JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2016 | Volume:1 | Issue:4|Papers Count:13

The basic assumption in data envelopment analysis patterns (DEA) (such as the CCR and BCC models) is that the value of data related to the inputs and outputs is a precise and positive number, but most of the time in real conditions of business, determining precise numerical value is not possible in for some inputs or outputs. For this purpose, different models have been proposed in DEA for imprecise data over recent years and also several researches have been conducted on DEA that are able to evaluate efficiency with negative data. The negative interval DEA pattern which has been introduced and used in the present study, addresses uncertainty both in inputs and outputs and provides user with more stable and reliable results for decision making.Now, in this paper a model is presented that is able to compute efficiency interval of units with interval input and output that while some indicators can also be negative and then we prove that the efficiency interval that this model gives us is more precise compared to efficiency interval of models previously proposed and finally, ten decision making units (DMUs) with the negative imprecise (interval) data are investigated by the proposed model and the results of the proposed model are compared with the results of the previous models.

Uncertainty is a prominent feature of real world problems and more especially financial markets; with this in mind, dealing with uncertainty becomes a necessary part of performance evaluation by means of data envelopment analysis. This paper presents three robust data envelopment analysis (DEA) models and their application for performance evaluation in Tehran Stock Exchange (TSE). Based on the results, the evaluated performance of stocks and the number of efficient stocks is decreased in all three models by increasing the level of uncertainty.

The main purpose of this research is "to study the effect of combined learning on students' educational achievement at girls' technical schools in Tehran". The research method in this study is semi-experimental or semi-empirical. The statistical universe of this study includes all girl students of Tehran technical schools. At the first stage, 6 technical schools were selected randomly and simply among all technical schools of the studied society and then 12 classes of the first year were chosen (2 test and control classes in mathematics per school). The sampling method of the schools was a simple random case in this study. Totally 240 students attended these classes. The applied tools in this research are writing fiches from pre-test and post-test scores of the students. In fact, the educational achievement has been used by two tests of pre-test and post-test for both test and control groups. The results of t- test in the dependent groups show that there is a significant difference regarding the computed significance level and obtained mean difference in the educational situation of the test group in the case of pre-test and post-test. Meanwhile, the study and comparison of the means in two situations of pre-test (17.1394) and post-test (18.2279) also confirm this issue.

In recent years, measuring and analyzing productivity changes is the main focus of various researches who study performance of organizations. All through widespread application of Malmquist Productivity Index, different types of data should be considered thoroughly, otherwise any defective study of the related data and deciding factors may yield poor results. Practical Malmquist Productivity Index (PMPI) models, presented in this research, are fundamentally capable of measuring the productivity of units in a competitive atmosphere, along with the hidden economic indexes such as time value of money, amortization and promoted skills of employees. Also these models would provide the productivity comparison over different periods of time. Moreover, these models are reliable as well as tangible for superior managers and it is noteworthy that they would offer significantly favorable conditions, lack of which may cause the unit under evaluation to face a great deal of regression.

Data Envelopment Analysis (DEA) is a mathematical programming technique for evaluating the relative efficiency of a set of Decision Making Units (DMUs) and can also be utilized for setting target. Target setting is one of the important subjects since according to its results efficiency can be increased. An important issue to be currently discussed, is to set target while considering share data. These data for each individual indicate the share of the unit, which takes part in an activity, from the whole amount which is a predefined constant. It is obvious that the sum of units’ share is equal to the entire amount. Thus, any changes in the magnitude of these data has to be dependent on the changes in data of other units. In this paper a two-stage procedure is developed to find benchmark units where share data exist. The fact that all DMUs are jointly projected onto the new efficient frontier and simplicity, are the significant features of the proposed method. With a numerical example we demonstrate how this method works.

Data Envelopment Analysis (DEA) has two fundamental approaches for assessing the efficiency with different characteristics; radial and non-radial models. This paper is concerned the non-radial model of Russell which is a non linear model. Conventional DEA for a large dataset with many inputs/outputs would require huge computer resources in terms of memory and CPU time. Artificial Neural Network (ANN) is one of the most popular techniques for non linear models and for measuring the relative efficiency of a large dataset with many inputs/ outputs. Also in the last decade researches focused on efficiency evaluation via DEA as well as using ANN. In this paper we will estimate the input excesses and the output shortfalls in addition to efficiency of Decision Making Units (DMUs) in Russell model through ANN. The proposed integrated approach is applied to an actual Iranian bank set; the result indicates that it yields a satisfactory solution. works.

The capacitated clustering problem (CCP) is a data mining technique utilized to categorize a number of objects with known demands into k distinct clusters such that the capacity of each cluster is not violated, every object is allocated to exactly one cluster and sum of distances from all cluster centers to all other nodes is minimized. The CCP is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of this problem cannot be solved by exact solution methodologies within acceptable computational time. Our interest was therefore focused on meta-heuristic solution approaches. For this reason, a modified imperialist competitive algorithm (MICA) is proposed for the CCP In this paper. The proposed MICA iterates steps between three basic phases, i.e., the random assignment phase to form clusters, the seed relocation phase to find a better median, and the local improvement phase to make a revision of the solution. The proposed algorithm is tested on several standard instances available from the literature. The computational results confirm the effectiveness of the presented algorithm and show that the proposed algorithm is competitive with other meta-heuristic algorithms for solving the CCP.

In this paper, we propose a feasible interior-point algorithm for mixed symmetric cone linear complementarity problems which are a general class of complementarity problems. The symmetrization of the search directions used in this paper is based on Nesterov and Todd scaling scheme. By using Euclidean Jordan algebra, we prove the convergence analysis of the proposed algorithm and show that the complexity bound of the algorithm matches the currently best known iteration bound for feasible interior-point methods.

in this paper, a linear programming problem is considered involving interval grey numbers as an extension of the classical linear programming problem to an inexact environment as well as fuzzy and stochastic environment. Hence, here a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. The proposed method is established based on the primal simplex algorithm where the cost coefficient row includes grey numbers. As an essential tool in the solving process, a theoretical discussion on grey arithmetic and in particular an ordering role for grey numbers is necessary to evaluate the optimality conditions of a candidate feasible solution. It is also emphasized that the discussed model and the solution process is useful for real situations and practical cases, when a kind of the grey number linear programming is appeared, such as Water Resource Management and Planning, Economics, etc. Finally, the proposed approach is illustrated by a numerical example.

Performance evaluation has always been a challenging issue in management. The evaluation of performance especially during two past decades has attracted much attention because of its importance. Today, organizations try to measure the performance comparing with other competitors to be able to reach to a level of performance keeping them in market.Banks and financial institutions are considered as the most important economic sectors performing the trades and commercial transactions by guiding and conducting the payments and getting the money to spread the markets and develop economic growth and prosperity. Due to the importance of the task, the increase of productivity is a matter of high necessity.Data envelopment analysis is a nonparametric linear programming technique for evaluating the performance of Decision Making Units (DMU) by multiple inputs and multiple outputs.In this paper, we focus on the deferred debts and impact of it’s on bank performance. So, data envelopment analysis and statistical test are to present relation between deferred debts and efficiency used. The present research is to evaluate the performance of 40 bank branches in Iran. In order to achieve the goal, the performance of bank branches will be assessed by using Data Envelopment Analysis and GAMS software during 2013-2014 and based on the researches conducted.

Ordering on fuzzy quantities have been attracted a wide domains of studies in fuzzy sets theory in the two last decades. In many practical situations as well as fuzzy mathematical programming, it is necessary to the decision makers consider L-R fuzzy numbers according to their aims. But in the most of methods which are presented to order fuzzy numbers, the authors have been considered a special kind of fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers and etc. But as we know the L-R fuzzy numbers as a general kind of these numbers have not been discussed. Hence in this paper, we focus on a general L-R fuzzy number and propose a new approach to order them as an extension of the method which is given by Nasseri in [14]. For validity of the proposed method, we will illustrate this method based on a convenient examples which is appeared in the literature of fuzzy ordering. Furthermore, we emphasize that the proposed method will be useful for evaluating the optimality conditions in the fuzzy primal simplex algorithms and the other related algorithms such as the fuzzy dual simplex algorithm and the fuzzy two phase simplex algorithm, fuzzy transportation models, fuzzy interval linear programming and etc.

Let B(X) and Mn (F) be the algebra of all bounded linear operators on a complex Banach space X with dimX³3 and the algebra of all n×n matrices over a field F with F¹2, respectively. Also let F(A)be the space of all fixed points of an operator AÎB(X). In this paper, we characterize the forms of linear maps f:B(X)®B(X) which satisfy F(A)=0ÛF(f(A))=0 and linear maps f: Mn(F)® Mn(F) which preserve the fixed points of matrices.

A CSS1 is a system with the continues-state components. When a component has the ability to obtain all the situations from completely working to completely failed, it named continues-state component. In the real world, performance rate of elements are continuous and decrease by time. Continuity of components causes infinite working states and grows up the system states. In this paper we propose a new method for series-parallel continues-state RAP2 using UGF3 for multi-state systems. In this method at first we consider a binary CFR4 system. Using Weibull distribution function for the performance rate of working state, this system upgraded to a CSC. Then the UGF for a series-parallel system has been studied and a numerical example presented to illustrate the reliability and availability computation.