In this thesis, we introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we studied some pawlak's concepts and generalization rough set theory, we introduce a new types for approximation rough digraphs depending on supra open digraphs. In addition, we present two various standpoints to define generalized membership relations, and state the implication between it, to classify the digraphs and help for measure exactness and roughness of digraphs. On the other hand, we define several kinds of fuzzy digraphs. We also introduce a topological space, which is induced by reflexive graph and tolerance graphs, such that the graph may be infinite. Furthermore, we offered some properties of this topologies such as connectedness, compactness, Lindelöf and separate properties. Finally, we study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces
In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.
The theory of Topological Space Fiber is a new and essential branch of mathematics, less than three decades old, which is created in forced topologies. It was a very useful tool and played a central role in the theory of symmetry. Furthermore, interdependence is one of the main things considered in topology fiber theory. In this regard, we present the concept of topological spaces α associated with them and study the most important results.
Hemorrhagic insult is a major source of morbidity and mortality in both adults and newborn babies in the developed countries. The mechanisms underlying the non-traumatic rupture of cerebral vessels are not fully clear, but there is strong evidence that stress, which is associated with an increase in arterial blood pressure, plays a crucial role in the development of acute intracranial hemorrhage (ICH), and alterations in cerebral blood flow (CBF) may contribute to the pathogenesis of ICH. The problem is that there are no effective diagnostic methods that allow for a prognosis of risk to be made for the development of ICH. Therefore, quantitative assessment of CBF may significantly advance the underst
Information security contributes directly to increase the level of trust between the government’s departments by providing an assurance of confidentiality, integrity, and availability of sensitive governmental information. Many threats that are caused mainly by malicious acts can shutdown the egovernment services. Therefore the governments are urged to implement security in e-government projects.
Some modifications were proposed to the security assessment multi-layer model (Sabri model) to be more comprehensive model and more convenient for the Iraqi government. The proposed model can be used as a tool to assess the level of security readiness of government departments, a checklist for the required security measures and as a commo
This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set, μ(u, v) ≤ σ(u) ᴧ σ(v) and η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un), if e = (u1, u2, …, un), n ≥ 2 is an edge in the semigraph G
... Show MoreThis is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally,
... Show MoreThe aim of this study is to develop a novel framework for managing risks in smart supply chains by enhancing business continuity and resilience against potential disruptions. This research addresses the growing uncertainty in supply chain environments, driven by both natural phenomena-such as pandemics and earthquakes—and human-induced events, including wars, political upheavals, and societal transformations. Recognizing that traditional risk management approaches are insufficient in such dynamic contexts, the study proposes an adaptive framework that integrates proactive and remedial measures for effective risk mitigation. A fuzzy risk matrix is employed to assess and analyze uncertainties, facilitating the identification of disr
... Show MoreIn this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.
In this research, we introduce and study the concept of fibrewise bitopological spaces. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces,(resp., open, locally sliceable and locally sectionable). We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise T_0 spaces, fibrewise pairwise T_1 spaces, fibrewise pairwise R_0 spaces, fibrewise pairwise Hausdorff spaces, fibrewise pairwise functionally Hausdorff spaces, fibrewise pairwise regular spaces, fibrewise
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