International Journal of Industrial Mathematics
Volume:4 Issue: 2, Spring 2012

In this work we prove that for any measurable admissible control w (·) and for any «> 0 there exists piecewise constant admissible control ¯ w (·) such that for fuzzy solutions of control fuzzy linear system are»-closed.

In the evaluation of decision making units (DMUs), by using the ordinary data envelopment analysis models, the projected point may be considered as a target point. Various orientations lead to various targets. The selection of one of these projected points or other designated efficient points as targets, is a considerable problem in target setting. There are different criteria for the selection of such suitable targets. In this article, we introduce a method for target setting, on the basis of ranking in Tv. Since most of the designated points for targets are non-extreme, we propose a method for ranking non-extreme DMUs,based on a convex combination (with the best score) of extreme efficient DMUs, located on the minimum face containing the non-extreme DMUs.

To remove the difficulty caused by different costs of the frontiers for calculating the changes of cost efficiency and its components, Tohidi, et al [G. Tohidi, S. Razavyan, S. Tohidnia,A global cost Malmquist productivity index using data envelopment analysis, Journal of the Operational Research Society, 63 (2012) 72-78] proposed a global cost Malmquist productivity index. This index is applicable when input costs are known and producers are going to minimize the cost of decision making units (DMUs). In this paper the above proposed index is generalized to compare the productivity of two different units at two different points of time under the constant returns to scale (CRS) and variable returns to scale (VRS). The global cost Malmquist productivity index developed here is unique and is computed using nonparametric linear programming models, known as data envelopment analysis (DEA). To illustrate the generalized index and its components, a numerical example at three successive periods of time is given.

In this paper, we provide the collocation method for natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear waste disposal. This problem is a non-linear, three-point boundary value problem on semi-infinite interval. We use two orthogonal functions namely rational Gegenbauer and modified generalized Laguerre functions which are defined as basis functions in this approach and compare them together. We also present the comparison of these works with Runge-Kutta solution, moreover, in the graph of the ∥Res∥2, we show that the present solutions are accurate and applicable.

Many models in DEA have been proposed to estimate returns to scale. Determining the nature of returns to scale has considerable of importance in the theory of production.Knowing the fact that returns to scale is a constant, ascending or descending decision making unit, proper actions can be performed to develop the decision making units. In this study, the efficiency of parallel production systems with shared resources is evaluated such that the data is inexact and interval, so the function of these systems is interval too.Then a model is proposed to estimate returns to scale of interval data on these systems;when the data is inexact, the nature of returns to scale of these units is inexact too, so returns to scale is estimated as multiple in best and worst conditions.

A numerical method for solving the Lane-Emden equations as singular initial value problems is presented. The method is based on using integral operator and convert Lane-Emden equations to integral equations and interpolation by radial basis functions (RBFs). Also,Legendre-Gauss quadrature integration method utilized to reduce the solution of integral equations to the solution of algebraic equations. Several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method.

A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number.In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert estimation problems, prediction problems, etc. Accordingly,the necessity to develop a method for the defuzzification of fuzzy numbers, allowing us to save their informative properties has arisen. The purpose of this paper is to develop such a method. The method allows us to find aggregative intervals for fuzzy numbers. These intervals are called the Regular weighted intervals. We start with the definition of regular weighted points for fuzzy numbers. The regular weighted interval for fuzzy number is defined as the set of regular weighted points of all unimodal numbers, that belong to this number. Some propositions and examples about regular weighted point and regular weighted intervals roperties are offered.