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

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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

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

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