JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)
Year:2006 | Volume:16 | Issue:58/1 (MATHEMATICS ISSUE)|Papers Count:8

Menendez (2000) published a paper on Shannon's entropy in exponential family and discussed some properties of them. He introduced an asymptotic distribution for it. In this paper we present an entropy characterization of general exponential model so that Menendez definition is particular state of it. Also we introduced another asymptotic distribution for (H(^q) - H (q0)),where H (q) is Shannon's entropy of X with distribution ¦q (x) , and ^q is MLE of q.

In this paper, the numerical solution of the improper fuzzy integral ~I=ò+¥~a ~¦(~x)~dx is proposed where, ~¦(~x) is a bounded and closed fuzzy valued function defined on the closed fuzzy real number system and a is ~a fuzzy number with triangular or bell-shape membership function. For this purpose, the a -level sets of the fuzzy number ~I, -Ia and -Ia, 0£a£1, are evaluated whose end points are the crisp improper integrals. Then, a reliable method is introduced to estimate -Ia and -Ia by using the stochastic arithmetic. In this case, an algorithm is presented which evaluates these integrals by using the Simpson rule. By using the CESTAC method, we find the optimal natural numbers -ma and -ma such that these improper integrals are estimated by definite integrals. Also, for a given r, we evaluate the approximate value of the membership function m~I (r) and determine the accuracy of the results. At last, two fuzzy integrals are computed using the given algorithm to show the results of the research.

In this paper various university Efficiency performance utilizing Data Envelopment Analysis models have been surveyed. This study includes the performances of 38 different universities including Azad, Payam Nour, Private, and State universities. Regarding the Islamic Azad universities, the Malmquist Productivity Index (MPI) is used to measure the rate of any progress or deterioration in university performance. At the end, the mean performance Efficiency of different universities has been compared.

Recently, Jahanshahloo et al. published a paper on efficiency measurements. Their method has some shortcomings. However, the proposed membership function in their paper is problematic in some cases. Commenting on our earlier paper, they have some misconceptions. We not only do not use the mentioned rule by Jahanshahloo et al. but also rather with proper variable substitutions, develop a linear model in which an optimizing point for each interval is found that not only satisfies the set of constraints but also optimizes the objective function. In this paper, we try to clarify their misconceptions.

In this paper a method for solving a general fuzzy linear system with crisp solution is considered. We consider the method in special case when the elements of the coefficient matrix and the right hand side are trapezoidal fuzzy numbers. The method in detail is discussed and followed by theorem and illustrated by solving some examples.

The current methods of statistical inferences are divided into two categories: Pre-experimental & Post- experimental. The pre- experimental methods are based on all the quantities of the sample space while the post- experimental methods only include the observed quantities of random variables. Many problems arise using pre experimental inferences. Inspite of these problems, existing methods (including unbiasedness, UMVU, etc.) have some merits between these two methods in statistics, the notion of conditional inference based on Relevant Subsets has been developed. The purpose of this paper is to discuss the issue of Relevant Subsets as a decision problem.The existence of these subsets in the Extremal Family is studied and some examples are given.

The area of linear programming has undergone a considerable change of orientation with the introduction of Karmarkar's algorithm in 1984. Because of, when we use AHP method, it needs long times that we assign preferences of objective functions, we use from steapest direction method for finding an acceptable convex combination of directions that help us to solve the problem.

This paper studies the effects on non-homogeneous variance on the following four types of estimators: (1) DEA joined to regression forms, (2) COLS-R, (3) COLS-M and (4) Goal programming with one-sided deviations as in Aigner and Chu (A&C).The data are simulated to form the frontier. The simulation result indicates DEA-based estimators are the best estimators of efficient output even under non-homogeneous variance.