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.

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .

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.

Our goal in the present paper is to recall the concept of general fuzzy normed space and its basic properties in order to define the adjoint operator of a general fuzzy bounded operator from a general fuzzy normed space V into another general fuzzy normed space U. After that basic properties of the adjoint operator were proved then the definition of fuzzy reflexive general fuzzy normed space was introduced in order to prove that every finite dimensional general fuzzy normed space is fuzzy reflexive.

The   study   of  torsion  {torsion   free)  fuzzy  modules   over   fuzzy

integtal  domain  as a generalization oftorsion (torsion free) modules.

 

The problem of independent motion control of mobile robot (МR) in conditions when unforeseen changes of conditions of interaction of wheels with a surface are considered. An example of such changes can be sudden entrance МR a slippery surface. The deployment of an autonomous unmanned ground vehicle for field applications provides the means by which the risk to personnel can be minimized and operational capabilities improved. In rough terrain, it is critical for mobile robots to maintain good wheel traction. Wheel slip could cause the rover to lose control and become trapped. This paper describes the application of fuzzy control to a feedback system within slippery environment. The study is conducted on an example of М

The main aim of this paper is to introduce the concept of a Fuzzy Internal Direct Product of fuzzy subgroups of group . We study some properties and prove some theorems about this concept ,which is very important and interesting of fuzzy groups and very useful in applications of fuzzy mathematics in general and especially in fuzzy groups.

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .