In this paper, we study a new concept of fuzzy sub-module, called  fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense.  This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

Let A be a unital algebra, a Banach algebra module M is strongly fully stable Banach A-module relative to ideal K of A, if for every submodule N of M and for each multiplier θ : N → M such that θ(N) ⊆ N ∩ KM. In this paper, we adopt the concept of strongly fully stable Banach Algebra modules relative to an ideal which generalizes that of fully stable Banach Algebra modules and we study the properties and characterizations of strongly fully stable Banach A-module relative to ideal K of A.

Let M be an R-module. We introduce in this paper the concept of strongly cancellation module as a generalization of cancellation modules. We give some characterizations about this concept, and some basic properties. We study the direct sum and the localization of this kind of modules. Also we prove that every module over a PID is strongly module and we prove every locally strong module is strongly module.

  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

Research summarized in applying the model  of fuzzy goal programming for aggregate production planning , in General Company for hydraulic industries / plastic factory to get an optimal production plan  trying to cope with the impact that fluctuations in demand and  employs all available resources using two strategies where they are available   inventories  strategy and  the strategy of  change in the level of the workforce, these   strategies  costs are usually imprecise/fuzzy. The plant administration trying to minimize total production costs, minimize carrying costs and minimize changes in labour levels. depending on the gained data from th

      The concept of semi-essential semimodule has been studied by many researchers.

     In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule  is prime, then  is fully prime. If every semi-essential subsemimodule of -semimodule  is essential then  is fully essential. Finally, a prime subsemimodule  of  is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule  in , if , and whenever  with  is a prime subsemimodule in , , then .  Furthermore, some res

A Module M is called cofinite  J- Supplemented  Module  if for every  cofinite submodule L of  M, there exists a submodule N of M such that M=L+N with   main properties of cof-J-supplemented modules.  An R-module M is called fully invariant-J-supplemented if for every fully invariant submodule N of M, there exists a submodule K of M, such that M = N + K with N  K K. A condition under which the direct sum of FI-J-supplemented modules is FI-J-supplemented was given. Also, some types of modules that are related to the FI-J-supplemented module were discussed.

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 we recall the definition of fuzzy length space on a fuzzy set after that we recall basic definitions and properties of fuzzy length. We define fuzzy bounded operator as an introduction to defined fuzzy length of an operator then we proved that the fuzzy length space FB ̃ ̃ consisting of all fuzzy bounded linear operators from a fuzzy length space ̃ into a fuzzy length space ̃ is fuzzy complete if ̃ is fuzzy complete. Also we proved that every finite dimensional fuzzy length space is fuzzy complete.

In this work, We introduce the concepts of an FP-Extending, FP-Continuous and FP-Quasi-Continuous which are stronger than P-Extending, P-Continuous and P-Quasi-Continuous. characterizations and properties of FP-Extending, FP-Continuous and FP-Quasi-Continuous are obtained . A module M is called FP-Extending ( FP-Continuous, FP-Quasi-Continuous) if every submodule is P-Extending (P-Continuous, P-Quasi-Continuous) .