Posted on Categories:Time Series, 数据科学代写, 时间序列, 统计代写, 统计代考

# 统计代写|时间序列和预测代写Time Series & Prediction代考|Stat131 Scope of Uncertainty Management by Fuzzy Sets

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 统计代写|时间序列和预测代写Time Series & Prediction代考|Scope of Uncertainty Management by Fuzzy Sets

Fuzzy sets are widely being used for uncertainty management in expert systems. Because of multiple sources of uncertainty in the prediction of a time-series, the logic of fuzzy sets can be used to handle the problem. Fuzzy logic primarily is an extension of classical logic of propositions and predicates. In propositional/ predicate logic, we use binary truth functionality to represent the truth value of a proposition/predicate. Because of strict binary truth functionality, propositional/ predicate logic fails to express the uncertainty of the real-world problems. In fuzzy logic, the truth values of a fuzzy (partially true) proposition lies in the closed interval of $[0,1]$, where the binary digits: 0 and 1 indicate the completely false and totally true.

Consider, for instance, a fuzzy production rule: if $x$ is $A$ then $y$ is $B$, where $\mathrm{x}$ and $\mathrm{y}$ are linguistic variables and $\mathrm{A}$ and $\mathrm{B}$ are fuzzy sets in respective universe $\mathrm{U}$ and $\mathrm{V}$ respectively. The connectivity between $\mathrm{x}$ is $\mathrm{A}$ and $\mathrm{y}$ is $\mathrm{B}$ is represented by a fuzzy implication relation, where $x \in\left{x_1, x_2, \ldots \ldots, x_n\right}=X, \quad y \in\left{y_1, y_2, \ldots \ldots, y_m\right}=Y$ and $\mathrm{R}(\mathrm{x}, \mathrm{y})$ denotes the strength of fuzzy relation for $x=x_i$ and $y=y_j$, satisfying the implication between $\mathrm{x}$ is $\mathrm{A}$ and $\mathrm{y}$ is $\mathrm{B}$.

Different implication functions are used in the direct use to describe the fuzzy if-then connectivity. A few of the well-known implication relations are Mamdani, Lucksiwcz and Diens-Rescher [35, 36] relations.
Mamdani implication relation
\begin{aligned} \mathrm{R}(x, y) & =\operatorname{Min}\left(\mu_A\left(x_i\right), \mu_B\left(y_j\right)\right) \ \text { or } \mathrm{R}(x, y) & =\mu_A\left(x_i\right) \times \mu_B\left(y_j\right) \end{aligned}
Lukasiewicz implication relation
$$\mathrm{R}(\mathrm{x}, \mathrm{y})=\operatorname{Min}\left[1,\left(1-\mu_A\left(x_i\right)+\mu_B\left(y_j\right)\right)\right]$$

## 统计代写|时间序列和预测代写Time Series & Prediction代考|Fuzzy Time-Series

Prediction of a time-series from its current and/or past samples is an open area of current research. Unfortunately, traditional statistical techniques or regression-based models are not appropriate for prediction of economic time-series as the external parameters influencing the series in most circumstances are not clearly known. Naturally, prediction of a time-series requires reasoning under uncertainty, which can be easily performed using the logic of fuzzy sets. Researchers are taking keen interest to represent a time-series using fuzzy sets for an efficient reasoning. One well-known approach, in this regard, is to partition the dynamic range of the time-series into intervals of equal size, where each interval is described by a fuzzy set. Several approaches of representation of the partitions of a time-series by fuzzy sets are available in the literature [37-95]. One simple approach is to represent each partition by a membership function (MF), typically a Gaussian curve, with its mean equal to the centre of the partition and variance equal to half of the height of the partition. Thus each partition $P_i$ can be represented as a fuzzy set $A_i$, where $A_i$ is a Gaussian MF of fixed mean and variance as discussed above.

Choice of the membership function also has a great role to play on the performance of prediction. For example, instead of Gaussian MF, sometimes researchers employ triangular, left shoulder and right shoulder MFs to model the partitions of a time-series. Selection of a suitable MF describing a partition and its parameters remained an open problem until this date.
Defining a Fuzzy Time-series
Let $\mathrm{Y}(\mathrm{t}) \subset \mathrm{R}$, the set of real numbers for $\mathrm{t}=0,1,2, \ldots$, be a time-varying universe of discourse of the fuzzy sets $A_1(t), A_2(t), \ldots$ at time $t$, where $A_i(t)=\left{y_i(t) /\right.$ $\left.\mu_{\mathrm{i}}\left(\mathrm{y}{\mathrm{i}}(\mathrm{t})\right)\right}$, for all $\mathrm{i}$ and $\mathrm{y}{\mathrm{i}}(\mathrm{t}) \in \mathrm{Y}(\mathrm{t})$ We following $[37,38]$ define a fuzzy time-series $\mathrm{F}(\mathrm{t})=\left{\mathrm{A}_1(\mathrm{t}), \mathrm{A}_2(\mathrm{t}), \ldots\right}$

The following observations are apparent from the definition of fuzzy time-series.

1. In general, a fuzzy time-series $F(t)$ includes an infinite number of time-varying fuzzy sets $A_1(t), A_2(t),$.
2. The universe of discourse $Y(t)$ is also time-varying.
3. $\mathrm{F}(\mathrm{t})$ is a linguistic variable and $\mathrm{A}_{\mathrm{i}}(\mathrm{t})$ is its possible linguistic values (fuzzy sets), for all $i$.

## 统计代写|时间序列和预测代写Time Series \& Prediction代考|Scope of Uncertainty Management by Fuzzy Sets

Mamdani 荁涵关系
$$\mathrm{R}(x, y)=\operatorname{Min}\left(\mu_A\left(x_i\right), \mu_B\left(y_j\right)\right) \text { or } \mathrm{R}(x, y) \quad=\mu_A\left(x_i\right) \times \mu_B\left(y_j\right)$$
Lukasiewicz 䔮涵关系
$$\mathrm{R}(\mathrm{x}, \mathrm{y})=\operatorname{Min}\left[1,\left(1-\mu_A\left(x_i\right)+\mu_B\left(y_j\right)\right)\right]$$

## 统计代与时间序列和预测代写Time Series \& Prediction代考|Fuzzy Time-Series

《left 缺少或无法识别的分隔符，，对所有人i和 $\mathrm{ii}(\mathrm{t}) \in \mathrm{Y}(\mathrm{t})$ 我们关注 $[37,38]$ 定义模㗅时间序列
\eft 缺少或无法识别的分隔符

1. 一般来说，模楜时间序列 $F(t)$ 包括无限数量的时变模葫集 $A_1(t), A_2(t)$,
2. 话语的宇宙 $Y(t)$ 也是时变的。
3. $\mathrm{F}(\mathrm{t})$ 是一个语言变量，并且 $\mathrm{A}_{\mathbf{i}}(\mathrm{t})$ 是它可能的语言值（模楜集），对于所有 $i$.

## 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。