This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.

In this paper, we study the effect of group homomorphism on the chain of level subgroups of fuzzy groups. We prove a necessary and sufficient conditions under which the chains of level subgroups of homomorphic images of an a arbitrary fuzzy group can be obtained from that of the fuzzy groups . Also, we find the chains of level subgroups of homomorphic images and pre-images of arbitrary fuzzy groups

      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.

In this paper we define and study new concepts of functions on fibrewise  topological spaces  over  B namely,  fibrewise  weakly  (resp., closure, strongly) continuoac; funttions which are analogous of weakly

(resp., closure,   strongly)   continuous  functions   and  the  main  result is   : Let  <p       : XY  be a fibrewise  closure  (resp.,  weakly,  closure, strongly,  strongly) continuous function,  where  Y  is fibrewise topological  space  over  B and  X  is  a  fibrewise set  which  has  the

in

 In this paper, we introduce and study the concept of a new class of generalized closed set which is called generalized b*-closed set in topological spaces ( briefly .g b*-closed) we study also. some of its  basic properties and investigate the relations between the associated topology. 

 We use the idea of Grill, this study generalized a new sort of linked space like –connected –hyperconnected and investigated its features, as well as the relationship between it and previously described notation. It also developed new sorts of functions, such as hyperconnected space, and identifying their relationship, by offering numerous instance and attributes that belong to this set. This set will serve as a starting point for further research into the sets many future possibilities. Also, we use some of the theorems and observations previously studied and relate them to the grill and the Alpha group, and benefit from them in order to obtain new results in this research. We applied the concept of Connected to them and obtained

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

          The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra  without identity can be embedded into fuzzy normed algebra  with identity  and  is an ideal in  is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.