JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)
Year:2010 | Volume:- | Issue:74/2 (MATHEMATICS ISSUE)|Papers Count:9

Introduction: The use of Information System (IS) to gain strategic dominance and its widespread use in many business functions has made IS project selection a major component of effective Information Technology (IT) management. In these situations, ranking IS project is a suitable approach.Aim: In this paper, by describing IS project selection problem in Iran Ministry of Commerce, we propose a new non parametric method for ranking IS projects.Materials and Methods: It is to be noted that two DEA models- which find most efficient DMU- have been used in proposed method.Results: Basic DEA models identified 7 projects as efficient units. Results of proposed method indicate that forth project is most efficient.Conclusion: Applicability of proposed method has been shown using real data of Iran Ministry of Commerce. As an advantage to Andersen & Petersen ranking method, proposed method finds most efficient DMU by solving only one MILP.

Introduction: Let G be a finite group and A be a normal subgroup of G. We denote by nee(A) the number of G-conjugacy classes of A and A is called n-decomposable, if ncc (A) = n. Set Ncc(G) = {ncc(A) | A D G}. Let X be a nonempty subset of positive integers. A group G is called X-decomposable, if Nee(G) =X.Aim: The aim of this paper is finding all subsets X of positive integers such that there is a X-decomposable finite group.Materials and Methods: In this paper, by using a method of Shahryari and Shahabi given in [10], we first obtain the center of the groups under consideration and then by applying some results of Karpilovsky, the characterization of the groups is obtained.Results: We first characterize the solvable n-decomposable finite groups and then by using some results of Breuer in the classification of finite simple groups, the characterization of n-decomposable finite groups, 1£n£8, are given.Conclusion: Using the methods presented here and some complicated calculations, it is possible to solve the problem for n£12.

Introduction: Today advantage of modeling in different science has abundantly used.In this paper budgetary manner of one imaginary bank during four years according of mathematical models was examined Aim: In this paper a prediction of a governmental bank's budget for four continuous years has been investigated by the use of a mathematical model.Materials and Methods: For this reason, the budget is simulated with an assumed element from a composite cylindrical structure, which its behavior is different in two opposite sides. Four external parameters such as inflation rate, governmental budgets, cash flow growth and GDP, as external forces which apply force to the assumed element and cause both spinning and pushing movements and at the end cause structure contraction. Five internal force such as incomes, costs, benefits and losses, sources and uses are simulated a orthotropic coefficient. Then the fore mentioned equations were solved with the PDE method with the boundary condition to make up to solution of the problem.Results: The result of the external equations of the model was the sum of the spinning and pushing forces. The results from the model showed that the assumed force for the prediction of the assumed bank's budget was appropriate and where budgeting is linear, the error percentage of the model is small according to the bank's performance.Conclusion: The results showed that this model has minimum of residual in nonlinear area, also when budgetary was interred in nonlinear area; however amount of residual in this model was increased with theoretical results.

introduction: In this paper, we propose a numerical method for approximating the solution of the fuzzy functional integral equations of Volterra and Fredholm type by using Lagrange interpolation. For this purpose, we convert the fuzzy Fredholm and Volterra integral equations to the crisp systems of integral equations. The proposed method is illustrated by various fuzzy numerical examples.Aim: In almost, the integral equations cannot be solved analytically or simply.Therefore, we propose the numerical methods for solving the integral equations.Material and Method: For solving fuzzy functional integral equations, at first, we introduce the parametric form of them and then we obtained (2n+2) x (2n+2) systems via Lagrange interpolation. In the following, this system convert to two (n+1) x (n+I) systems.By solving them, we have the support points which can be approximate the exact solution.Results: In this work, for solving Fredholm or Volterra fuzzy functional integral equation, we replaced each of this fuzzy integral equation by two crisp integral equations. For numerical solution of these equations, we applied the Lagrange interpolation with different r_cuts that is between zero and one. At last, by substituting x in the crisp equations by Xj for j = 0,1,...,n we obtained a linear system of equations with 2n + 2 equations and 2n + 2 unknown. By solving two (n+l) x (n+l) systems, y(xj.;r) and ȳ (xj;r) for j=0,1,...,n and 0£r£1 are calculated. Consequently, the approximation for exact solution is given by putting y(xj .;r) and . ȳ (xj;r) for j = 0, 1,...,n in Lagrange interpolation function. The advantage of this method in comparison with the other methods is that the solution of the integral equation is approximated by having the supported points. Also, the proposed method in comparison with Freidman et al.'s method converges to the exact solution with less number of the iterations and node points.Conclusion: This By the proposed method, we can numerically solve the fuzzy functional integral equations of Volterra and Fredholm of the second kind, Also, the proposed method in comparison with Freidman et al.' s method converges to the exact solution with less number of the iterations and node points.

Introduction: Data envelopment analysis (DEA) is a new technique developed in operations research and management science over the last three decades for measuring productive efficiency. In some situations some inputs and outputs are unknown decision variables such as bounded data, ordinal data, and ratio bounded data, then the resulting DEA model is a non-linear and is called Imprecise DEA (IDEA). DEA treats each DMU as a black box by considering only the inputs consumed and outputs produced by each DMU. In a network model, we focus on the transformation process in the black box.Aim: In some situations, DMUs have network structure and imprecise data. This paper wants to propose a method to evaluate these DMUs.Material and Method: Network Data Envelopment Analysis (DEA) models allow the researcher to study the inside of the usual black-box (production process). In this paper, we deal with imprecise data on network, and propose a method for evaluation network Decision Making Units (DMUs) with imprecise data. This method uses standard linear programming DEA model by converting imprecise data into interval data.Results: In this paper we obtain an envelopment model, which is a generalized form of the basic DEA model.Conclusion: This paper considered a network DEA model and proposed model to compute interval efficiency for DMUs with network structure and imprecise data. Similar discussion can be developed for any network DEA model.

Introduction: The theory and application of integral equation is an important subject within applied mathematics. There are several numerical approaches for solving linear Volterra integral equations of the second kind.Aim: In this paper, the Romberg's extrapolation is applied on quadrature method of numerical solution of linear Volterra integral equations of the second kind.Materials and Methods: An algorithm for new numerical solution calculated by Romberg's method is given.Results: The calculated solutions show more efficiency and accuracy with less computation than solution with quadrature method over more points of integration.Conclusion: The numerical results prove that the presented method is very effective and simple. The next advantage of this method respect to some other methods, is high accuracy and also convergence of the method which is very fast respect to similar method.

Introduction: one important aspect of mathematics curriculum in every educational system should be utilitarian aspect of mathematics. This aspect provides that the curriculum designers pay more attention to application of mathematics and read problem of the world and in other subjects, especially by considering the aims and standard of the committee responsible for the change of school mathematics in 1967 and 1997 reforms, and also the NCTM standards.Aim: The aim of this article is to study critically the present situation of mathematics application within the secondary school mathematics and give some recommendation for the improvement of mathematics curriculum.Results: In the present mathematics curriculum in educational system in Iran there was not much attention to application in spite of its importance of a mathematics education, we believe that there should be some considerable changes in school mathematics.Conclusion: The curriculum designers should be convinced that it is necessary to include application of mathematics within mathematics curriculum by considering real situations from other subjects and it is also necessary to include some real world problems and modeling.

Introduction: In this paper, the solution of fuzzy differential inclusions (FDIs) with Lower-Upper Representation is established.Aim: Finding an approximate solution of fuzzy differential inclusions.Materials and Methods: Instead of a precise fuzzy number as an initial value, we have just some information in some a -cuts of it, which shows the value of initial value at the endpoints of a -cuts and also the slopes of the fuzzy number's membership function in the mentioned points.Results: Using the intervals formed with the a -cut of initial value we apply the Euler method and solve the FDIs to find the same information for the solution of the given problem.Also to determine the slopes of the estimated fuzzy solution again we use the Euler method and solve the fuzzy differential equations (FDEs). Finally with an specific interpolation polynomial we obtain the approximated solution.Conclusion: The method presented in this paper is based on the LU-representation of fuzzy numbers with N=1. We find the solution set just in two a -cuts and then the approximate solution will introduce via interpolation polynomials.

Introduction: In the evaluation of decision making units (DMUs) by using ordinary data envelopment analysis models, for instance in output orientation, the projected point may be considered as a target point. But in real problems, there are usually restrictions that make it impossible to use these targets. One of these restrictions is the limitation of some outputs.This means that DMUs cannot be free in choosing output targets and they also influence other DMUs.Aim: In this paper we deal with this problem and propose a method for solving it. In the end, we use the proposed model for setting output targets for some commercial banks in Iran.Materials and Methods: For evaluating DMUs, model BCC must be solved separately for each DMU. By defining independent variables, we evaluate all DMUs in one model. For constructed Multi Objective Decision Making (MODM) problem, we consider an equivalent problem. Then by adding relevant constraint(s) to it, we introduce a model for setting targets in bounded aggregate output case.Results: The proposed model in this article can be solved in two phases. After solving this two-phase model, targets are introduced for all under studied DMUs with the property that the summation of a specific output of the targets cannot exceed a fixed predetermined value. The proposed model is linear and can be easily solved by using existing software capable of solving linear programming problems.Conclusion: In practical problems, it happens very often that some units want to set targets which have limited quantities. Although the targets obtained by the projections of ordinary DEA models are points on efficient frontier, but sometimes they can be very optimistic, especially when DMUs influence the performance of each other. The proposed model in this paper can help us to set more realistic targets for DMUs whose targets (or projections) cannot be free, and are related to targets of other DMUs.