Doug I. Jones

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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商科代写|商业数学代写business mathematics代考|Strengths and Limitations of Analytic Hierarchy Process

Similar to all modeling and MADM methods, the AHP has strengths and limitations.

The main strength of the AHP is its ability to rank choices in the order of their effectiveness in meeting objectives. If the judgments made about the relative importance of criteria and those about the alternatives’ ability to satisfy those objectives have been made in good faith and effort, then the AHP calculations lead to the logical consequence of those judgments. It is quite hard, but not impossible, to manually change the pairwise judgments to get some predetermined result. A further strength of the AHP is its ability to detect inconsistent judgments in the pairwise comparisons using the $C R$ value. If the $C R$ value is greater than $0.1$, then the judgments are deemed to be inconsistent.

The limitations of the AHP are that it only works because the matrices are all of the same mathematical form. This is known as a positive reciprocal matrix. The reasons for this are explained in Saaty’s book (1990), so we will simply state that point in the form that is required. To create such a matrix requires that, if we use the number 9 to represent that $A$ is absolutely more important than $B$, then we have to use $1 / 9$ to define the relative importance of $B$ with respect to $A$. Some people regard that as reasonable; others do not.
Another suggested limitation is in the possible scaling. However, understanding that the final values obtained simply say that one alternative is relatively better than another alternative. For example, if the AHP values for alternatives ${A, B, C}$ found were $(0.392,0.406,0.204)$, then they imply that only alternatives $A$ and $B$ are about equally good at approximately $0.4$, whereas $C$ is worse at $0.2$. It does not mean that $A$ and $B$ are twice as good as $C$.

The AHP is a useful technique for discriminating between competing options in the light of a range of objectives to be met. The calculations are not complex, and although the AHP relies on what might be seen as a mathematical trick, you do not need to understand the mathematics to use the technique. Be aware that it only shows relative values.

As AHP, at least in the pairwise comparisons, is based on subjective inputs using the nine-point scale, then sensitivity analysis is extremely important. Leonelli (2012) in his master’s thesis outlines procedures for sensitivity analysis to enhance decision support tools, including numerical incremental analysis of a weight, probabilistic simulations, and mathematical models. How often do we change our minds about the relative importance of an object, place, or thing? Often enough that we should alter the pairwise comparison values to determine how robust our rankings are in the AHP process. We suggest doing enough sensitivity analysis to find the break point values, if they exist, of the decision-maker weights that change the rankings of our alternatives. As the pairwise comparisons are subjective matrices that are compiled using the Saaty method, we suggest a minimum trial and error sensitivity analysis using the numerical incremental analysis of the weights.
Chen and Kocaoglu (2008) grouped sensitivity analysis into three main groups that he called: numerical incremental analysis, probabilistic simulations, and mathematical models. The numerical incremental analysis, also known as one-at-a-time (OAT) or trial and error works by incrementally changing one parameter at a time, finds the new solution and shows graphically how the ranks change. There exist several variations of this method (Hurly, 2001; Barker, 2011). Probabilistic simulations employ the use of Monte Carlo simulation (Butler, 1997) that allows random changes in the weights and simultaneously explores the effect on the ranks. Modeling may be used when it is possible to express the relationship between the input data and the solution results.

Wé used Equation $4.7$ (Alinezzad and Amini, 2011) for adjusting weights that fall under the incremental analysis:
$$w_{j}^{\prime}=\frac{1-w_{p}^{\prime}}{1-w_{p}} w_{j}$$
where $w_{j}^{\prime}$ is the new weight and $w_{p}$ is the original weight of the criterion to be adjusted and $w_{p}^{\prime}$ is the value after the criterion was adjusted. We found this to be an easy method to adjust weights to reenter back into our model.

商科代写|商业数学代写business mathematics代考|Strengths and Limitations of Analytic Hierarchy Process

Chen 和 Kocaoglu (2008) 将敏感性分析分为三个主要组，他称之为：数值增量分析、概率模 拟和数学模型。数值增量分析，也称为一次一个 (OAT) 或反晶试验，通过一次增量地更改一 个参数来工作，找到新的解决方宴并以图形方式显示等级如何变化。这种方法存在几种变体 (Hurly，2001；Barker，2011)。概率模拟使用蒙特卡洛模拟 (Butler，1997)，它允许 权重随机忩化，同时探客对等级的影响。当可以表达输入数据和求解结果之间的关系时，可 以使用建模。

$$w_{j}^{\prime}=\frac{1-w_{p}^{\prime}}{1-w_{p}} w_{j}$$

有限元方法代写

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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。

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