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Author: Hung T. Nguyen Publisher: CRC Press ISBN: 1420010611 Category : Mathematics Languages : en Pages : 268
Book Description
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i
Author: Hung T. Nguyen Publisher: CRC Press ISBN: 1420010611 Category : Mathematics Languages : en Pages : 268
Book Description
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i
Author: Ilya Molchanov Publisher: Springer Science & Business Media ISBN: 9781852338923 Category : Mathematics Languages : en Pages : 508
Book Description
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
Book Description
This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty about statistical experiments. The authors lay bare the existence of two streams of works using the same mathematical ground, but differing form their use of sets, according to whether they represent objects of interest naturally taking the form of sets, or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields ranging from mathematical morphology, economics, artificial intelligence, information processing and statistics per se, especially in areas where the outcomes of random experiments cannot be observed with full precision. This book also emphasizes the link between random sets and fuzzy sets with some techniques related to the theory of imprecise probabilities. This small book is intended for graduate and doctoral students in mathematics or engineering, but also provides an introduction for other researchers interested in this area. It is written from a theoretical perspective. However, rather than offering a comprehensive formal view of random (fuzzy) sets in this context, it aims to provide a discussion of the meaning of the proposed formal constructions based on many concrete examples and exercises. This book should enable the reader to understand the usefulness of representing and reasoning with incomplete information in statistical tasks. Each chapter ends with a list of exercises.
Author: Vincenzo Capasso Publisher: Springer ISBN: 3319945777 Category : Mathematics Languages : en Pages : 143
Book Description
This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.
Author: Ilya Molchanov Publisher: Springer ISBN: 144717349X Category : Mathematics Languages : en Pages : 688
Book Description
This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.
Author: Dominique Jeulin Publisher: Springer Nature ISBN: 3030754529 Category : Mathematics Languages : en Pages : 919
Book Description
This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.
Author: Roy M. Howard Publisher: John Wiley & Sons ISBN: 1119046785 Category : Mathematics Languages : en Pages : 742
Book Description
A fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of material not typically found in introductory books Emphasis on modeling and notation that facilitates development of random process theory Coverage of the prototypical random phenomena encountered in electrical engineering Detailed proofs of results A related website with solutions to the problems found at the end of each chapter A Signal Theoretic Introduction to Random Processes is a useful textbook for upper-undergraduate and graduate-level courses in applied mathematics as well as electrical and communications engineering departments. The book is also an excellent reference for research engineers and scientists who need to characterize random phenomena in their research.
Author: Alexander Drewitz Publisher: Springer ISBN: 3319058525 Category : Mathematics Languages : en Pages : 124
Book Description
This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.
Author: Witold Pedrycz Publisher: MIT Press ISBN: 9780262161718 Category : Computers Languages : en Pages : 506
Book Description
The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice. The authors explain what fuzzy sets are, why they work, when they should be used (and when they shouldn't), and how to design systems using them. The authors take an unusual top-down approach to the design of detailed algorithms. They begin with illustrative examples, explain the fundamental theory and design methodologies, and then present more advanced case studies dealing with practical tasks. While they use mathematics to introduce concepts, they ground them in examples of real-world problems that can be solved through fuzzy set technology. The only mathematics prerequisites are a basic knowledge of introductory calculus and linear algebra.
Author: Hung T. Nguyen
Author: Hung T. Nguyen
Author: Hung T. Nguyen
Author: Ilya Molchanov
Author: Inés Couso
Author: Vincenzo Capasso
Author: Ilya Molchanov
Author: Dominique Jeulin
Author: Roy M. Howard
Author: Alexander Drewitz
Author: Witold Pedrycz