基于不確定靜態(tài)和動(dòng)態(tài)問(wèn)題解的仿射算術(shù)(英文)/國(guó)外優(yōu)秀數(shù)學(xué)著作原版系列
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叢書名：國(guó)外優(yōu)秀數(shù)學(xué)著作原版系列
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- 作者：[印]斯內(nèi)哈希什·查克拉弗蒂，紹達(dá)米尼·勞特著
- 出版時(shí)間：2023/3/1
- ISBN：9787576707311
- 出 版 社：哈爾濱工業(yè)大學(xué)出版社
- 中圖法分類：O159
- 頁(yè)碼：158
- 紙張：
- 版次：1
- 開本：16開
本書共包含7章，第1章包含了對(duì)書名所列問(wèn)題的詳細(xì)介紹和文獻(xiàn)研究。第2章包括區(qū)間分析和模糊集合論的基本定義、術(shù)語(yǔ)和性質(zhì)。第3章討論了區(qū)間依賴性問(wèn)題背后的原因和對(duì)仿射算數(shù)的詳細(xì)的解釋。為了有效地處理模糊數(shù)形式的帶不確定性的現(xiàn)實(shí)生活中的問(wèn)題，第4章提出了新的模糊一仿射算數(shù)。在第5章中，關(guān)于不確定靜態(tài)問(wèn)題的研究已經(jīng)被合并了，其可能導(dǎo)致區(qū)間或模糊的線性方程組。帶有不確定材料的動(dòng)態(tài)分析和各種實(shí)際問(wèn)題的幾何性質(zhì)可以通過(guò)區(qū)間或模糊特征值問(wèn)題建模。這樣一來(lái)，在第6章和第7章中分別展示了解決不確定線性和非線性動(dòng)態(tài)問(wèn)題的不同方法。
本書試圖在不確定的環(huán)境中嚴(yán)謹(jǐn)?shù)匮芯扛鞣N科學(xué)和工程領(lǐng)域的靜態(tài)和動(dòng)態(tài)問(wèn)題。作者相信本書將為全球的本科生、研究生、研究人員、工業(yè)界、學(xué)院和其他人提供幫助。
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
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