In this work, we introduce an intuitionistic fuzzy ideal on a KU-semigroup as a generalization of the fuzzy ideal of a KU-semigroup. An intuitionistic fuzzy k-ideal and some related properties are studied. Also, a number of characteristics of the intuitionistic fuzzy k-ideals are discussed. Next, we introduce the concept of intuitionistic fuzzy k-ideals under homomorphism along with the Cartesian products.

     Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complement    of D.

he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga

   Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXW for all fully invariant R-submodule X of M, implies XW.         M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.

    In this study, the concept of fuzzy α-topological vector space is introduced by using the concept  fuzzy α-open set , some properties of fuzzy α-topological vector spaces are proved .We also show that the space is -space iff every singleton set is fuzzy α- closed .Finally, the convex property and its relation with the interior points are discussed.

The aim of this study is to use style programming goal and technical programming goal fuzzy to study assessing need annual accurately and correctly depending on the data and information about the quantity the actual use of medicines and medical supplies in all hospitals and health institutions during a certain period where they were taking the company public for the marketing of medicines and medical supplies sample for research. Programming model was built goal to this problem, which included (15) variable decision, (19) constraint and two objectives:

1 - rational exchange of budget allocated for medicines and supplies.
2 - ensure that the needs of patients of medicines and supplies needed to improve

In this paper, we introduce and study the concepts of hollow – J–lifting modules and FI – hollow – J–lifting modules as a proper generalization of both hollow–lifting and J–lifting modules . We call an R–module M as hollow – J – lifting if for every submodule N of M with is hollow, there exists a submodule K of M such that M = K Ḱ and K N in M . Several characterizations and properties of hollow –J–lifting modules are obtained . Modules related to hollow – J–lifting modules are  given .

In this work we study gamma modules which are implying full stability or implying by full stability. A gamma module is fully stable if for each gamma submodule of and each homomorphism of into . Many properties and characterizations of these classes of gamma modules are considered. We extend some results from the module to the gamma module theories.

      This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models.

The fuzzy sets theory has been applied in many fields, such as operations research, control theory and management sciences, etc. In particular, an application of this theory in decision making problem is linear programming problems with fuzzy technological coefficients numbers, as well as studying the parametric linear programming problems in the case of changes in the objective function. In this paper presenting a new procedure which connects and makes link between fuzzy linear programming problem with fuzzy technological coefficients numbers and parametric linear programming problem with change in coefficients of the objective function, then develop a numerical example illustrates the steps of solution to this kind of problems.