الفهرس 
Introduction to Partially Ordered Sets (posets)Only 14 pages are availabe for public view
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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