The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =. for all a1,…,an,b1,…,bm ? G

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

This study aimed to identify the degree of use computers in administrative functions (planning, organization, controlling, and evaluation) among school leaders and assistants in public education schools in Sharoorah governorate ، as well as to identify obstacles of  use computers in administrative functions from the perspective of school leaders and assistants male and female in public schools during the academic year 1439-1440, the study sample  (66) school leaders and assistants, males (58), a and females (44), , and to answer the questions of the study, the researchers developed a questionnaire consisting of  (60) items, has been verified sincerity and persistence, and data analysis was used frequencies, percentages an

 
      The process of soil classification in Iraq for industrial purposes is important topics that need to be extensive and specialized studies. In order for the advancement of reality service and industrial in our dear country, that a lot of scientific research touched upon the soil classification in the agricultural, commercial and other fields. No source and research can be found that touched upon the classification of land for industrial purposes directly. In this research specialized programs have been used such as geographic information system software The geographical information system permits the study of local distribution of phenomena, activities and the aims that can be determined in the loca

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The purpose of the research is to present and discuss the concept of grants and aid, with the study and analysis of the role and importance of grants and assistance on the activities of In government units, and then to determine the factors of obtaining grants and assistance, and the importance of providing accounting information in order to enhance the financial reporting of grants and assistance. The accounting system of the government and determine the areas of shortness, taking into account the failure to issue a local accounting base to determine the basis of accounting measurement and disclosure of grants and assistance to guide, and this is the starting point of the current research and so has been intr

Background: The adenomatoid odontogenic tumor is a relatively rare benign epithelial odontogenic tumor. It contains both epithelial and mesenchymal components. Few cases presented as an extrafollicular lesion or involve the mandible or associated with other odontogenic lesions. This paper represents a rare case of an extrafollicular AOT. Case presentation: A 24-year-old female had a painless swelling on the right side of the lower jaw since one-month duration. Intraorally there was a well defined fluctuant-blue swelling in the right alveolar premolar region measuring 1×2 cm obliterating the right lower buccal vestibule. Grade II mobility in the vital 44 and 45 teeth were observed. Panoramic radiographs showed a well-defined pear shaped

    Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking f

Research indicates that the second half of the twentieth century marked large interests in the service industry by government and private organizations in that one, and the service industry has become the bedrock of plans in achieving economic and social development. From this standpoint felt specialists and researchers the importance of transport modes, including rail, which should be available between Almnltq Civil populated as services organized by the competent authorities to achieve the active participation of citizens in economic and social development in the region and that the term services means economic activities, which are the results Pollack concrete such as accepting the situation and satisfaction them or satisfacti

This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.