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1 online resource (xvi, 152 pages) : illustrations (some color) 

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Series 
Synthesis lectures on mathematics and statistics, 19381751 ; #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. Fuzzyaffine arithmetic  4.1. Acut 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. Fuzzyaffine form  4.6. Fuzzyaffine arithmetic operations  4.7. Efficacy of fuzzyaffine 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 

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Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with realworld problems. Finding solutions to reallife 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 

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Subject 
Measurement uncertainty (Statistics)


Interval analysis (Mathematics)


Fuzzy systems


System theory


interval arithmetic


fuzzy set theory


interval dependency problem


affine arithmetic


fuzzyaffine arithmetic


static and dynamic problems


system of linear equations


generalize eigenvalue problem


standard eigenvalue problem


nonlinear eigenvalue problem


polynomial eigenvalue problem


damped springmass system


structural dynamics


multistory frame structure


Electronic books

Alt Author 
Rout, Saudamini, author
