基于不確定靜態(tài)和動(dòng)態(tài)問(wèn)題的仿射算術(shù)（GP）

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