# 统计代写|运筹学作业代写operational research代考|MTH360

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## 统计代写|运筹学作业代写operational research代考|Quantiles of Neutrosophic Normal Distribution

The quantile function is useful in the construction of confidence interval, drawing $Q-Q$ plot, and hypothesis testing. It is the inverse of the neutrosophic cumulative distribution function or neutrosophic distribution function. For a neutrosophic random variable with mean and variance, the quantile function for a neutrosophic normal probability distribution is defincd as
$$F^{-1}(p)=\mu_{N}+\sigma_{N} \Phi^{-1}(p)=\mu_{N}+\sigma_{N} Z_{p}, \quad p \in(0,1)$$
where $Z_{p}=\Phi^{-1}(p)$ is the quantile of the standard normal distribution. A neutrosophic random variable $X_{N}$ will exceed $\mu_{N}+\sigma_{N} Z_{p}$ with probability $(1-p)$ and will fall outside the interval $\mu_{N} \pm \sigma_{N} Z_{p}$ with probability $2(1-p)$. For larger values of $p$, we use $Z_{p}=\Phi^{-1}\left(\frac{p+1}{2}\right)$ in place of $Z_{p}=\Phi^{-1}(p)$. Let the neutrosophic random variable $X_{N} \sim N_{N}\left([10,15], 2^{2}\right)$, and assume that the variable $X_{N}$ will fall within the range $\mu_{N} \pm \sigma_{N} Z_{p}$ with a specified probability $p$; then the values of the neutrosophic quantiles are provided in Table 1 .

In Fig. 4, we presented the neutrosophic $Q-Q$ plot for the neutrosophic normal probability distribution. It is a scatter plot of theoretical and observed quantiles. The gap between the two dotted lines shows the level of indeterminacy in the $Q-Q$ plot due to the indeterminate values in the mean of the neutrosophic normal distribution. From the $Q-Q$ plot, it is evident that the supposed neutrosophic random variable $X_{N}$ with indeterminate mean $\mu_{N}=[10,15]$ and variance 4 follows a neutrosophic normal probability distribution.

## 统计代写|运筹学作业代写operational research代考|Review of Literature

Samantha and Pal [8] proposed irregular bipolar fuzzy graphs. Akram and Davvaz [6] defined strong intuitionistic fuzzy graphs. Alshehri and Akram [9] introduced Cayley bipolar fuzzy graphs. Karunambigai et al. [10] determined domination in bipolar fuzzy graphs. Rosline and Pathinathan [11] dealt with scheduling job using fuzzy graphs concepts. Akram et al. [7] introduced the concept of balance bipolar fuzzy graphs. Rashmanlou et al. $[12,13]$ defined new operations on bipolar fuzzy graphs with their properties. Rashmanlou et al. [12, 13] discussed some of the properties of bipolar fuzzy graphs. Akram et al. [14] introduced some of the operations and described dominating and independent sets of bipolar neutrosophic graph and discussed outranking approach for risk analysis using the proposed concepts. Delia et al. [15] introduced the concept of bipolar neutrosophic set and its operations and applied in a decision-making problem. Broumi et al. (2016a) defined the concept of bipolar single-valued neutrosophic graph. Gani and Latha [16] proposed new algorithms to find the Hamiltonian cycle for a fuzzy network.

Akram and Akmal [17] introduced some of the operations on intuitionistic fuzzy graph theory. Deli et al. [18] proposed the concept of interval-valued bipolar neutrosophic set and applied in pattern recognition. Sahin et al. [19] presented Jaccard vector similarity measure of bipolar neutrosophic set and solved a decisionmaking problem using the proposed similarity measure. Pramanik and Mondal [20] developed a hybrid structure called rough bipolar neutrosophic set. Ulucay et al. [21] introduced some of the similarity measure with their properties and applied in a decision-making problem. Broumi et al. [22, 23] examined the properties of different types of degrees, order, and size of a single-valued neutrosophic graph. Mathew et al. [24] introduced the concept of bipolar fuzzy graphs and strong bipolar fuzzy graphs. Gani and Rahman [25] defined lower and upper truncations of intuitionistic fuzzy graphs. Broumi et al. [26] introduced complex neutrosophic graphs of type 1 with its properties and its matrix representation. Gani et al. [27] determined domination on intuitionistic fuzzy graphs. Prabhu et al. [28] introduced finite state machine using the concept of bipolar neutrosophic set. Akram et al. [29] presented some concepts and properties of bipolar single-valued neutrosophic graph structure. Girao et al. [30] determined long cycles in Hamiltonian graphs.

## 统计代写|运筹学作业代写operational research代考|Quantiles of Neutrosophic Normal Distribution

quantile 函数可用于构建置信区间，绘制 $Q-Q$ 情节和假设检验。它是中智異积分布函数 或中智分布函数的倒数。对于具有均值和方差的中智随机变量，中智正态概率分布的分位数 函数定义为
$$F^{-1}(p)=\mu_{N}+\sigma_{N} \Phi^{-1}(p)=\mu_{N}+\sigma_{N} Z_{p}, \quad p \in(0,1)$$

## 统计代写|运筹学作业代写operational research代考|Review of Literature

Samantha 和 Pal [8] 提出了不规则双极模糊图。Akram 和 Davvaz [6] 定义了强直觉模糊图。Alshehri 和 Akram [9] 介绍了 Cayley 双极模糊图。Karunambigai 等人。[10] 确定了双极模糊图中的支配地位。Rosline 和 Pathinathan [11] 使用模糊图概念处理调度作业。阿克拉姆等人。[7] 引入了平衡双极模糊图的概念。拉什曼卢等人。[12,13]定义了双极模糊图的新操作及其属性。拉什曼卢等人。[12, 13] 讨论了双极模糊图的一些特性。阿克拉姆等人。[14] 介绍了一些操作并描述了主导和独立的双极中智图集，并讨论了使用提出的概念进行风险分析的排序方法。迪莉娅等人。[15] 介绍了双极中智集的概念及其运算，并应用于决策问题。布鲁米等人。（2016a）定义了双极单值中智图的概念。Gani 和 Latha [16] 提出了寻找模糊网络的哈密顿循环的新算法。

Akram 和 Akmal [17] 介绍了直觉模糊图论的一些操作。熟食店等人。[18] 提出了区间值双极中智集的概念，并应用于模式识别。沙欣等人。[19] 提出了双极中智集的 Jaccard 矢量相似性度量，并使用所提出的相似性度量解决了决策问题。Pramanik 和 Mondal [20] 开发了一种称为粗糙双极中智集的混合结构。乌鲁凯等人。[21] 介绍了一些相似性度量及其属性，并应用于决策问题。布鲁米等人。[22, 23] 研究了单值中智图的不同类型的度数、阶数和大小的属性。马修等人。[24] 引入了双极模糊图和强双极模糊图的概念。Gani 和 Rahman [25] 定义了直觉模糊图的上下截断。布鲁米等人。[26] 介绍了类型 1 的复杂中智图及其属性和矩阵表示。加尼等人。[27] 确定了直觉模糊图的支配地位。普拉布等人。[28] 使用双极中智集的概念引入了有限状态机。阿克拉姆等人。[29] 提出了双极单值中智图结构的一些概念和性质。Girao 等人。[30] 在哈密顿图中确定了长周期。[28] 使用双极中智集的概念引入了有限状态机。阿克拉姆等人。[29] 提出了双极单值中智图结构的一些概念和性质。Girao 等人。[30] 在哈密顿图中确定了长周期。[28] 使用双极中智集的概念引入了有限状态机。阿克拉姆等人。[29] 提出了双极单值中智图结构的一些概念和性质。Girao 等人。[30] 在哈密顿图中确定了长周期。

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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。

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