### 统计代写|运筹学作业代写operational research代考|MGSC373

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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|运筹学作业代写operational research代考|Multicriteria Decision-Making Method

Decision-making plays a vital role in everyone’s life nowadays. There are many important factors included in decision-making. It is one of the primary skills which everyone needs to lead a final choice that should be a good one. There are many techniques being used in decision-making. One of the techniques is multicriteria decision-making (MCDM) which includes the essential steps of defining the context, deciding the objectives, and selecting the right criteria that represent the value. The advantage of using MCDM is open and explicit. It is possible to compare many different factors with one another and also the chosen criteria can be adjusted. Many decision-making scenarios include indefinite, uncertainty, insufficient, and inconsistent information which should be handled in an effective manner to make the decisions in a better way. This multicriteria decision-making problem includes the process of identifying the best alternative among suitable alternatives which can be evaluated based on the number of criteria or attributes that are used in the particular problem.

This section deals about the multicriteria decision-making problem under quadripartitioned single-valued neutrosophic environment with the proposed crossentropy measure of QSVNSs. Let $A=\left{A_{1}, A_{2}, \ldots, A_{n}\right}$ and $C=\left{C_{1}, C_{2}, \ldots, C_{n}\right}$ be sets of alternative and criteria, respectively. Let $W_{j}(j=1,2, \ldots, n)$ denote the weight of the criterion $C_{j}$ and it belongs to the interval of $[0,1]$ provided $\sum_{i=1}^{n} w_{j}=1$. Here the characteristic of the alternative $A_{i}(i=1,2, \ldots, m)$ is denoted by QSVNS as $A_{i}=\left{\left\langle C_{j}, T_{A_{i}}\left(C_{j}\right), C_{A_{i}}\left(C_{j}\right), U_{A_{i}}\left(C_{j}\right), F_{A_{i}}\left(C_{j}\right)\right\rangle \mid C_{j} \in C\right}$ where $T_{A_{i}}\left(C_{j}\right), C_{A_{i}}\left(C_{j}\right), U_{A_{i}}\left(C_{j}\right), F_{A_{i}}\left(C_{j}\right) \in[0,1], i=1,2, \ldots, m$ and $j=$ $1,2, \ldots, n$.

To write the criterion value $\left\langle C_{j}, T_{A_{i}}\left(C_{j}\right), C_{A_{i}}\left(C_{j}\right), U_{A_{i}}\left(C_{j}\right), F_{A_{i}}\left(C_{j}\right)\right\rangle$ in a simple way is denoted by $\alpha_{i j}=\left\langle T_{i j}, C_{i j}, U_{i j}, F_{i j}\right\rangle(i=1,2, \ldots, m$ and $j=1,2, \ldots, n)$. The concept of ideal point plays a vital role in multicriteria decision-making environments which helps to identify the best alternative in the decision set. Though it is not possible to get ideal alternative in real world, it needs to construct the theoretical approach against evaluating the alternatives. Hence the ideal alternative $A^{}$ is denoted by the criterion value $\alpha_{j^{}}=\left\langle T_{j^{}}, C_{j^{}}, U_{j^{}}, F_{j^{}}\right\rangle=\langle 1,1,0,0\rangle$.

## 统计代写|运筹学作业代写operational research代考|Cross-Entropy for IQNS

This section deals about cross-entropy of an interval quadripartitioned neutrosophic set which is based on the cross-entropy of QSVNSs discussed in the previous section.
Definition 5.1 Let us consider an interval quadripartitioned neutrosophic set
$$A=\left\langle\left[T_{A}^{L}(x), T_{A}^{U}(x)\right],\left[C_{A}^{L}(x), C_{A}^{U}(x)\right],\left[U_{A}^{L}(x), U_{A}^{U}(x)\right],\left[F_{A}^{L}(x), F_{A}^{U}(x)\right]\right\rangle,$$
and $g_{\delta}: \operatorname{IQNS}(X) \rightarrow Q S V N S(X)$ is a mapping given by
$$\begin{array}{r} g_{\delta}(A)=\left\langle T_{A}^{L}(x)+\delta \Delta T_{A}(x), C_{A}^{L}(x)+\delta \Delta C_{A}(x), U_{A}{ }^{L}(x)+(1-\delta) \Delta U_{A}(x)\right. \ \left.F_{A}^{L}(x)+(1-\delta) \Delta F_{A}(x)\right\rangle \end{array}$$
where $\Delta T_{A}(x)=T_{A}^{U}(x)-T_{A}^{L}(x), \Delta C_{A}(x)=C_{A}^{U}(x)-C_{A}^{L}(x), \Delta U_{A}(x)$ $=U_{A}^{U}(x)-U_{A}^{L}(x)$, and $\Delta F_{A}(x)=F_{A}^{U}(x)-F_{A}^{L}(x)$ for $x \in X$ and $\delta \in[0,1]$. Here $g_{\delta}$ is known as reduction operator which helps to assign an interval quadripartitioned neutrosophic set to quadripartitioned single-valued neutrosophic set. Hence we get quadripartitioned single-valued neutrosophic set $A_{\delta}$ in universe $X$.

Example 5.2 Let $A=\left\langle\left(x_{1},[0.3,0.5],[0.1,0.2],[0.3,0.6],[0.4,0.7]\right): x_{1} \in X\right\rangle$ be an interval quadripartitioned neutrosophic set in the universe set $X=\left{x_{1}\right}$. For $\delta=0.5$, we get the following QSVNS $g_{0.5}(A)$ as $g_{0.5}(A)=\left\langle\left(x_{1}, 0.4,0.15,0.45,0.55\right): x_{1} \in X\right\rangle$.
Proposition $5.3$ Consider two IQNSs A and B in the universe of discourse $X=\left{x_{1}, x_{2}, \ldots, x_{n}\right}$ where $A=\left\langle\left[T_{A}^{L}(x), T_{A}^{U}(x)\right],\left[C_{A}^{L}(x), C_{A}^{U}(x)\right],\left[U_{A}\right.\right.$ $\left.L(x), U_{A}^{U}(x)\right],\left[F_{A}^{L}(x), F_{A}\right.$
$\left.\left.U^{U}(x)\right]\right\rangle, B=\left\langle\left[T_{B}^{L}(x), T_{B}^{U}(x)\right],\left[C_{B}^{L}(x), C_{B}^{U}(x)\right],\left[U_{B}^{L}(x), U_{B}^{U}(x)\right],\left[F_{B}^{L}(x), F_{B}^{U}(x)\right]\right\rangle$
Let $g_{\delta}: \operatorname{IQNS}(X) \rightarrow Q S V N S(X)$ be a reduction operator and $\delta, \rho \in[0,1]$. Then
i. if $0 \leq \delta \leq \rho$ then $g_{\delta}(A) \subseteq g_{\rho}(A)$
ii. if $A \subseteq B$ then $g_{\delta}(A) \subseteq g_{\delta}(B)$
iii. $g_{\delta}\left(g_{\rho}(A)\right)=g_{\rho}(A)$
iv. $\left.g_{\delta}\left(A^{C}\right)\right)^{C}=g_{1}-\delta(A)$

## 统计代写|运筹学作业代写operational research代考|Multicriteria Decision-Making Method

A=Ileft{A_{1}, A_{2}, \dots, A_{n}}right $} \mathrm{~ 和 ~ C = I l e f t { C _ { 1 } , ~ C _ { 2 } , ~}$ $W_{j}(j=1,2, \ldots, n)$ 表示标准的权重 $C_{j}$ 并且属于区间 $[0,1]$ 假如 $\sum_{i=1}^{n} w_{j}=1$. 这里的替代品的特点 $A_{i}(i=1,2, \ldots, m)$ 由 QSVNS 表示为
\begin{tabular}{|l|l|l} \end{tabular} 在哪里 $T_{A_{i}}\left(C_{j}\right), C_{A_{i}}\left(C_{j}\right), U_{A_{i}}\left(C_{j}\right), F_{A_{i}}\left(C_{j}\right) \in[0,1], i=1,2, \ldots, m$ 和 $j=1,2, \ldots, n$.

$\alpha_{i j}=\left\langle T_{i j}, C_{i j}, U_{i j}, F_{i j}\right\rangle(i=1,2, \ldots, m$ 和 $j=1,2, \ldots, n)$. 理想点的概念在多标准决策环境中起着至关重 要的作用，有助于确定决策集中的最佳选择。尽管在现实世界中不可能得到理想的替代方案，但需要构建用于评估 替代方案的理论方法。因此，理想的选择 $A$ 由标准值表示 $\alpha_{j}=\left\langle T_{j}, C_{j}, U_{j}, F_{j}\right\rangle=\langle 1,1,0,0\rangle$.

## 统计代写|运筹学作业代写operational research代考|Cross-Entropy for IQNS

$$A=\left\langle\left[T_{A}^{L}(x), T_{A}^{U}(x)\right],\left[C_{A}^{L}(x), C_{A}^{U}(x)\right],\left[U_{A}^{L}(x), U_{A}^{U}(x)\right],\left[F_{A}^{L}(x), F_{A}^{U}(x)\right]\right\rangle,$$

$$g_{\delta}(A)=\left\langle T_{A}^{L}(x)+\delta \Delta T_{A}(x), C_{A}^{L}(x)+\delta \Delta C_{A}(x), U_{A}^{L}(x)+(1-\delta) \Delta U_{A}(x) F_{A}^{L}(x)+(1-\delta) \Delta F_{A}(x)\right)$$

$g_{0.5}(A)=\left\langle\left(x_{1}, 0.4,0.15,0.45,0.55\right): x_{1} \in X\right\rangle .$

$A=\left\langle\left[T_{A}^{L}(x), T_{A}^{U}(x)\right],\left[C_{A}^{L}(x), C_{A}^{U}(x)\right],\left[U_{A} L(x), U_{A}^{U}(x)\right],\left[F_{A}^{L}(x), F_{A}\right.\right.$
$\left.\left.U^{U}(x)\right]\right\rangle, B=\left\langle\left[T_{B}^{L}(x), T_{B}^{U}(x)\right],\left[C_{B}^{L}(x), C_{B}^{U}(x)\right],\left[U_{B}^{L}(x), U_{B}^{U}(x)\right],\left[F_{B}^{L}(x), F_{B}^{U}(x)\right]\right\rangle$

ii. 如果 $A \subseteq B$ 然后 $g_{\delta}(A) \subseteq g_{\delta}(B)$
iii. $g_{\delta}\left(g_{\rho}(A)\right)=g_{\rho}(A)$
iv. $\left.g_{\delta}\left(A^{C}\right)\right)^{C}=g_{1}-\delta(A)$

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