| Descript |
1 online resource (xvi, 152 pages) : illustrations (some color) |
|
text rdacontent |
|
electronic isbdmedia |
|
online resource rdacarrier |
| Series |
Synthesis lectures on mathematics and statistics, 1938-1751 ; #32
|
|
Synthesis digital library of engineering and computer science
|
|
Synthesis lectures on mathematics and statistics ; #32
|
| Note |
Part of: Synthesis digital library of engineering and computer science |
|
Includes bibliographical references |
|
1. Introduction -- 1.1. Literature review -- 1.2. References |
|
2. Preliminaries -- 2.1. Interval -- 2.2. Basic terminologies of interval -- 2.3. Equality of intervals -- 2.4. Interval set operations -- 2.5. Interval arithmetic -- 2.6. Interval algebraic properties -- 2.7. Fuzzy sets -- 2.8. Basic terminologies of fuzzy set -- 2.9. Fuzzy set operations -- 2.10. Arithmetic of fuzzy sets -- 2.11. Fuzzy numbers -- 2.12. Different types of fuzzy numbers -- 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 -- 3.6. Efficacy of affine arithmetic -- 3.7. Exercises -- 3.8. References |
|
4. Fuzzy-affine arithmetic -- 4.1. A-cut of fuzzy number -- 4.2. Parametric form of fuzzy number -- 4.3. Basic terminologies of parametric fuzzy number -- 4.4. Parametric fuzzy arithmetic -- 4.5. Fuzzy-affine form -- 4.6. Fuzzy-affine arithmetic operations -- 4.7. Efficacy of fuzzy-affine 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) -- 6.3. Solution of CGEP -- 6.4. Interval generalized eigenvalue problem (IGEP) -- 6.5. Solution of IGEP -- 6.6. Fuzzy generalized eigenvalue problem (FGEP) -- 6.7. Solution of FGEP -- 6.8. Exercises -- 6.9. References |
|
7. Uncertain nonlinear dynamic problems -- 7.1. Crisp nonlinear eigenvalue problem (CNEP) -- 7.2. Linearization of CNEP -- 7.3. Solution of CNEP -- 7.4. Interval nonlinear eigenvalue problem (INEP) -- 7.5. Solution of INEP -- 7.6. Fuzzy nonlinear eigenvalue problem (FNEP) -- 7.7. Solution of FNEP -- 7.8. Exercises -- 7.9. References |
|
Abstract freely available; full-text restricted to subscribers or individual document purchasers |
|
Compendex |
|
INSPEC |
|
Google scholar |
|
Google book search |
|
Mode of access: World Wide Web |
|
System requirements: Adobe Acrobat Reader |
|
Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches |
|
Also available in print |
|
Title from PDF title page (viewed on May 4, 2020) |
| Link |
Print version: |
| Subject |
Measurement uncertainty (Statistics)
|
|
Interval analysis (Mathematics)
|
|
Fuzzy systems
|
|
System theory
|
|
interval arithmetic
|
|
fuzzy set theory
|
|
interval dependency problem
|
|
affine arithmetic
|
|
fuzzy-affine arithmetic
|
|
static and dynamic problems
|
|
system of linear equations
|
|
generalize eigenvalue problem
|
|
standard eigenvalue problem
|
|
nonlinear eigenvalue problem
|
|
polynomial eigenvalue problem
|
|
damped spring-mass system
|
|
structural dynamics
|
|
multi-story frame structure
|
|
Electronic books
|
| Alt Author |
Rout, Saudamini, author
|
