International Journal of Industrial Mathematics
Volume:1 Issue: 3, Summer 2009

In the present paper, we show the some properties of the fuzzy solution of the controllinear fuzzy dierential equations and research the optimal time problems for it.

Fuzzy systems have gained more and more attention from researchers and practitioners ofvarious elds. In such systems, the output represented by a fuzzy set sometimes needs to be transformed into a scalar value, and this task is known as the defuzzication process.Several analytic methods have been proposed for this problem, but in this paper, theresearcher suggests a new approach to the problem of defuzzication using the weightedmetric (weighted distance) between two fuzzy numbers. In this study some preliminaryresults on properties of such defuzzication will be reported.

Data Envelopment Analysis (DEA) models which evaluate the eciency of a set of decisionmaking units (DMUs) are unable to discriminate between ecient DMUs. The problemof discriminating between these ecient DMUs is an interesting subject. A large numberof methods for fully ranking both ecient and inecient DMUs have been proposed.Through real world applications, analysis may encounter data that are not deterministicor on have a stochastic essence but whose distribution can be dened by collecting data in successive periods and by statistical methods. In this paper, a method for ranking stochastic ecient DMUs is suggested which is based on the full inecient frontier method. Using a numerical example, we will demonstrate how to use the result.

One important issue in DEA which has been studied by many DEA researchers is thesensitivity analysis of a specic DMUo, the unit under evaluation.Moreover, we know that in most models of DEA, the best DMUs have the eciency scoreof unity. In some realistic situations, the performance of some inecient DMUs is similarto that of ecient ones.In this paper, we dene a new eciency category, namely; quasi 􀀀 efficient;. Then, wedevelop a procedure for performing a sensitivity analysis of the ecient and quasi-ecientdecision making units.The procedure yields an exact; stability radius; within which data variations will not altera DMU;s classication from ecient or quasi-ecient to inecient status (or vice versa).

In this paper, a numerical method for solving 'fuzzy dierential inclusion's is considered.The fuzzy reachable set can be approximated by the proposed method with complete error analysis which is discussed in detail. Moreover, the extrapolation method is employed for increasing the accuracy of the approximate solution. The method is illustrated by solving some linear and nonlinear fuzzy initial value problems.

In this paper, we present a new two-parameters family of iterative methods for solvingnon-linear equations and prove that the order of convergence of these methods is at least four. Per iteration of these new methods require two evaluations of the function and two evaluations of its rst derivative. Several numerical examples are given to illustrate the performance of the presented methods.

ABS method provides the general solution of a system by computing a solution anda matrix, called the Abaan matrix, with rows generating the null space of the coef-cient matrix. We present an algorithm for computing a biconjugate pair (V,P), suchthat V TAP = is a diagonal and nonsingular matrix, using ABS algorithm. Then wepropose an algorithm for computing an equivalent diagonal form of a matrix A by usingthe extended ABS algorithm.

Data envelopment analysis (DEA) is a method to estimate the relative eciency of decisionmaking units(DMUs) performing similar tasks in a production system that consumesmultiple inputs to produce multiple outputs. So far, a number of DEA models have beendeveloped: The CCR model and the BCC model are well known as basic DEA models. Thegeneric regularity condition for the CCR model is introduced so that each weakly ecientdecision making unit in the CCR model of data envelopment analysis is also CCR-ecient.In this study, we give a general regularity condition under which each weakly ecient decision making unit in the BCC model and Additive model of data envelopment analysis isalso BCC-ecient and Additive-ecient,respectively.