### 统计代写|决策与风险作业代写decision and risk代考|Assessment in the Presence

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• 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

## 统计代写|决策与风险作业代写decision and risk代考|Preferences Elicitation and Reliability

Fuzzy risk assessment methods are developed to handle risks that involve uncertainty. One of the established fuzzy concepts that concerns with the uncertainty is the Znumbers (Bakar and Gegov 2015; Kang et al. 2012; Zadeh 2011; Allahviranloo and Ezadi 2019). Established fuzzy risk assessment methods based on Z-numbers often describe each risk under consideration as an ordered pair of restriction of the preferences elicited by the risk analyst’s and the reliability of the restriction (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). In the literature on fuzzy risk assessment, incorporation of the pair (restriction and reliability components) has complemented established fuzzy risk assessment methods to successfully resolve numerous risk assessment problems such as risk assessment evaluations in failure mode of rotor blades of an aircraft turbine (Jiang et al. 2017), investigation on risk components in manufacturing and medical industries (Wu et al. 2018) and assessment of risk in food security (Abiyev et al. 2018). In order to define risks, established fuzzy risk assessment methods based on Z-numbers evaluate each risk under consideration based on two common risk factors, namely, the risk severity of loss and the risk probability of failure (Bakar et al. 2020; Zhao et al. 2020; Natha Reddy and Gokulachandran 2020 ; Chukwuma et al. 2020). Each of these factors that are usually expressed based on the preferences elicited by the risk analysts, is in this case represented by their own ordered pair of restriction and reliability (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018).

The literature on established fuzzy risk assessment methods based on Z-numbers signify that they possess great capability to deal with the presence of uncertainty (Marhamati et al. 2018; Peng et al. 2019; Hendiani et al. 2020; Azadeh and Kokabi 2016). However, their acknowledgement in terms of the presence of uncertainty on each risk under consideration is graded as partially complete. This is because established fuzzy risk assessment methods based on Z-numbers take into account only the presence of uncertainty when preferences elicited by the risk analysts are partially known (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). Nonetheless, the presence of uncertainty can also happen when preferences elicited by the risk analysts are completely known, completely unknown and partially unknown (Bakar et al. 2020; Yang and John 2012; Huang et al. 2008). This points out that established fuzzy risk assessment methods based on Z-numbers do not have the holistic feature as they restrict the presence of uncertainty in the preferences elicited by the risk analysts to be homogeneous (partially known only), even if the presence of uncertainty is actually heterogeneous in nature (Bakar et al. 2020). Apart from that, the interactions between the common and uncommon heterogeneous preferences elicited by the risk analysts also indicate that the established fuzzy risk assessment methods based on Z-numbers are unable to holistically track the performance of risks in the presence of uncertainty. The above-mentioned inefficiencies of the established fuzzy risk assessment methods based on Z-numbers point out the motivations for this study.

## 统计代写|决策与风险作业代写decision and risk代考|Z-Number

As overcoming the uncertainty in human decision making is crucial, the concept of Z-numbers (Zadeh 2011) is introduced by incorporating the element of reliability along with the decision restriction. This concept enhances the established concepts of type-1 fuzzy numbers and type- 2 fuzzy numbers, where both consider uncertain decision with confidence level (Bakar and Gegov 2014) and inter-intra uncertainty (Bakar et al. 2019; Jana and Ghosh 2018; Wallsten and Budescu 1995; Yaakob et al. 2015 ; John and Coupland 2009), respectively. Based on (Zadeh 2011 ), the definition of Z-number is given as the following Definition $1 .$

Definition 1 (Zadeh 2011) A Z-number is an ordered pair of type-1 fuzzy numbers denoted as $Z=(A, B)$. The first component, $A$, is known as the restriction component where it is a real-valued uncertain on $X$ whereas the second component, $B$, is the measure of reliability for $A$, presented as Fig. 4.1.

With respect to application of Z-numbers in fuzzy risk assessment, risks are represented as an ordered pair of risk restriction and the reliability of the restriction (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). This can be seen when Z-numbers complement risk assessment problems in the literature such as risk assessment evaluations in failure mode of rotor blades of an aircraft turbine (Jiang et al. 2017), investigation on risk components in manufacturing and medical industries (Wu et al. 2018) and assessment of risk in food security (Abiyev et al. 2018).

## 统计代写|决策与风险作业代写decision and risk代考|Grey Number

The concept of grey numbers is introduced in the literature as to acknowledge the presence of non-homogeneous decision makers’ preferences that are completely known, partially known, completely unknown and partially unknown (Bakar et al. 2020,2019 ; Yang and John 2012; Huang et al. 2008). Definition of grey number and its further extensions are given as follows.

Definition 2 (Yang and John 2012) A grey number, $G_{A}$, is a number with clear upper and lower boundaries but has an unknown position within the boundaries. Mathematically, a grey number for the system is expressed as
$$G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}$$
where $t$ is information about $g^{\pm}$while $g^{-}$and $g^{+}$are the upper and lower limits of information $t$, respectively.

Definition 3 (Bakar et al. 2020; Yang and John 2012) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A}^{\pm}(x)$, can be expressed with a grey number, $g_{A}^{\pm}(x) \in \bigcup_{i=1}^{n}\left[a_{i}^{-}, a_{i}^{+}\right] \in D[0,1]^{\pm}$, then $A$ is a grey set, where $D[0,1]^{\pm}$is the set of all grey numbers within the interval $[0,1]$.

Definition 4 (White Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a white number, then $A$ is a white set.

Definition 5 (Black Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a black number, then $A$ is a black set.

Definition 6 (Grey Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a grey number, then $A$ is a grey set.

The following Table $4.1$ presents comparison between white number, black number and grey number.

Established fuzzy risk assessment methods based on Z-numbers capable at dealing with the presence of uncertainty (Marhamati et al. 2018; Peng et al. 2019; Hendiani et al. 2020; Azadeh and Kokabi 2016) but the presence of uncertainty the risk faced is not well acknowledged. This is depicted when they consider only the presence of uncertainty when preferences elicited by the risk analysts are partially known (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). Nonetheless, the presence of uncertainty can also happen when preferences elicited by the risk analysts are completely known, completely unknown and partially unknown (Bakar et al. 2020.

## 统计代写|决策与风险作业代写decision and risk代考|Grey Number

G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。