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 .

Fuzzy logic is used to solve the load flow and contingency analysis problems, so decreasing computing time and its the best selection instead of the traditional methods. The proposed  method is very accurate with outstanding computation time, which made the fuzzy load flow (FLF) suitable for real time application for small- as well as large-scale power systems. In addition that, the FLF efficiently able to solve load flow problem of ill-conditioned power systems and contingency analysis. The FLF method using Gaussian membership function requires less number of iterations and less computing time than that required in the FLF method using triangular membership function. Using sparsity technique for the input Ybus sparse matrix data gi

In this paper, we will study a concepts of sectional intuitionistic fuzzy continuous and prove the schauder fixed point theorem in intuitionistic fuzzy metric space as a generalization of fuzzy metric space and prove a nother version of schauder fixed point theorem in intuitionistic fuzzy metric space as a generalization to the other types of fixed point theorems in intuitionistic fuzzy metric space considered by other researchers, as well as, to the usual intuitionistic fuzzy metric space.

    The main objective of this research is to study and to introduce a concept of strong fully stable Banach -algebra modules related to an ideal.. Some properties and characterizations of full stability are studied.

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function i

The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz

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.

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

  In this paper it was presented the idea quasi-fully cancellation fuzzy modules and we will denote it by  Q-FCF(M), condition universalistic idea quasi-fully cancellation modules It .has been circulated to this idea quasi-max fully cancellation fuzzy modules and we will denote it by Q-MFCF(M). Lot of results and properties have been studied in this research.

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states,  a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal  , if and only if  for any two ɱ-element sub-sets and of Ӽ^ɳ, if , for each j = 1, …, ɱ,  i = 1,…, ɳ  and   implies _Ạɳ( ) _Ạɳ(  have been proved..