# International Journal of Industrial Mathematics Volume:5 Issue: 4, Autumn 2013

• تاریخ انتشار: 1392/08/17
• تعداد عناوین: 11
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• K. Jaikumar, S. Sunantha Pages 275-280
The SST decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. In this topic we are going to consider vectors as fuzzy vectors. We have considered a numerical example and tried to find out solution vector x in fuzzified form using method of SST decomposition.
Keywords: Triangular fuzzy numbers, System of Linear Equations, SST Decomposition Method
• M. Mosleh Pages 281-297
In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large eld called neural computing or soft computing. The model nds the approximated solution of fuzzy differential equation inside of its domain for the close enough neighborhood of the fuzzy initial point. We propose a learning algorithm from the cost function for adjusting of fuzzy weights.
Keywords: Fuzzy neural networks, Fuzzy di erential equations, Feedforward neural network, Learning algorithm
• A. Jafarian, S. Measoomy Nia Pages 299-307
This paper intends to offer a new iterative method based on arti cial neural networks for finding solution of a fuzzy equations system. Our proposed fuzzi ed neural network is a ve-layer feedback neural network that corresponding connection weights to output layer are fuzzy numbers. This architecture of arti cial neural networks, can get a real input vector and calculates its corresponding fuzzy output. In order to nd the approximate solution of the fuzzy system that supposedly has a real solution, rst a cost function is de ned for the level sets of the fuzzy network and target output. Then a learning algorithm based on the gradient descent method is used to adjust the crisp input signals. The present method is illustrated by several examples with computer simulations.
Keywords: System of fuzzy equations, Fuzzy feed, back neural network (FFNN), Cost function, Learning algorithm
• Sh. Nasseri, E. Behmanesh, F. Taleshian, M. Abdolalipoor, N. A. Taghinezhad Pages 309-316
Fuzzy linear programming problem occur in many elds such as mathematical modeling, Control theory and Management sciences, etc. In this paper we focus on a kind of Linear Programming with fuzzy numbers and variables namely Fully Fuzzy Linear Programming (FFLP) problem, in which the constraints are in inequality forms. Then a new method is proposed to ne the fuzzy solution for solving (FFLP). Numerical examples are providing to illustrate the method.
Keywords: Fuzzy numbers, Linear programming, Fuzzy linear programming, membership function, Ranking function
• M. Nikuie, M. K. Mirnia Pages 317-323
In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise in electrical network theory.
Keywords: Singular matrix, Drazin inverse, Constrained systems, Bott, Dun inverse
• S. Dhawan, S. Kumar Pages 325-339
Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modi ed Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion coecients using the initial value and boundary conditions. The physical structures of the nonlinear dispersive equation have been investigated for different parameters involved. It is shown how the nature of the waves look like in a simple way by considering the value of a certain single combination of constant parameters. The proposed scheme is standard, direct and computerized, which allow us to do complicated and tedious algebraic calculations. The ease of using this method to determine shock or solitary type of solutions, shows its power.
Keywords: Nonlinear partial differential equations, solitary waves, Homotopy perturbation method (HPM)
• E. Soori Pages 341-354
We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for a minimization problem and is also a common xed point for a sequence of nonexpansive mappings and a representation of nonexpansive mappings.
Keywords: Representation, Equilibrium problem, Fixed point, Nonexpansive mapping, Variational inequality
• K. Parand, Z. Roozbahani, F. Bayat Babolghani Pages 355-366
In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-in nite domain. The proposed approach is based on an Unsupervised Combined Arti cial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks containing adjustable parameters (the weights and biases); results are then optimized with the combined neural network. The proposed method is tested on series of Lane-Emden differential equations and the results are reported. Afterward, these results are compared with the solution of other methods demonstrating the eciency and applicability of the proposed method.
Keywords: Lane, Emden type equations, Nonlinear ODE, Semi, infinite domain, Astrophysics, Artificial neural network, Combined neural network
• M. A. Fariborzi Araghi, S. Naghshband Pages 367-374
In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region of convergence.
Keywords: Schrodinger equation, Power law nonlinearity, Homotopy analysis method (HAM), Convergence
• S. Jabbarzadeh Kangarlouei, B. Kavasi, M. Motavassel Pages 375-386
The aim of this study is to investigate the effects of outside board on rm value in Tehran Stock Exchange (TSE) from the perspective of information transaction costs. To do so, a sample of 96 firms listed in TSE is selected to be studied during the period of 2003-2012. Tobin q ratio is used to measure rm''s value and bid-ask spread for information transaction costs. In addition to these variables, four control variables are adapted namely rm''s characteristic, age, size and duality. The results of the study show that there is not a signi cant relationship between outside board and firm''s value. Investigating the relationship between outside board and rm''s value, the results indicate that only in food and non-metal industries, there is a negative relationship between outside board and firm''s performance. Therefore, it can be concluded that not in all of industries outside board affects rm''s value. Further, results do not prove the effects of outside board on information transaction cost. In addition, the results do not support that information transaction cost aect rm''s value. Finally, the results also suggest that independence and presence of outside board of director member does not a effect firm''s value in rms with lower information transaction cost.
Keywords: Outside Board, Firm Value, Information Transaction Costs, Tehran Stock Exchange
• M. Momeni, G. R. Jahanshahloo, M. Rostamy Malkhalifeh, S. Razavi, K. Yakideh Pages 387-395
In the real world there are groups which composed of independent units. The conventional data envelopment analysis(DEA) model treats groups as units, ignoring the operation of individual units within each group.The current paper, investigates parallel system network approach proposed by Kao and modifies it. As modi ed Kao'' model is more eligible to recognize ecient groups, a new ranking method is proposed based on a model which calculates eciencies with additional constraint that made model share constant ineciency among groups.To show advantages, modi es model is applied to eciency calculation of both arti cial and real groups and results is compared with conventional DEA model and parallel system network model as well.Finally it is shown by tow numerical and empirical examples that ecient groups recognized by modi ed model how can be ranked according to proposed ranking model.
Keywords: Data Envelopment Analysis, Group Ranking, Network DEA, Parallel Systems Efficiency, Efficient Groups