Soft Computing Approach for Mathematical Modeling of Engineering Problems

This book describes different mathematical modeling and soft computing techniques used to solve practical engineering problems. It gives an overview of the current state of soft computing techniques and describes the advantages and disadvantages of soft computing compared to traditional hard computing techniques. Through examples and case studies, the editors demonstrate and describe how problems with inherent uncertainty can be addressed and eventually solved through the aid of numerical models and methods. The chapters address several applications and examples in bioengineering science, drug delivery, solving inventory issues, Industry 4.0, augmented reality and weather forecasting. Other examples include solving fuzzy-shortest-path problems by introducing a new distance and ranking functions. Because, in practice, problems arise with uncertain data and most of them cannot be solved exactly and easily, the main objective is to develop models that deliver solutions with the aid of numerical methods. This is the reason behind investigating soft numerical computing in dynamic systems. Having this in mind, the authors and editors have considered error of approximation and have discussed several common types of errors and their propagations. Moreover, they have explained the numerical methods, along with convergence and consistence properties and characteristics, as the main objectives behind this book involve considering, discussing and proving related theorems within the setting of soft computing. This book examines dynamic models, and how time is fundamental to the structure of the model and data as well as the understanding of how a process unfolds
- Discusses mathematical modeling with soft computing and the implementations of uncertain mathematical models
- Examines how uncertain dynamic systems models include uncertain state, uncertain state space and uncertain state's transition functions
- Assists readers to become familiar with many soft numerical methods to simulate the solution function's behavior
This book is intended for system specialists who are interested in dynamic systems that operate at different time scales. The book can be used by engineering students, researchers and professionals in control and finite element fields as well as all engineering, applied mathematics, economics and computer science interested in dynamic and uncertain systems.

Ali Ahmadian is a Senior Lecturer at the Institute of IR 4.0, The National University of Malaysia.
Soheil Salahshour is an associate professor at Bahcesehir University.

本書描述了不同的數學建模和軟計算技術，用於解決實際的工程問題。它概述了軟計算技術的現狀，並描述了軟計算相對於傳統硬計算技術的優缺點。通過示例和案例研究，編者展示並描述了如何通過數值模型和方法來解決具有不確定性的問題。這些章節涉及生物工程科學、藥物傳遞、解決庫存問題、工業4.0、擴增實境和天氣預報等多個應用和示例。其他例子包括通過引入新的距離和排名函數來解決模糊最短路徑問題。由於在實踐中，問題往往涉及不確定數據，而且大多數問題無法準確且輕鬆地解決，主要目標是開發能夠通過數值方法提供解決方案的模型。這就是研究動態系統中的軟數值計算的原因。在這方面，作者和編者考慮了近似誤差，並討論了幾種常見的錯誤類型及其傳播。此外，他們還解釋了數值方法，以及收斂性和一致性的特性，因為本書的主要目標是在軟計算的框架下考慮、討論和證明相關定理。本書探討了動態模型，以及時間對模型和數據結構的基本性質，以及對過程展開的理解。

- 討論了使用軟計算的數學建模和不確定數學模型的實現
- 檢視了不確定動態系統模型包括不確定狀態、不確定狀態空間和不確定狀態轉換函數
- 幫助讀者熟悉許多軟數值方法，以模擬解決函數的行為

本書面向對不同時間尺度運作的動態系統感興趣的系統專家。本書可供工程學生、研究人員和控制和有限元領域的專業人士使用，以及所有對動態和不確定系統感興趣的工程、應用數學、經濟學和計算機科學專業人士。

Ali Ahmadian是馬來西亞國立大學IR 4.0研究所的高級講師。
Soheil Salahshour是巴赫謝希爾大學的副教授。

Ali Ahmadian is visiting Assistant Professor at Mediterranea University of Reggio Calabria and Senior Fellow Researcher at Institute of IR 4.0, The National University of Malaysia.

Soheil Salahshour is an Associate Professor at Bahcesehir University.

阿里·阿赫馬迪安（Ali Ahmadian）是意大利雷焦卡拉布里亞地中海大學（Mediterranea University of Reggio Calabria）的訪問助理教授，也是馬來西亞國立大學（The National University of Malaysia）IR 4.0研究所的高級研究員。

索海爾·薩拉舒爾（Soheil Salahshour）是土耳其巴赫塞希爾大學（Bahcesehir University）的副教授。