International Journal of Industrial Mathematics
Volume:12 Issue: 2, Spring 2020

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective function. We prove some theorems and we suggest conditions in which the fuzzy dual matrix system of AX + B = CX + D and the fuzzy matrix system of (A -H C)X = (D - H B) have the same LR fuzzy solution and we discuss about the conditions where LR fuzzy dual matrix system has crisp solution. Finally numerical examples are solved to illustrate the ability, accuracy and capability of the proposed method.

To proposing a voting model for groups with members of unequal power and proficiency, we present some models for rank ordering efficient candidates, by extending the ideas of some authors. Then, we propose a new methodology to rank the ranking models for the performance indices of only DEA efficient candidates based on a classical voting model. Also, an approach for combining the results obtained from the ranking models is presented.

The aim of this paper is to present algebraic method which is called Wu's method to solving fuzzy complex systems of linear equations. Wu's method is used as a solution procedure for solving the crisp polynomial equations system. This algorithm leads to solving characteristic sets that are amenable to easy solution. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.

In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate filter in pseudo-hoops. Then we investigated these notions and proved some properties of them. Also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold filters such as n-fold(positive) implicative filter and n-fold fantastic filter in pseudo-hoops. For example, we proved that any $n$-fold obstinate filter is a maximal filter. Finally, we obtain a characterization of n-fold obstinate filters in terms of congruences and we show that any n-fold obstinate pseudo-hoop is an n-fold fantastic, n-fold positive implicative, n-fold implicative pseudo-hoop and simple pseudo-‎hoop.‎

In this study, we review the elliptic differential operators and filters, and due to a wide range of elliptic operators, focus on a batch of elliptic operators with constant coefficients second order and then generalizing them to a higher order. Finally by discretization of the elliptic operators, we express and prove two theorems and show that the obtained filters are the high pass.

In the present paper, MHD flow past a vertical rotating plate with chemical reaction and mass diffusion in the presence of Hall current is studied. The fluid is electrically conducting and the flow is along the plate. The model under consideration is solved by Laplace transform method. This study is useful in magnetic field controlled material processing, planetary systems and MHD energy generators, etc.

In this paper we present a new mathematical model for designing a reverse logistic network. The model is multi-product, multi-level, and multi-period. It minimizes transportation cost, facilities establishing cost, and lowers purchasing from suppliers. The price of products depends on the cost of purchases and suppliers present different discounts on their product prices. Because the presented problem belongs to Np. Hard problems, we use genetic algorithm to solve it.

In this work, the absolute value equation (AVE) $ Ax-vert x vert= b$ is solved by the Gauss-Seidel and Jacobi iterative methods based on the stochastic arithmetic, where $A$ is an arbitrary square matrix whose singular values exceed one. An algorithm is proposed to find the optimal number of iterations in the given iterative scheme and obtain the optimal solution with its accuracy. To this aim, the CESTAC $^{1}$footnote{Controle et Estimation Stochastique des Arrondis de Calculs} method and the CADNA $^{2}$footnote{Control of Accuracy and Debugging for Numerical Application} library are applied which allows us to estimate the round-off error effect on any computed result. The classical criterion to terminate the iterative procedure is replaced by a criterion independent of the given accuracy $(epsilon)$ such that the best solution is evaluated numerically. Numerical examples are solved to validate the results and show the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic. Moreover, this method is applied to solve two-point boundary value ‎problem.‎

In this paper, we use the context-dependent method for ranking decision making units (DMUs) with non-discretionary data in data envelopment analysis (DEA). This methodology partitions a set DMUs into the several levels of efficient frontier, then obtains the efficiency of each DMU against of every calculate efficient frontier. We calculate a ranking score for each DMU by this efficiency indexes. Therefore we can rank DMUs by this score.

The primary goal of this work is to introduce general family Steffensen-like methods with memory of the high efficiency indices.To achieve this target two parameters are introduced which are calculated with the help of Newton’s interpolatory polynomial.It is shown that the R-order convergence of the proposed methods has been increased from 2;4;8,and 2^n to 3.5,7,14;and 3.5*2^n-1,respectively without any extra evaluation.Computational results confirm the efficient and robust character of presented methods.