INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2013 | Volume:5 | Issue:1|Papers Count:9

In this paper, the Black-Scholes equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. A numerical example is studied to demonstrate the accuracy of the presented methods.

Many methods for ranking fuzzy numbers have been proposed. The existing methods for ranking generalized fuzzy numbers based on the optimistic index (a) gives different values for comparing the numbers by using different values of the optimistic index (a) and it is the shortcoming of this method. So we introduce a new defuzzification using a crisp number for ordering and comparing the fuzzy numbers. The calculation of the proposed method is simpler and easier in comparison the other methods and it provides the correct ordering of generalized fuzzy numbers. It is shown that the proposed modification satisfies all the reasonable properties of fuzzy quantities (I) and (II) proposed by X. Wang, E. E. Kerre [18, 19].

In this paper, we propose a method to obtain fuzzy solutions of duality fully fuzzy linear system (DFFLS) of the form A~X~=B~X~+C~, where A~, B~ are fuzzy matrices and C~, X~ are fuzzy number vectors. To this end, we solve the 1-cut of DFFLS (which is a crisp system here), then some unknown spreads are allocated to any row of a 1-cut of dual fully fuzzy linear system in 1-cut position. Also, by using this method we determine fuzzy solutions will be placed in the tolerable solution set (TSS) and in the controllable solution set (CSS).

In this paper, we introduce an iterative algorithm free from second derivative for solving algebraic nonlinear equations. The analysis of convergence shows that this iterative algorithm has seventh-order convergence. Per iteration of the new algorithm requires three evaluations of the function and two evaluation of its first derivative. Therefore this algorithm has the efficiency index which equals to 1.477. The results obtained using the algorithm presented here show that the iterative algorithm is very effective and convenient for the algebraic nonlinear equations.

Recently, an innovative single-stage approach was developed in [J. Aparicio, J. L. Ruiz, I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA, Journal of Productivity Analysis 28 (2006) 209-218], to determine the closest Pareto-efficient targets for a given inefficient decision making unit (DMU). The purpose of this paper is to perfect this approach via integrating it with the concepts of Holder norms and directional distance function. To this purpose, first, we introduce a furthest-target based directional, named Linear FDHDF, Holder distance function. Then, we characterize the set of Pareto-efficient points of the production possibility set dominating directionally the assessed DMU. Finally, we develop a closest-target based directional, named Linear CDHDF, Holder distance function that, as well as providing an efficiency index, determines the closest targets. Comparing to the earlier approach, our approach is more general and the decision maker’s preference information can be appropriately incorporated into efficiency assessment and target setting. Furthermore, it is more flexible in computer programming.

For any fuzzy number value and ambiguity are very important, hence we propose a method for finding the nearest triangular approximations of fuzzy number by definitions of value and ambiguity functions. Initially, we de ne the value and ambiguity functions for each fuzzy number. This evident that, two fuzzy numbers will be close if functions of value and ambiguity is close, therefor for finding nearest triangular fuzzy number of any fuzzy number we find the nearest value and ambiguity functions by least square approach, such that the computational complexity is less than other methods. At last, we show some examples of fuzzy numbers and its triangular approximation obtained by this method.

Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method when multiple inputs and outputs are present in a set of decision making units (DMUs). In conventional DEA we assume that the produced outputs are perfect. However in real applications, there are systems which their produced outputs are possibly imperfect and defective. These outputs enter the system as inputs once again and after rebuilding, they will be completed. The present paper proposes a modification of the standard DEA model to incorporate such imperfect outputs. Numerical example is used to demonstrate the approach.

In this paper, we will investigate existence, comparison and some stability results of set solutions of fuzzy intergo-differential systems under the formDHx (t)=f(t, x (t))+∫tt0 g (t, h, x (h)) dh, x (t0) =x0ÎEnNwith some suitable conditions.

In this paper, we propose radial basis functions (RBF) to solve the two dimensional flow of fluid near a stagnation point named Hiemenz flow. The Navier-Stokes equations governing the flow can be reduced to an ordinary differential equation of third order using similarity transformation. Because of its wide applications the flow near a stagnation point has attracted many investigations during the past several decades. We satisfy boundary conditions such as infinity condition, by using Gaussian radial basis function through the both differential and integral operations. By choosing center points of RBF with shift on one point in uniform grid, we increase the convergence rate and decrease the collocation points.