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基於不確定靜態和動態問題解的仿射算術(英文)/國外優秀數學著作原版系列

  • 作者：(印)斯內哈希什·查克拉弗蒂//紹達米尼·勞特|責編:關虹玲//張嘉芮
  • 出版社：哈爾濱工業大學
  • ISBN：9787576707311
  • 出版日期：2023/03/01
  • 裝幀：平裝
  • 頁數：158
人民幣：RMB 38 元      售價：元
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    本書共包含7章，第1章包含了對書名所列問題的詳細介紹和文獻研究。第2章包括區間分析和模糊集合論的基本定義、術語和性質。第3章討論了區間依賴性問題背後的原因和對仿射算數的詳細的解釋。為了有效地處理模糊數形式的帶不確定性的現實生活中的問題，第4章提出了新的模糊一仿射算數。在第5章中，關於不確定靜態問題的研究已經被合併了，其可能導致區間或模糊的線性方程組。帶有不確定材料的動態分析和各種實際問題的幾何性質可以通過區間或模糊特徵值問題建模。這樣一來，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態問題的不同方法。
    本書試圖在不確定的環境中嚴謹地研究各種科學和工程領域的靜態和動態問題。作者相信本書將為全球的本科生、研究生、研究人員、工業界、學院和其他人提供幫助。
作者介紹
(印)斯內哈希什·查克拉弗蒂//紹達米尼·勞特|責編:關虹玲//張嘉芮
目錄
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 Cubic Eigenvalue Problem (CCEP)
  7.2  Linearization of CNEP
  7.3  Solution of CNEP
  7.4  Interval Nonlinear Eigenvalue Problem (INEP)
    7.4.1  Interval Quadratic Eigenvalue Problem (IQEP)
    7.4.2  Interval Cubic Eigenvalue Problem (ICEP)
  7.5  Solution of INEP
  7.6  Fuzzy Nonlinear Eigenvalue Problem (FNEP)
    7.6.1  Fuzzy Quadratic Eigenvalue Problem (FQEP)
    7.6.2  Fuzzy Cubic Eigenvalue Problem (FCEP)
  7.7  Solution of FNEP
  7.8  Exercises
  7.9  References
Authors' Biographies
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