This paper is concerned with introducing and studying the new approximation operators based on a finite family of d. g. 'swhich are the core concept in this paper. In addition, we study generalization of some Pawlak's concepts and we offer generalize the definition of accuracy measure of approximations by using a finite family of d. g. 's.

Breast cancer was one of the most common reasons for death among the women in the world. Limited awareness of the seriousness of this disease, shortage number of specialists in hospitals and waiting the diagnostic for a long period time that might increase the probability of expansion the injury cases. Consequently, various machine learning techniques have been formulated to decrease the time taken of decision making for diagnoses the breast cancer and that might minimize the mortality rate. The proposed system consists of two phases. Firstly, data pre-processing (data cleaning, selection) of the data mining are used in the breast cancer dataset taken from the University of California, Irvine machine learning repository in this stage we

In this paper, we define the concept of soft -connected sets and soft -connected spaces by using the notion of soft -open sets in soft topological spaces. Several properties of these concepts are investigated.

     Machine learning-based techniques are used widely for the classification of images into various categories. The advancement of Convolutional Neural Network (CNN) affects the field of computer vision on a large scale. It has been applied to classify and localize objects in images. Among the fields of applications of CNN, it has been applied to understand huge unstructured astronomical data being collected every second. Galaxies have diverse and complex shapes and their morphology carries fundamental information about the whole universe. Studying these galaxies has been a tremendous task for the researchers around the world. Researchers have already applied some basic CNN models to predict the morphological classes

    This paper is concerned with a Coupled Reaction-diffusion system defined in a ball with homogeneous Dirichlet boundary conditions. Firstly, we studied the blow-up set showing that, under some conditions, the blow-up in this problem occurs only at a single point. Secondly, under some restricted assumptions on the reaction terms, we established the upper (lower) blow-up rate estimates. Finally, we considered the Ignition system in general dimensional space as an application to our results.

The aim of this research is to prove the idea of maximum m_X-N-open set, m-N-extremally disconnected with respect to t and provide some definitions by utilizing the idea of m_X-N-open sets. Some properties of these sets are studied.

 Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each   f ∈ Hom(N,M), f ≠ 0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related modules

The aim of this paper is to introduce the definition of a general fuzzy norned space as a generalization of the notion fuzzy normed space after that some illustrative examples are given then basic properties of this space are investigated and proved.

For example when V and U are two general fuzzy normed spaces then the operator  is a general fuzzy continuous at u  V if and only if u in V implies S(u) in U.

      This paper intends to initiate a new type of generalized closed set in topological space with the theoretical application of generalized topological space. This newly defined set is a weaker form than the -closed set as well as -closed set. Some phenomenal characterizations and results of newly defined sets are inculcated in a proper manner. The characteristics of normal spaces and regular spaces are achieved in the light of the generalized pre-regular closed set.

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.