iran
pedarabi@gmail.com


S.
Moloudzadeh
Department of Mathematics, Faculty of Education, Soran University, Soran/Erbil, Kurdistan Region, Iraq.
Department of Mathematics, Faculty of Education,
Iran


H.
Khandani
Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran.
Department of Mathematics, Mahabad Branch,
Iran
Fuzzy differential equations (FDE)
Strongly generalized Hdifferentiability
rcut solutions
Numerical Solution of Fractional Control System by Haarwavelet Operational Matrix Method
2
2
In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haarwavelet functions. In this paper, we will introduce one dimensional Haarwavelet functions and the Haarwavelet operational matrices of the fractional order integration. Also the Haarwavelet operational matrices of the fractional order differentiation are obtained. Then we propose the Haarwavelet operational matrix method to achieve the Haarwavelet time response output solution of fractional order linear systems where a fractional derivative is defined in the Caputo sense. Using collocation points, we have a Sylvester equation which can be solve by Block Krylov subspace methods. So we have analyzed the errors. The method has been tested by a numerical example. Since wavelet representations of a vector function can be more accurate and take less computer time, they are often more useful.
1

303
312


M.
Mashoof
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Department of Mathematics, Lahijan Branch,
Iran


A. H.
Refahi Sheikhani
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Department of Mathematics, Lahijan Branch,
Iran
ah\_refahi@liau.ac.ir
Fractional control system
Haar wavelet
Sylvester equation