Posted on Categories:Graph Theory, 图论, 数学代写

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## 数学代写|图论代写GRAPH THEORY代考|AApplication of Fuzzy Graph in Ecology

The ecological system can be successfully modeled using crisp graph as well as fuzzy graph. In this section, we explain how an ecological problem can be modeled using FG.

Different types of organisms are present in an ecosystem. Each organism depends for food on one or more organisms for food, except primary producers (plants and some chemicals). The organisms are divided into two groups â Preys and Predators. A predator can be a prey for another predator as well. The prey-predator relationship can be explained easily with the help of a food web, i.e. a directed graph (digraph). For example, the food chilli-chicken is made by chicken, but hen is not a primary producer. Hen eats grass which is a primary producer. So we eat chicken and hen eats grass. This is a very simple food web with three species-grass, hen, and human.
Let us consider a small ecosystem.

(a) sharks eat sea otters;
(b) sea otters eat sea stars and sea urchins;
(c) sea stars eat sea urchins and small fishes;
(d) sea urchins eat kelp;
(e) small fishes eat kelp.
These relationships can be represented by a digraph, called food web, depicted in Fig. 10.1.

For this food web, one can construct a digraph $(\overrightarrow{\mathscr{G}})$ using the following principal: The six species, viz. kelp, sea urchin, small fish, sea star, sea otter, and shark are taken as vertices. There is a directed edge from the species $A$ to the species $B$ if $A$ is a prey for the predator $B$. Using this principle the food web of Fig. $10.1$ can be represented as a digraph $\overrightarrow{\mathscr{G}}$ shown in Fig. 10.2. For simplicity, we rename the species kelp, sea urchin, small fish, sea star, sea otter, shark by $a_1, a_2, a_3, a_4, a_5, a_6$ respectively.

## 数学代写|图论代写GRAPH THEORY代考|Competition Graph

In the food web, there is also a competition among the species. In the food web of Fig. 10.1, the small fishes and sea urchins both eat kelp. Thus, these two species are competitors to each other. Similarly, sea stars and sea otters are competitors as sea urchins are their common prey. The entire competition of a food web can be represented by another type of graph called competition graph (discussed in detail in Chap. 4).
The competition graph is constructed as follows:
The vertices in the competition graph $(\mathscr{C}(\overrightarrow{\mathscr{G}}))$ are the species and there exists an edge between the species $a$ and $b$ iff $a$ and $b$ have a common prey, say $x$, i.e. there is an undirected edge $(a, b)$ in the competition graph if there are directed edges $(x, a)$ and $(x, b)$ in the food web.
Many results are available for competition graphs in [16, 17, 25-28].
For the digraph of Fig. 10.2, sea urchin $\left(a_2\right)$ and small fish $\left(a_3\right)$ are competitors for kelp $\left(a_1\right)$. So we draw an (undirected) edge between the vertices $\left(a_2\right)$ and $\left(a_3\right)$. Similarly, the vertices $\left(a_4\right)$ and $\left(a_5\right)$ are competitors and hence there is an edge between them in $\mathscr{C}(\overrightarrow{\mathscr{G}})$.
The weight $\left(W_{i j}\right)$ of the edge $(i, j)$ in $\mathscr{C}(\overrightarrow{\mathscr{G}})$ is calculated by
$$\left(W_{i j}\right)=\frac{\mid \text { prey }{a_i} \cap \text { prey }{a_j} \mid}{\mid \text { prey }{a_i} \cup \text { prey }{a_j} \mid},$$
where $|\cdot|$ represents the number of elements in the set.
In the present example, prey $a_{a_2}=$ prey $_{a_3}=\left{a_1\right}$ and prey $_{a_4}=\left{a_2, a_3\right}$ and prey $_{a_5}=\left{a_2, a_4\right}$
Therefore,
$$W_{a_2 a_3}=\frac{\left|\left{a_1\right}\right|}{\left|\left{a_1\right}\right|}=1$$
and
$$W_{a_4 a_5}=\frac{\left|\left{a_2\right}\right|}{\left|\left{a_2, a_3, a_4\right}\right|}=\frac{1}{3} .$$

（a）畨鱼吃海獭;
(b) 海濑吃海星和海胆;
(c) 海星吃海胆和小鱼;
(d) 海胆吃海带;
(e) 小鱼吃海带。

## 数学代写图论代写GRAPH THEORY代考|Competition Graph

[16、17、25-28] 中的许多结果可用于竞争图。

$$\left(W_{i j}\right)=\frac{\mid \text { prey } a_i \cap \text { prey } a_j \mid}{\mid \text { prey } a_i \cup \text { prey } a_j \mid},$$

《left 缺少或无法识别的分隔符

〈left 缺少或无法识别的分隔符

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Graph Theory, 图论, 数学代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 数学代写|图论代写GRAPH THEORY代考|Application of if Min-Tolerance Graph

Consider a group of employees each scheduled to work for a fixed interval of time in a company. Each employee is each assigned to a single work for their entire work interval. A conflict arises if two employees are assigned to work on the same work station at the same time. Then a tolerance arises in a natural way. Let three employees $p_1, p_2, p_3$ are assigned for the same work and their time intervals be $\mathscr{I}_1=[2,4], \mathscr{I}_2=[6,9], \mathscr{I}_3=[11,14]$. These are taken as core of the intervals. The time interval $[2,4]$ means the working time of an employee from 2 a.m. to 4 a.m. (say). Also, assume that they are working inactively as well as actively in the time intervals $[1,6],[3,10],[8,15]$, which are taken as the support of the intervals.
Then $h\left(\mathscr{I}_1 \cap \mathscr{I}_2\right)=(0.6,0.4), h\left(\mathscr{I}_2 \cap \mathscr{I}_3\right)=(0.5,0.5), h\left(\mathscr{I}_1 \cap \mathscr{I}_3\right)=(0,0)$, which is shown in Fig.9.15.

Since the time intervals intersect, the tolerance needs to be considered. Let $\mathscr{T}_1, \mathscr{T}_2, \mathscr{T}_3$ be the tolerances. Therefore,
$C L\left(\mathscr{T}_1\right)=1, C L\left(\mathscr{T}_2\right)=2, C L\left(\mathscr{T}_3\right)=3$ and $S L\left(\mathscr{T}_1\right)=2, S L\left(\mathscr{T}_2\right)=1, S L\left(\mathscr{T}_3\right)=$ 1 , and, $\mu\left(p_1, p_2\right)=(0.4,0.27), \mu\left(p_2, p_3\right)=(0.25,0.25)$ and $\mu\left(p_1, p_3\right)=(0,0)$. Then there is a relation between the employees $p_1$ and $p_2 ; p_2$ and $p_3$. But there is no relation between the employees $p_1$ and $p_3$. Then the corresponding IF min-tolerance graph is shown in Fig.9.16.

## 数学代写|图论代写GRAPH THEORY代考|Intuitionistic Fuzzy Max-Tolerance Graphs

Like min-tolerance graph one can define max-tolerance graph by defining the function $\phi$ as $\phi(x, y)=\max {x, y}$. Then the IF $\phi$-TG is said to be intuitionistic fuzzy max-tolerance graph (IFMxTG).

Definition 9.66 An IF $\phi$-TG is said to be intuitionistic fuzzy max-tolerance graph if $\phi(x, y)=\max {x, y}$ for any $x, y$.
The following example describes an IFMxTG.
Example 9.14 Let us consider three IFIs $\mathscr{I}_1, \mathscr{I}_2, \mathscr{I}_3$ with corresponding IFTs $\mathscr{T}_1$, $\mathscr{T}_2, \mathscr{T}_3$. Let $[2,4],[6,9],[11,14]$ be the cores and $[0,6],[5.5,12],[10.5,16]$ be the supports of the IFIs respectively. For these three IFIs, we consider three nodes $p_1, p_2, p_3$.

Therefore, $C L\left(\mathscr{T}_1\right)=2, C L\left(\mathscr{T}_2\right)=1, C L\left(\mathscr{T}_3\right)=3$ and $S L\left(\mathscr{T}_1\right)=0.2, S L\left(\mathscr{T}_2\right)$ $=0.4, S L\left(\mathscr{T}_3\right)=0.7$
Then $h\left(\mathscr{I}_1 \cap \mathscr{I}_2\right)=(0.2,0.8), h\left(\mathscr{I}_2 \cap \mathscr{I}_3\right)=(0.43,0.56)$.
The graph has three nodes for three IFIs and two arcs. The membership and nonmembership values of the arcs are $\mu\left(p_1, p_2\right)=(0.04,0.16), \mu\left(p_2, p_3\right)=(0.23$, $0.30)$

## 数学代写|图论代写GRAPH THEORY代考|Application of if MinTolerance Graph

$\mu\left(p_1, p_2\right)=(0.4,0.27), \mu\left(p_2, p_3\right)=(0.25,0.25)$ 和 $\mu\left(p_1, p_3\right)=(0,0)$. 然后是员工之间的关系 $p_1$ 和 $p_2 ; p_2$ 和 $p_3$. 但是员工之间没有关系 $p_1$ 和 $p_3$. 然后相应的 IF 最小容差图如图 $9.16$ 所示。

## 数学代写|图论代写GRAPH THEORY代考|Intuitionistic Fuzzy MaxTolerance Graphs

$\mu\left(p_1, p_2\right)=(0.04,0.16), \mu\left(p_2, p_3\right)=(0.23,0.30)$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。