A refined approach for forecasting based on neutrosophic time series

This research introduces a neutrosophic forecasting approach based on neutrosophic time series (NTS). Historical data can be transformed into neutrosophic time series data to determine their truth, indeterminacy and falsity functions. The basis for the neutrosophication process is the score and accuracy functions of historical data. In addition, neutrosophic logical relationship groups (NLRGs) are determined and a deneutrosophication method for NTS is presented. The objective of this research is to suggest an idea of first-and high-order NTS. By comparing our approach with other approaches, we conclude that the suggested approach of forecasting gets better results compared to the other existing approaches of fuzzy, intuitionistic fuzzy, and neutrosophic time series

Research of fuzzy time series model based on fuzzy entropy and fuzzy clustering

时间序列预测是通过对有限个历史观测样本进行分析来建立模型，并利用模型来解释数据之间的统计规律，以期达到控制和预报目的的一门学科，在众多领域中都有非常广泛的应用。对于时间序列的建模和预测，目前已经有了许多成熟的技术和方法，但传统时间序列预测方法往往依赖大量的历史数据，而在实际问题中由于不确定性的广泛存在导致历史数据往往是不完整的、不准确的和含糊的，因而限制了传统预测模型的应用。为了解决这些问题，Song和Chissom提出了模糊时间序列的概念，其主要是在传统时间序列预测的基础上引入了模糊理论，通过建立相应的模糊逻辑关系进行预测。由于模糊时间序列在处理数据的不确定性和模糊性方面上所显示的优势，关于...Time series forecasting is modeled by limited historical observations sample, it is a technology of using the model to explain the statistical regularity of data in order to achieve the purpose of control and forecast and having a wide range of applications in many fields. For time series modeling and forecasting, there are many mature technologies and methods. The traditional time series predicti...学位：理学硕士院系专业：数学科学学院_概率论与数理统计学号：1902010115250

Numerical Prediction of Time Series Based on FCMs with Information Granules

The prediction of time series has been widely applied to many fields suchas enrollments, stocks, weather and so on. In this paper, a new prediction methodbased on fuzzy cognitive map with information granules is proposed, in which fuzzy cmeansclustering algorithm is used to automatically abstract information granules andtransform the original time series into granular time series, and subsequently fuzzycognitive map is used to describe these granular time series and perform prediction.two benchmark time series are used to validate feasibility and effectiveness of proposedmethod. The experimental results show that the proposed prediction method canreach better prediction accuracy. Additionally, the proposed method is also able toprecess the modeling and prediction of large-scale time series

Kapılı tekrarlayan hücreler tabanlı bulanık zaman serileri tahminleme modeli

Time series forecasting and prediction are utilized in various industries, such as e-commerce, stock markets, wind power, and energy demand forecasting. An accurate forecast in these applications is an essential and challenging task because of the complexity and uncertainty of time series. Nowadays, deep learning methods are popular in time series forecasting and show better performance than classical methods. However, in the literature, only some studies use deep learning methods in fuzzy time series (FTS) forecasting. In this study, we propose a novel FTS forecasting model based upon the hybridization of Recurrent Neural Networks with FTS to deal with the complexity and uncertainty of these series. The proposed model utilizes Gated Recurrent Unit (GRU) to make predictions using a combination of membership values and past values from original time series data as model input and produce real forecast value. Moreover, the proposed model can handle first-order fuzzy relations and high-order ones. In experiments, we have compared our model results with state-of-art methods by using two real-world datasets; The Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Nikkei Stock Average. The results indicate that our model outperforms or performs similarly to other methods. The proposed model is validated using the Covid-19 active case dataset and BIST100 Index dataset and performs better than Long Short-term Memory (LSTM) networks.Zaman serisi tahminleme hava durumu, iş dünyası, satış verileri ve enerji tüketimi tahminleme gibi bir çok alanda uygulama alanına sahiptir. Bu alanlarda tahminleme yaparken kesin sonuçlar elde etmek çok önemlidir ama aynı zamanda zaman serilerinin karmaşık ve de belirsizlik içeren veriler olması nedeniyle çok zordur. Günümüzde, derin öğrenme metotları bu alanda klasik metotlara göre daha iyi sonuçlar vermektedir. Fakat literatürde bulanık zaman serileri tahminleme konusunda çok az çalışma vardır. Bu çalışmada, zaman serilerindeki karmaşıklığın ve belirsizliğin doğurduğu problemleri yok etmek için Yinelemeli sinir Ağları ile bulanık zaman serilerini bir arada kullanan bir model ortaya konumuştur. Bu çalışmada, Kapılı Tekrarlayan Hücreler kullanarak geçmiş veriler ile bulanık verilerin üyelik değerleri birleştirilerek tahminleme değeri hesaplanmıştır. Ayrıca, bu çalışmadaki model ilk seviye bulanık ilişkileri ele alabildiği gibi, çoklu seviye bulanık ilişkileri de kapsamaktadır. Testlerde literatürde var olan çalışmalar ilgili model ile iki açık veri seti ile karşılaştırılmış olup bahsi geçen modelin daha iyi veya benzer sonuçlar verdiği gözlemlenmiştir. Ayrıca model Covid-19 ve BIST100 borsa verileri kullanılarak da test edilmiş ve Uzun-Kısa Süreli Bellek modellerinden daha iyi sonuç vermiştir

Data Science: Measuring Uncertainties

With the increase in data processing and storage capacity, a large amount of data is available. Data without analysis does not have much value. Thus, the demand for data analysis is increasing daily, and the consequence is the appearance of a large number of jobs and published articles. Data science has emerged as a multidisciplinary field to support data-driven activities, integrating and developing ideas, methods, and processes to extract information from data. This includes methods built from different knowledge areas: Statistics, Computer Science, Mathematics, Physics, Information Science, and Engineering. This mixture of areas has given rise to what we call Data Science. New solutions to the new problems are reproducing rapidly to generate large volumes of data. Current and future challenges require greater care in creating new solutions that satisfy the rationality for each type of problem. Labels such as Big Data, Data Science, Machine Learning, Statistical Learning, and Artificial Intelligence are demanding more sophistication in the foundations and how they are being applied. This point highlights the importance of building the foundations of Data Science. This book is dedicated to solutions and discussions of measuring uncertainties in data analysis problems

Fuzzy model predictive control. Complexity reduction by functional principal component analysis

En el Control Predictivo basado en Modelo, el controlador ejecuta una optimización en tiempo real para obtener la mejor solución para la acción de control. Un problema de optimización se resuelve para identificar la mejor acción de control que minimiza una función de coste relacionada con las predicciones de proceso. Debido a la carga computacional de los algoritmos, el control predictivo sujeto a restricciones, no es adecuado para funcionar en cualquier plataforma de hardware. Las técnicas de control predictivo son bien conocidos en la industria de proceso durante décadas. Es cada vez más atractiva la aplicación de técnicas de control avanzadas basadas en modelos a otros muchos campos tales como la automatización de edificios, los teléfonos inteligentes, redes de sensores inalámbricos, etc., donde las plataformas de hardware nunca se han conocido por tener una elevada potencia de cálculo. El objetivo principal de esta tesis es establecer una metodología para reducir la complejidad de cálculo al aplicar control predictivo basado en modelos no lineales sujetos a restricciones, utilizando como plataforma, sistemas de hardware de baja potencia de cálculo, permitiendo una implementación basado en estándares de la industria. La metodología se basa en la aplicación del análisis de componentes principales funcionales, proporcionando un enfoque matemáticamente elegante para reducir la complejidad de los sistemas basados en reglas, como los sistemas borrosos y los sistemas lineales a trozos. Lo que permite reducir la carga computacional en el control predictivo basado en modelos, sujetos o no a restricciones. La idea de utilizar sistemas de inferencia borrosos, además de permitir el modelado de sistemas no lineales o complejos, dota de una estructura formal que permite la implementación de la técnica de reducción de la complejidad mencionada anteriormente. En esta tesis, además de las contribuciones teóricas, se describe el trabajo realizado con plantas reales en los que se han llevado a cabo tareas de modelado y control borroso. Uno de los objetivos a cubrir en el período de la investigación y el desarrollo de la tesis ha sido la experimentación con sistemas borrosos, su simplificación y aplicación a sistemas industriales. La tesis proporciona un marco de conocimiento práctico, basado en la experiencia.In Model-based Predictive Control, the controller runs a real-time optimisation to obtain the best solution for the control action. An optimisation problem is solved to identify the best control action that minimises a cost function related to the process predictions. Due to the computational load of the algorithms, predictive control subject to restric- tions is not suitable to run on any hardware platform. Predictive control techniques have been well known in the process industry for decades. The application of advanced control techniques based on models is becoming increasingly attractive in other fields such as building automation, smart phones, wireless sensor networks, etc., as the hardware platforms have never been known to have high computing power. The main purpose of this thesis is to establish a methodology to reduce the computational complexity of applying nonlinear model based predictive control systems subject to constraints, using as a platform hardware systems with low computational power, allowing a realistic implementation based on industry standards. The methodology is based on applying the functional principal component analysis, providing a mathematically elegant approach to reduce the complexity of rule-based systems, like fuzzy and piece wise affine systems, allowing the reduction of the computational load on modelbased predictive control systems, subject or not subject to constraints. The idea of using fuzzy inference systems, in addition to allowing nonlinear or complex systems modelling, endows a formal structure which enables implementation of the aforementioned complexity reduction technique. This thesis, in addition to theoretical contributions, describes the work done with real plants on which tasks of modeling and fuzzy control have been carried out. One of the objectives to be covered for the period of research and development of the thesis has been training with fuzzy systems and their simplification and application to industrial systems. The thesis provides a practical knowledge framework, based on experience