2016
8
1
1
0
Fuzzy efficiency: Multiplier and enveloping CCR models
2
2
Comparing the performance of a set of activities or organizations under uncertainty environment has been performed by means of Fuzzy Data Envelopment Analysis (FDEA) since the traditional DEA models require accurate and precise performance data. As regards a method for dealing with uncertainty environment, many researchers have introduced DEA models in fuzzy environment. Some of these models are solved by transforming fuzzy models into their crisp counterparts. In this paper applying a fuzzy metric and a ranking function, obtained from it, the multiplier fuzzy CCR model converts to its crisp counterpart. Solving this model yields the optimal solution of fuzzy multiplier model. Moreover, in the following some properties and theorems about mentioned enveloping and multiplier models have been proved.
1

1
8


A. A.
Hosseinzadeh
Department of Mathematics, Lahijan Branch, Islamic Azad University, Guilan, Iran.
Department of Mathematics, Lahijan Branch,
Iran
hosseinzadeh_ali@yahoo.com


F.
Hosseinzadeh Lotfi
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and R
Iran


Z.
Moghaddas
Department of Electrical, Computer and Biomedical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
Department of Electrical, Computer and Biomedical
Iran
Fuzzy number
Fuzzy DEA
Ranking
Bessel multipliers on the tensor product of Hilbert $C^ast$ modules
2
2
In this paper, we first show that the tensor product of a finite number of standard gframes (resp. fusion frames, frames) is a standard gframe (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast$ modules and vice versa, then we consider tensor products of gBessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast$modules. Moreover, we obtain some results for the tensor product of duals using Bessel multipliers.
1

9
16


M.
Mirzaee Azandaryani
Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran.
Department of Mathematics, Faculty of Science,
Iran
m.mirzaee@qom.ac.ir
Gframes
Bessel multipliers
tensor products
Hilbert $C^ast$ modules
Error estimation of fuzzy NewtonCotes method for Integration of fuzzy functions
2
2
Fuzzy NewtonCotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy NewtonCotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and fuzzy Simpson rule is accurate for polynomial of degree three. The accuracy of fuzzy Trapezoidal rule and fuzzy Simpson rule for integration of fuzzy functions are illustrated by two examples.
1

17
23


N.
Ahmady
Department of Mathematics, VaraminPishva Branch, Islamic Azad University, Varamin, Iran.
Department of Mathematics, VaraminPishva
Iran
n.ahmadi@iauvaramin.ac.ir


E.
Ahmady
Department of Mathematics, ShahreQods Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, ShahreQods Branch,
Iran
Fuzzy integration
Fuzzy NewtonCotes method
Fuzzy trapezoidal's rule
Fuzzy Simpson's rule
An approach to fault detection and correction in design of systems using of Turbo codes
2
2
We present an approach to design of fault tolerant computing systems. In this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. Code combining techniques are very effective, which one of these codes are turbo codes. The Algorithmbased fault tolerance techniques that to detect errors rely on the comparison of parity values computed in two ways, the parallel processing of input parity values produce output parity values comparable with parity values regenerated from the original processed outputs, can apply turbo codes for the redundancy. The goal is to describe new protection techniques that are easily combined with normal data processing methods, leading to more effective fault tolerance. The error detection structures are developed and they not only detected subsystem errors but also corrected errors introduced in the data processing system. Concurrent parity values techniques are very useful in detecting numerical error in the data processing operations, where a single error can propagate to many output errors. This method is a new approach to concurrent error correction in faulttolerant computing systems. In this paper we present methods for employ turbo codes into systematic forms and evaluation them with class of Convolutional codes, which is based on burstcorrecting codes, and bounds on the fault tolerance redundant computations are given. The methods and analysis of the fault tolerance for the data processing systems are presented. A new technique is presented for protecting against both hard and soft errors at the data sample level using the errordetecting properties of turbo codes. The data processing system is surrounded with parallel parity defined by a turbo code. Erroneous behavior is detected by comparing externally the calculated and regenerated parity values.
1

25
39


H.
Hamidi
Information Technology Engineering Group, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran.
Information Technology Engineering Group,
Iran
h_hamidi@kntu.ac.ir
Turbo codes
Fault Detection
Error correction
redundancy
Computing Systems.
Threeaxis optimal control of satellite attitude based on Ponteryagin maximum principle
2
2
A long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a threeaxis optimal control on the sixdimensional system which describes the kinetic and kinematic equations of a satellite subjected to deterministic external perturbations which induce chaotic motion. At first, the chaotic behavior of system using Lyapunov exponents (LE) and numerical simulations is investigated when no control is affected. Then, a threeaxis optimal control is presented by the Pontryagin maximum principle (PMP). This optimal control stabilizes the satellite attitude around the equilibrium point of origin. Finally, we give some simulation results to visualize the effectiveness and feasibility of the proposed method.
1

41
48


M. R.
Niknam
Department of Mathematics, Payame Noor University, P.O.Box 193953697, Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
rezanik82@yahoo.com


K.
Kheiri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University
Iran


A.
Heydari
Department of Mathematics, Payame Noor University, P.O.Box 193953697, Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
Lyapunov exponent
Satellite attitude
Pontryagin maximum principle
Optimal control
A hybrid fuzzy multiple attribute decision making approach for identification and ranking influencing factors on Bullwhip Effect in supply chain: real case of Steel industry
2
2
Bullwhip effect phenomenon is what reduces the efficiency of the supply chain. The effect occurs when demand changes in the supply chain face with a lot of volatility. So far, several key factors have been identified as causes of this phenomenon. Since the steel industry, is the basic one, its efficiency is of great importance. Therefore, in this study influencing factors on Bullwhip Effect in the industry will be identified and ranked so that by identifying the most important factors in its creation, proper decisions can be made to deal with this costly phenomenon. This study aims to review several reasons of the effect, identified by various authors. Then its impacts on the steel industry supply chain are mentioned. With views of experts from the steel industry, among the factors identified in the occurrence of the Bullwhip effect, by applying fuzzy Delphi method in the industry the most important ones are identified. The factors in previous phase, in the structure of SCOR model, are matched with the processes of this model then, ultimately, prioritized in order of importance with FANP method in aspect of SCOR criteria by the experts of the steel industry.
1

49
63


N.
Pilevari
Department of Industrial Management, College of Management and Accounting, YadegareImam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran.
Department of Industrial Management, College
Iran
pilevari@iausr.ac.ir


M.
Hasanzade
Department of Management and Economies, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Management and Economies, Science
Iran


M.
Shahriari
Department of Management, Islamic Azad University UAE Branch, Dubai, UAE.
Department of Management, Islamic Azad University
Iran
Bullwhip Effect
Fuzzy ANP
SCOR
Steel Industry
Supply Chain
Variance analysis of control variate technique and applications in Asian option pricing
2
2
This paper presents an analytical view of variance reduction by control variate technique for pricing arithmetic Asian options as a financial derivatives. In this paper, the effect of correlation between two random variables is shown. We propose an efficient method for choose suitable control in pricing arithmetic Asian options based on the control variates (CV). The numerical experiment shows the productivity of the proposed method.
1

65
71


B.
Fathi Vajargah
Department of Statistics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran.
Department of Statistics, Faculty of Mathematical
Iran
behrouz.fathi@gmail.com


A.
Salimipour
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran.
Department of Applied Mathematics, Faculty
Iran


S.
Salahshour
Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Iran.
Young Researchers and Elite Club, Mobarakeh
Iran
Monte Carlo simulation
Arithmetic Asian options
Variance reduction technique
Control variates
Correlation
Solution of fuzzy differential equations
2
2
Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior. The hybrid differential equations have a wide range of applications in science and engineering. The hybrid systems are devoted to modeling, design, and validation of interactive systems of computer programs and continuous systems. Hybrid fuzzy differential equations (HFDEs) is considered by Kim et al. [11]. In the present paper it is shown that the example presented by Kim et al. in the Case I is not very accurate and in the Case II, is incorrect. Namely, the exact solution proposed by the authors in the Case II are not solutions of the given HFDE. The correct exact solution is also presented here, together with some results for characterizing solutions of FDEs under Hukuhara differentiability by an equivalent system of ODEs. Then, the homotopy analysis method (HAM) is applied to obtained the series solution of the HFDEs. Finally, we illustrate our approach by a numerical example.
1

73
80


M.
Otadi
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.
Department of Mathematics, Firoozkooh
Iran
mahmoodotadi@yahoo.com


M.
Mosleh
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.
Department of Mathematics, Firoozkooh
Iran
Fuzzy Differential Equations
Homotopy analysis method
Approximate solution
Numerical solution of general nonlinear FredholmVolterra integral equations using Chebyshev approximation
2
2
A numerical method for solving nonlinear FredholmVolterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has lowest operation count in contrast to other early methods which use operational matrices (with huge number of operations) or involve intermediate numerical techniques for evaluating intermediate integrals which presented in integral equation or solve special case of nonlinear integral equations. Also rate of convergence are given. The numerical examples show the applicability and accuracy of the method.
1

81
86


F.
Fattahzadeh
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Central Tehran
Iran
farfattahzadeh@iauctb.ac.ir
Nonlinear FredholmVolterra integral equation
Chebyshev polynomials
Error analysis
Fast Fourier Transform.
A nonlinear model for common weights set identification in network Data Envelopment Analysis
2
2
In the Data Envelopment Analysis (DEA) the efficiency of the units can be obtained by identifying the degree of the importance of the criteria (inputsoutputs).In DEA basic models, challenges are zero and unequal weights of the criteria when decision making units are evaluated. One of the strategies applied to deal with these problems is using common weights of the each input/output in all decision making units (DMUs). In practice the DMUs are containing intermediate process. However, these units are considered as a black box in DEA basic models, disregarding internal process. This was the main reason network data envelopment analysis was introduced. On the other hand, similar challenges mentioned for DEA, zero and unequal weights of the criteria, exist for network structures as well. This paper suggests a common set of the weights for network structures to deal with the above problems using nonlinear models, for general case. Also some numerical examples using proposed models are presented.
1

87
98


J.
Pourmahmoud
Department of Applied Mathematics, Azarbaijan Shahid madani University, Tabriz, Iran.
Department of Applied Mathematics, Azarbaijan
Iran
pourmahmoud@azaruniv.ac.ir


Z.
Zeynali
Department of Applied Mathematics, Azarbaijan Shahid madani University, Tabriz, Iran.
Department of Applied Mathematics, Azarbaijan
Iran
Network Data Envelopment Analysis (NDEA)
Decision Making Units (DMU)
Efficiency
Epsilon
Assurance Value