The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

Consider a simple graph   on vertices and edges together with a total  labeling . Then ρ is called total edge irregular labeling if there exists a one-to-one correspondence, say  defined by  for all  where  Also, the value  is said to be the edge weight of . The total edge irregularity strength of the graph G is indicated by  and is the least  for which G admits   edge irregular h-labeling.  In this article,   for some common graph families are examined. In addition, an open problem is solved affirmatively.

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that  functions as an act over S if and only if  functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and  is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following,  is acting over S if and only if  is a module where T is a nilpotent operator, is a

 الأثر V بالنسبة إلى   sinshT و خواصه قد تم دراسته في هذا البحث حيث تم دراسة علاقة الأثر المخلص والاثر المنتهى التولد والاثر المنفصل وربطها بالمؤثرات المتباينة حيث تم بهنة العلاقات التالية ان الاثر اذا وفقط اذا مقاس في حالة كون المؤثر هو عديم القوة وكذلك في حالة كون المؤثر شامل فان الاثر هو منتهي التولد اي ان الغضاء هو منتهي التولد وايضا تم برهن ان الاثر مخلص لكل مؤثر مقيد وك\لك قد تم التحقق من انه لاي مؤثر مقي

The aim of this paper is to introduce and study the notion type 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}.

In this paper, Min-Max composition fuzzy relation equation are studied. This study is a generalization of the works of Ohsato and Sekigushi. The conditions for the existence of solutions are studied, then the resolution of equations is discussed.

Recently, Image enhancement techniques can be represented as one of the most significant topics in the field of digital image processing. The basic problem in the enhancement method is how to remove noise or improve digital image details. In the current research a method for digital image de-noising and its detail sharpening/highlighted was proposed. The proposed approach uses fuzzy logic technique to process each pixel inside entire image, and then take the decision if it is noisy or need more processing for highlighting. This issue is performed by examining the degree of association with neighboring elements based on fuzzy algorithm. The proposed de-noising approach was evaluated by some standard images after corrupting them with impulse

Producing pseudo-random numbers (PRN) with high performance is one of the important issues that attract many researchers today. This paper suggests pseudo-random number generator models that integrate Hopfield Neural Network (HNN) with fuzzy logic system to improve the randomness of the Hopfield Pseudo-random generator. The fuzzy logic system has been introduced to control the update of HNN parameters. The proposed model is compared with three state-ofthe-art baselines the results analysis using National Institute of Standards and Technology (NIST) statistical test and ENT test shows that the projected model is statistically significant in comparison to the baselines and this demonstrates the competency of neuro-fuzzy based model to produce