الفهرس | Only 14 pages are availabe for public view |
Abstract Partially ordered sets are characterized by the fact that it contains groups of various applications, such as: Computer Science Applications, Engineering Applications and Chemical Applications, etc... Some of these applications contain vague, unclear and inaccurate data, so it was appropriate to use one of the techniques that deal with vague data. One of these techniques that deals with ambiguous data is the fuzzy 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑒𝑑 𝑏𝑦 𝐿𝑢𝑡𝑓𝑖 𝑍𝑎𝑑𝑒ℎ 𝑖𝑛 [1965]. The neutrosophic direction presented by Florentin [1999] also deals with fuzzy data and is considered a generalization of the fuzzy direction. In this thesis, we present a comparative study between the fuzzy approach and the neutrosophic approach to study partially ordered groups. Three contributions are proposed in this thesis: The first contribution introduce the concept of domination in a neutrosophic digraph, provide the characteristics of the minimum dominating set of neutrosophic digraphs, and model the domination number of a neutrosophic dipath and a neutrosophic dicycle. The domination number in a neutrosophic dipath and a neutrosophic dicycle presented and proved. provided some examples that illustrate this. The second contribution introduce the mathematical modelling in terms of neutrosophic digraph by using neutrosophic rule with generalized modus tollens method and define degree of a vertex in neutrosophic digraph, Indegree of a vertex in neutrosophic digraph, out degree of a vertex in neutrosophic digraph and generalized modus tollens are discussed. The third contribution talk about the directed acyclic graph(DAG) problem between fuzzy and neutrosophic approaches. We will compare between fuzzy approach and neutrosophic approach for partially ordered sets (DAG) The thesis consists of five chapters: Chapter 1: Introduction to Partially ordered sets This chapter introduces the history of partially ordered sets and its application. Also we introduce some basic definitions of partially ordered sets and definition of directed acyclic graph. Chapter 2: Fuzzy partially ordered sets In this chapter, we introduce some definitions of fuzzy graph, fuzzy directed acyclic graph and domination in fuzzy directed acyclic graph, and we discuss the previous research Chapter 3: Neutrosophic partially ordered sets In this chapter, we introduce some definitions of neutrosophic graph, neutrosophic directed acyclic graph, characteristics of Neutrosophic Digraph with Generalized Modus Tollens Using Mathematical Models and Domination in neutrosophic directed acyclic graph, and we discuss the previous research. Chapter 4: Main results We introduced the domination of directed graphs, characteristics of Neutrosophic Digraph with Generalized Modus Tollens Using Mathematical Models and the directed acyclic graph (posets)problem between fuzzy and neutrosophic approaches. Chapter 5: Conclusion and future works In this chapter, we introduce three contributions: The first contribution introduces the concept of domination in a neutrosophic digraph, provided the characteristics of the minimum dominating set of neutrosophic digraphs, and modeled the domination number of a neutrosophic dipath and a neutrosophic dicycle. The domination number in a neutrosophic dipath and a neutrosophic dicycle was present and proved. provide some examples that illustrate this. The second contribution introduce the mathematical modelling in terms of neutrosophic digraph by using neutrosophic rule with generalized modus tollens method and define degree of a vertex in neutrosophic digraph, Indegree of a vertex in neutrosophic digraph, out degree of a vertex in neutrosophic digraph and generalized modus tollens are discussed. The third contribution talk about the directed acyclic graph(DAG) problem between fuzzy and neutrosophic approaches. We will compare between fuzzy approach and neutrosophic approach for partially ordered sets (DAG). Some future work will also be explained. Future work: In this section, we introduce some future works such as: Radius, Diameter and Center of a Directed neutrosophic Graph Using Algorithm. Colouring of COVID-19 Affected Region Based on neutrosophic Directed Graphs. Neutrosophic based weight to mine frequent patterns from human interaction in meeting using directed acyclic graph. Neutrosophic chromatic Polynomial of neutrosophic Graphs with Crisp and neutrosophic Vertices Using 𝛼-Cuts. Nikfar Domination in neutrosophic directed acyclic graphs. Key Terms: Dominating set; digraph; neutrosophic graph; neutrosophic digraph; domination number, Generalized Modus Tollens, directed acyclic graph, fuzzy approach, neutrosophic approach |