In this research was to use the method of classic dynamic programming (CDP) and the method of fuzzy dynamic programming (FDP) to controlling the inventory in N periods and only one substance ,in order to minimize the total cost and determining the required quantity in warehouse rusafa principal of the ministry of commerce . A comparison was made between the two techniques، We found that the value of fuzzy total cost is less than that the value of classic total cost

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

    In this paper, some new types of regularity axioms, namely pairwise quasi-regular, pairwise semi-regular, pairwise pseudo regular and pairwise regular are defined and studied in both ech fuzzy soft bi-closure spaces (  bicsp’s) and their induced fuzzy soft bitopological spaces. We also study the relationships between them. We show that in all these types of axioms, the hereditary property is satisfied under closed fs bi-csubsp of . Furthermore, we define some normality axioms, namely pairwise semi-normal, pairwise pseudo normal, pairwise normal and pairwise completely normal in both  bicsp’s and their induced fuzzy soft bitopological spaces, as well as their basic properties and the relationships between them are studied.

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

The study of fixed points on the  maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of prox

In this paper we introduce the notions of bi-ideal with respect to an element r
denoted by (r-bi- ideal ) of a near ring , and the notion fuzzy bi- ideal with respect
to an element of a near ring and the relation between F-r-bi-ideal and r-bi-ideal of
the near ring, we studied the image and inverse image of r-bi- ideal under
epimomorphism ,the intersection of r-bi- ideals and the relation between this ideal
and the quasi ideal of a near ring, also we studied the notion intuitionistic fuzzy biideal
with respect to an element r of the near ring N, and give some theorem about
this ideal .

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).