V. Kreinovich's Books

Computational Complexity and Feasibility of Data Processing and Interval Computations

By: V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl

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Computational Complexity and Feasibility of Data Processing and Interval Computations

By: V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl

Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

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Page Count

460

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475727933

ISBN 13

9781475727937

Applications of Continuous Mathematics to Computer Science

By: Hung T. Nguyen,V. Kreinovich

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Applications of Continuous Mathematics to Computer Science

By: Hung T. Nguyen,V. Kreinovich

This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.

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Page Count

440

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792347226

ISBN 13

9780792347224

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

By: Shoumei Li,Y. Ogura,V. Kreinovich

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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

By: Shoumei Li,Y. Ogura,V. Kreinovich

After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.

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Page Count

399

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401599327

ISBN 13

9789401599320

Book's by V. Kreinovich

Computational Complexity and Feasibility of Data Processing and Interval Computations

Computational Complexity and Feasibility of Data Processing and Interval Computations

Applications of Continuous Mathematics to Computer Science

Applications of Continuous Mathematics to Computer Science

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

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