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

2022年7月7日

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## 统计代写|运筹学作业代写operational research代考|Suggested Cosine Similarity Measures for Single-Valued Neutrosophic Sets

Improved cosine similarity measıres presented hy Ye have unreasonahle results in some situations, as we illustrated previously. To improve presented measures and make them produce reasonable and harmonious results, we will improve the first similarity measure (i.e., Eq. (1)) and keep the second as it was (i.e., Eq. (2)). The first similarity measure in case $B={\mid x \in X}$ and $C={\mid x \in X}$ and $C={\mid x \in X}$, the first similarity measure will produce zero, although two sets are similar in indeterminacy and falsity degrees. There is the same result in case $B={\langle x, 0,1,1\rangle \mid x \in X}$ and $C={\langle x, 0,1,0\rangle \mid x \in X}$. So, in case $B={\mid x \in X}$. The main reason for these results is that in the first similarity measure of Ye, he depended only on one maximum value of $\left|T_{B}\left(x_{j}\right)-T_{c}\left(x_{j}\right)\right|,\left|I_{B}\left(x_{j}\right)-I_{c}\left(x_{j}\right)\right|, \mid F_{B}\left(x_{j}\right)-F_{c}\left(x_{j}\right)$. We can note these problems clearly in binary values (i.e., zero and one) of sets.

So, we enhanced only the first similarity measure (i.e., Eq. (1)) and named it $\operatorname{NewSC}{1}(B, C)$ to handle all situations precisely and remove the large gap between first and second similarity measures of Ye in some cases as follows: $$N e w S C{1}(B, C)=\operatorname{Cos}\left(\frac{\pi}{2} \times\left(\frac{M_{1}+M_{2}}{2}\right)\right)$$
Since
$$M_{1}=\operatorname{Max}\left(\left|T_{B}\left(x_{j}\right)-T_{c}\left(x_{j}\right)\right|,\left|I_{B}\left(x_{j}\right)-I_{c}\left(x_{j}\right)\right|,\left|F_{B}\left(x_{j}\right)-F_{c}\left(x_{j}\right)\right|\right),$$
$$M_{2}=\operatorname{Min}\left(\left|T_{B}\left(x_{j}\right)-T_{c}\left(x_{j}\right)\right|,\left|I_{B}\left(x_{j}\right)-I_{c}\left(x_{j}\right)\right|, \mid F_{B}\left(x_{j}\right)-F_{c}\left(x_{j}\right)\right) .$$
Our enhanced similarity measure also satisfies the following properties:
(a) $0 \leq N e w S C_{1}(B, C) \leq 1$.

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

Fuzzy Set: (Zadeh [8]) A $f u z z y$ set $\tilde{A}$ in $U$ is a set of ordered pairs
$$\tilde{A}=\left{\left(x, \mu_{A}^{\sim}(x)\right) \mid x \in U\right}$$
where $U$ is a collection of objects denoted generically by $x$ and $\mu_{A}(x): U \rightarrow[0,1]$ is called the membership function or grade of membership of $x$ in $A$.

Fuzzy Number: A fuzzy number is a quantity whose esteem is imprecise, as opposed to correct similar to the case with single-valued number. A fuzzy number measurement does not allude to one single value; it is an associated set of conceivable qualities, where every conceivable quality has a weight somewhere in the range of 0 and 1 . This weight is called membership function, which has the form
$$\mu \underset{B}{\mu}(x): R \rightarrow[0,1]$$
where $\mu_{\tilde{B}}(x)$ is a membership function of the fuzzy set $\tilde{B}$.
Generalized Fuzzy Number (GFN): Chen [28, 29] represents a generalized trapezoidal fuzzy number (GTrFN) $A$ as $\tilde{A}=\left(a_{1}, a_{2}, a_{3}, a_{4} ; w\right)$, where $0<w \leq 1$ and $a_{1}, a_{2}, a_{3}$, and $a_{4}$ are real numbers. The generalized fuzzy number (GFN) $A$ is a fuzzy subset of real line $R$, whose membership function $\mu_{A}^{\sim}(x)$ satisfies the following properties:

1. $\mu_{\tilde{A}}(x)$ is a continuous mapping from $\mathrm{R}$ to the closed interrval $[0,1]$.
2. $\mu_{\tilde{A}}(x)=0$, for all $x \in\left(-\infty, a_{1}\right]$.
3. $\mu_{\tilde{A}}(x)$ is strictly increasing with constant rate on $\left[a_{1}, a_{2}\right]$.
4. $\mu_{\tilde{A}}(x)=w$ for all $x \in\left[a_{2}, a_{3}\right]$.
5. $\mu_{\tilde{A}}(x)$ is strictly decreasing with constant rate on $\left[a_{3}, a_{4}\right]$.
6. $\mu_{\tilde{A}}(x)=0$ where $x \in\left[a_{4}, \infty\right)$.

## 统计代写|运筹学作业代写operational research代考|Suggested Cosine Similarity Measures for Single-Valued Neutrosophic Sets

$$\operatorname{NewSC}(B, C)=\operatorname{Cos}\left(\frac{\pi}{2} \times\left(\frac{M_{1}+M_{2}}{2}\right)\right)$$

$$M_{1}=\operatorname{Max}\left(\left|T_{B}\left(x_{j}\right)-T_{c}\left(x_{j}\right)\right|,\left|I_{B}\left(x_{j}\right)-I_{c}\left(x_{j}\right)\right|,\left|F_{B}\left(x_{j}\right)-F_{c}\left(x_{j}\right)\right|\right),$$
$$M_{2}=\operatorname{Min}\left(\left|T_{B}\left(x_{j}\right)-T_{c}\left(x_{j}\right)\right|,\left|I_{B}\left(x_{j}\right)-I_{c}\left(x_{j}\right)\right|, \mid F_{B}\left(x_{j}\right)-F_{c}\left(x_{j}\right)\right)$$

(a) $0 \leq N e w S C_{1}(B, C) \leq 1$

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

$\backslash$ tilde{A $\left{=\backslash\right.$ eft $\left{\backslash e f t\left(x, \backslash \operatorname{mu}{-}{\mathrm{A}} \wedge{\operatorname{sim}}(\mathrm{x}) \backslash\right.\right.$ right $) \backslash$ mid $x \backslash \mathrm{~ i n ~ U}$ 在哪里 $U$ 是一个对象的集合，通常由 $x$ 和 $\mu{A}(x): U \rightarrow[0,1]$ 称为莍属函数或隶属等级 $x$ 在
$A$

$$\underset{B}{\mu} \mu(x): R \rightarrow[0,1]$$

$\tilde{A}=\left(a_{1}, a_{2}, a_{3}, a_{4} ; w\right) ，$ 在哪里 $0<w \leq 1$ 和 $a_{1}, a_{2}, a_{3}$ ， 和 $a_{4}$ 是实数。广义模。秙数 (GFN) $A$ 是实线的模楜子集 $R$, 其求属函数 $\mu_{A}^{\sim}(x)$ 满足以下性质：

1. $\mu_{\tilde{A}}(x)$ 是来自的连续映射 $\mathrm{R}$ 到闭区间 $[0,1]$.
2. $\mu_{\tilde{A}}(x)=0$, 对所有人 $x \in\left(-\infty, a_{1}\right]$.
3. $\mu_{\tilde{A}}(x)$ 以恒定速率严格增加 $\left[a_{1}, a_{2}\right]$.
4. $\mu_{\tilde{A}}(x)=w$ 对所有人 $x \in\left[a_{2}, a_{3}\right]$.
5. $\mu_{\hat{A}}(x)$ 以恒定速率严格递减 $\left[a_{3}, a_{4}\right]$.
6. $\mu_{\tilde{A}}(x)=0$ 在咖里 $x \in\left[a_{4}, \infty\right)$.

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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。