Zadah in [1] introduced the notion of a fuzzy subset A of a nonempty set S as a mapping from S into [0,1], Liu in [2] introduced the concept of a fuzzy ring, Martines [3] introduced the notion of a fuzzy ideal of a fuzzy ring.         A non zero proper ideal I of a ring R is called an essential ideal if I  J  (0), for any non zero ideal J of R, [4].         Inaam in [5] fuzzified this concept to essential fuzzy ideal of fuzzy ring and gave its basic properties.         Nada in [6] introduced and studied notion of semiessential ideal in a ring R, where a non zero i

  Many production companies suffers from big losses because of  high production cost and low profits for several reasons, including raw materials high prices and no taxes impose on imported goods also consumer protection law deactivation and national product and customs law, so most of consumers buy imported goods because it is characterized by modern specifications and low prices.

  The production company also suffers from uncertainty in the cost, volume of production, sales, and availability of raw materials and workers number because they vary according to the seasons of the year.

  I had adopted in this research fuzzy linear program model with fuzzy figures

This paper presents a robust algorithm for the assessment of risk priority for medical equipment based on the calculation of static and dynamic risk factors and Kohnen Self Organization Maps (SOM). Four risk parameters have been calculated for 345 medical devices in two general hospitals in Baghdad. Static risk factor components (equipment function and physical risk) and dynamics risk components (maintenance requirements and risk points) have been calculated. These risk components are used as an input to the unsupervised Kohonen self organization maps. The accuracy of the network was found to be equal to 98% for the proposed system. We conclude that the proposed model gives fast and accurate assessment for risk priority and it works as p

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators

In this paper, the error distribution function is estimated for the single index model by the empirical distribution function and the kernel distribution function. Refined minimum average variance estimation (RMAVE) method is used for estimating single index model. We use simulation experiments to compare the two estimation methods for error distribution function with different sample sizes, the results show that the kernel distribution function is better than the empirical distribution function.

     The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.

To ensure that a software/hardware product is of sufficient quality and functionality, it is essential to conduct thorough testing and evaluations of the numerous individual software components that make up the application. Many different approaches exist for testing software, including combinatorial testing and covering arrays. Because of the difficulty of dealing with difficulties like a two-way combinatorial explosion, this brings up yet another problem: time. Using client-server architectures, this research introduces a parallel implementation of the TWGH algorithm. Many studies have been conducted to demonstrate the efficiency of this technique. The findings of this experiment were used to determine the increase in speed and co

Iraq within the ranks of the fledgling communities characterized by a broad base of the population pyramid, because they pose the age group (under 15 years) of a large proportion of the community, as it exceeded the proportion (40%) during the years of research extended (1986-2010) Despite the relative decline in the rates fertility during that period, but the proportion of young people remained high, especially for groups of at least five years, amounting to about 14% in 2012, a little more than the proportion of what constitutes age group (5-9 above) years, where it was (13%) and this naturally predicts continuing population increases in coming decades, due to the entry of those numbers of individuals in the reproductive stage,