基于不确定静态和动态问题解的仿射算术(英文)/国外优秀数学著作原版系列

定　　价：38 元

丛书名：国外优秀数学著作原版系列

• 作者：[印]斯内哈希什·查克拉弗蒂，绍达米尼·劳特著
• 出版时间：2023/3/1
• ISBN：9787576707311
• 出 版 社：哈尔滨工业大学出版社

• 中图法分类：O159 
• 页码：158
• 版次：1
• 开本：16开

内容简介

本书共包含7章，第1章包含了对书名所列问题的详细介绍和文献研究。第2章包括区间分析和模糊集合论的基本定义、术语和性质。第3章讨论了区间依赖性问题背后的原因和对仿射算数的详细的解释。为了有效地处理模糊数形式的带不确定性的现实生活中的问题，第4章提出了新的模糊一仿射算数。在第5章中，关于不确定静态问题的研究已经被合并了，其可能导致区间或模糊的线性方程组。带有不确定材料的动态分析和各种实际问题的几何性质可以通过区间或模糊特征值问题建模。这样一来，在第6章和第7章中分别展示了解决不确定线性和非线性动态问题的不同方法。
本书试图在不确定的环境中严谨地研究各种科学和工程领域的静态和动态问题。作者相信本书将为全球的本科生、研究生、研究人员、工业界、学院和其他人提供帮助。

目 录

Preface
Acknowledgments
1 Introduction
1.1 Literature Review
1.1.1 Interval Analysis
1.1.2 Fuzzy Set Theory
1.1.3 Affine Arithmetic
1.1.4 Uncertain Static Problems
1.1.5 Uncertain Linear Dynamic Problems
1.1.6 Uncertain Nonlinear Dynamic Problems
1.2 References
2 Preliminaries
2.1 Interval
2.2 Basic Terminologies of Interval
2.2.1 Interval Center (xc)
2.2.2 Interval Width (xω)
2.2.3 Interval Radius (X△)
2.3 Equality of Intervals
2.4 Interval Set Operations
2.4.1 Interval Union
2.4.2 Interval Intersection
2.4.3 Interval Hull
2.5 Interval Arithmetic
2.5.1 Interval Addition
2.5.2 Interval Subtraction
2.5.3 Interval Scalar Multiplication
2.5.4 Interval Multiplication
2.5.5 Interval Reciprocal
2.5.6 Interval Division
2.5.7 Interval Power
2.6 Interval Algebraic Properties
2.6.1 Commutative
2.6.2 Associative
2.6.3 Identity
2.6.4 Inverse
2.6.5 Sub-Distributive
2.6.6 Cancellation Law
2.7 Fuzzy Sets
2.8 Basic Terminologies of Fuzzy Set
2.8.1 Boundary (B(F))
2.8.2 Support (S(F))
2.8.3 Core (C(F))
2.8.4 Height (H(F))
2.9 Fuzzy Set Operations
2.9.1 Fuzzy Union
2.9.2 Fuzzy Intersection
2.9.3 Fuzzy Complement
2.10 Arithmetic of Fuzzy Sets
2.10.1 Algebraic Sum
2.10.2 Algebraic Product
2.10.3 Bounded Sum
2.10.4 Bounded Difference
2.10.5 Power
2.11 Fuzzy Numbers
2.12 Different Types of Fuzzy Numbers
2.12.1 Triangular Fuzzy Number (TFN)
2.12.2 Trapezoidal Fuzzy Number (TrFN)
2.13 Exercises
2.14 References
3 Affine Arithmetic
3.1 Interval Dependency Problem
3.2 Definition and Notation
3.3 Conversion of Affine to Interval
3.4 Conversion of Interval to Affine
3.5 Affine Arithmetic Operations
3.5.1 Affine Addition
3.5.2 Affine Subtraction
3.5.3 Affine Scalar Multiplication
3.5.4 Affine Multiplication
3.5.5 Affine Division
3.6 Efficacy of Affine Arithmetic
3.7 Exercises
3.8 References
4 Fuzz-y-Afline Arithmetic
4.1 a-Cut of Fuzzy Number
4.2 Parametric Form of Fuzzy Number
4.2.1 Parametric Form of TFN
4.2.2 Parametric Form of TrFN
4.3 Basic Terminologies of Parametric Fuzzy Number
4.3.1 Parametric Fuzzy Center (Pc)
4.3.2 Parametric Fuzzy Width (Fω)
4.3.3 Parametric Fuzzy Radius (F△)
4.4 Parametric Fuzzy Arithmetic
4.4.1 Parametric Fuzzy Addition
4.4.2 Parametric Fuzzy Subtraction
4.4.3 Parametric Fuzzy Scalar Multiplication
4.4.4 Parametric Fuzzy Multiplication
4.4.5 Parametric Fuzzy Reciprocal
4.4.6 Parametric Fuzzy Division
4.4.7 Parametric Fuzzy Power
4.5 Fuzzy-Affine Form
4.5.1 Fuzzy-Affine Form of TFN
4.5.2 Fuzzy-Affine Form of TrFN
4.6 Fuzzy-Affine Arithmetic Operations
4.7 Efficacy of Fuzzy-A/fine Arithmetic
4.8 Exercises
4.9 References
5 Uncertain Static Problems
5.1 Crisp System of Linear Equations (CSLE)
5.2 Interval System of Linear Equations (ISLE)
5.3 Solution of ISLE
5.4 Fuzzy System of Linear Equations (FSLE)
5.5 Solution of FSLE
5.6 Exercises
5.7 References
6 Uncertain Linear Dynamic Problems
6.1 Linear Eigenvalue Problem (LEP)
6.2 Crisp Generalized Eigenvalue Problem (CGEP)
6.2.1 Crisp Standard Eigenvalue Problem (CSEP)
6.3 Solution of CGEP
6.4 Interval Generalized Eigenvalue Problem (IGEP)
6.4.1 Interval Standard Eigenvalue Problem (ISEP)
6.5 Solution ofIGEP
6.6 Fuzzy Generalized Eigenvalue Problem (FGEP)
6.6.1 Fuzzy Standard Eigenvalue Problem (FSEP)
6.7 Solution of FGEP
6.8 Exercises
6.9 References
7 Uncertain Nonlinear Dynamic Problems
7.1 Crisp Nonlinear Eigenvalue Problem (CNEP)
7.1.1 Crisp Quadratic Eigenvalue Problem (CQ_EP)
7.1.2 Crisp Cub