Possibility Theory

Author : Basel Solaiman,Éloi Bossé
Publisher : Springer Nature
Page : 294 pages
File Size : 47,6 Mb
Release : 2019-12-26
Category : Mathematics
ISBN : 9783030328535

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Possibility Theory for the Design of Information Fusion Systems by Basel Solaiman,Éloi Bossé Pdf

This practical guidebook describes the basic concepts, the mathematical developments, and the engineering methodologies for exploiting possibility theory for the computer-based design of an information fusion system where the goal is decision support for industries in smart ICT (information and communications technologies). This exploitation of possibility theory improves upon probability theory, complements Dempster-Shafer theory, and fills an important gap in this era of Big Data and Internet of Things. The book discusses fundamental possibilistic concepts: distribution, necessity measure, possibility measure, joint distribution, conditioning, distances, similarity measures, possibilistic decisions, fuzzy sets, fuzzy measures and integrals, and finally, the interrelated theories of uncertainty..uncertainty. These topics form an essential tour of the mathematical tools needed for the latter chapters of the book. These chapters present applications related to decision-making and pattern recognition schemes, and finally, a concluding chapter on the use of possibility theory in the overall challenging design of an information fusion system. This book will appeal to researchers and professionals in the field of information fusion and analytics, information and knowledge processing, smart ICT, and decision support systems.

Author : Irina Georgescu
Publisher : Springer
Page : 128 pages
File Size : 54,6 Mb
Release : 2012-01-12
Category : Technology & Engineering
ISBN : 9783642247408

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Possibility Theory and the Risk by Irina Georgescu Pdf

The book deals with some of the fundamental issues of risk assessment in grid computing environments. The book describes the development of a hybrid probabilistic and possibilistic model for assessing the success of a computing task in a grid environment

Author : P.P. Wang
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461337546

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Advances in Fuzzy Sets, Possibility Theory, and Applications by P.P. Wang Pdf

Since its inception by Professor Lotfi Zadeh about 18 years ago, the theory of fuzzy sets has evolved in many directions, and is finding applications in a wide variety of fields in which the phenomena under study are too complex or too ill-defined to be analyzed by conventional techniques. Thus, by providing a basis for a systematic approach to approximate reasoning and inexact inference, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, engineering, law, medicine, decision-analysis, information retrieval, and artificial intelli gence. This volume consists of 24 selected papers invited by the editor, Professor Paul P. Wang. These papers cover the theory and applications of fuzzy sets, almost equal in number. We are very fortunate to have Professor A. Kaufmann to contribute an overview paper of the advances in fuzzy sets. One special feature of this volume is the strong participation of Chinese researchers in this area. The fact is that Chinese mathematicians, scientists and engineers have made important contributions to the theory and applications of fuzzy sets through the past decade. However, not until the visit of Professor A. Kaufmann to China in 1974 and again in 1980, did the Western World become fully aware of the important work of Chinese researchers. Now, Professor Paul Wang has initiated the effort to document these important contributions in this volume to expose them to the western researchers.

Author : J. Kacprzyk,Mario Fedrizzi
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9789400921092

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Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory by J. Kacprzyk,Mario Fedrizzi Pdf

Decision making is certainly a very crucial component of many human activities. It is, therefore, not surprising that models of decisions play a very important role not only in decision theory but also in areas such as operations Research, Management science, social Psychology etc . . The basic model of a decision in classical normative decision theory has very little in common with real decision making: It portrays a decision as a clear-cut act of choice, performed by one individual decision maker and in which states of nature, possible actions, results and preferences are well and crisply defined. The only compo nent in which uncertainty is permitted is the occurence of the different states of nature, for which probabilistic descriptions are allowed. These probabilities are generally assumed to be known numerically, i. e. as single probabili ties or as probability distribution functions. Extensions of this basic model can primarily be conceived in three directions: 1. Rather than a single decision maker there are several decision makers involved. This has lead to the areas of game theory, team theory and group decision theory. 2. The preference or utility function is not single valued but rather vector valued. This extension is considered in multiattribute utility theory and in multicritieria analysis. 3.

Author : J. Kacprzyk,S.A. Orlovski
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 48,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789400938694

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Optimization Models Using Fuzzy Sets and Possibility Theory by J. Kacprzyk,S.A. Orlovski Pdf

Optimization is of central concern to a number of discip lines. Operations Research and Decision Theory are often consi dered to be identical with optimizationo But also in other areas such as engineering design, regional policy, logistics and many others, the search for optimal solutions is one of the prime goals. The methods and models which have been used over the last decades in these areas have primarily been "hard" or "crisp", i. e. the solutions were considered to be either fea sible or unfeasible, either above a certain aspiration level or below. This dichotomous structure of methods very often forced the modeller to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real prob lems. This is particularly true if the problem under considera tion includes vaguely defined relationships, human evaluations, uncertainty due to inconsistent or incomplete evidence, if na tural language has to be modelled or if state variables can only be described approximately. Until recently, everything which was not known with cer tainty, i. e. which was not known to be either true or false or which was not known to either happen with certainty or to be impossible to occur, was modelled by means of probabilitieso This holds in particular for uncertainties concerning the oc currence of events.

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 51,5 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

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Probability by Rick Durrett Pdf

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Author : Didier Dubois,Henri Prade
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468452877

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Possibility Theory by Didier Dubois,Henri Prade Pdf

In the evolution of scientific theories, concern with uncertainty is almost invariably a concomitant of maturation. This is certainly true of the evolution· of physics, economics, operations research, communication sciences, and a host of other fields. And it is true of what has been happening more recently in the area of artificial intelligence, most notably in the development of theories relating to the management of uncertainty in knowledge-based systems. In science, it is traditional to deal with uncertainty through the use of probability theory. In recent years, however, it has become increasingly clear that there are some important facets of uncertainty which do not lend themselves to analysis by classical probability-based methods. One such facet is that of lexical elasticity, which relates to the fuzziness of words in natural languages. As a case in point, even a simple relation X, Y, and Z, expressed as if X is small and Y is very large then between Z is not very small, does not lend itself to a simple interpretation within the framework of probability theory by reason of the lexical elasticity of the predicates small and large.

Author : Paul E. Pfeiffer
Publisher : Courier Corporation
Page : 416 pages
File Size : 49,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486165660

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Concepts of Probability Theory by Paul E. Pfeiffer Pdf

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Author : Valeriĭ Borisovich Nevzorov,Mohammad Ahsanullah,Sergei Ananjevskiy
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 2021
Category : Probabilities
ISBN : 1536191736

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Probability Theory by Valeriĭ Borisovich Nevzorov,Mohammad Ahsanullah,Sergei Ananjevskiy Pdf

This book is written for people who are interested to know the basics of probability theory. The basic knowledge of high school math will be enough to know the probability theory covered in the book. It covers basic theories of probability, statistical distributions, order statistics and record values, The use of characterization methods are described to identify various probability distributions. The book will be useful for undergraduate, graduate students and applied statisticians.

Author : E. T. Jaynes
Publisher : Cambridge University Press
Page : 764 pages
File Size : 42,5 Mb
Release : 2003-04-10
Category : Science
ISBN : 9781139435161

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Probability Theory by E. T. Jaynes Pdf

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 51,5 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9789401579490

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Fuzzy Set Theory — and Its Applications by Hans-Jürgen Zimmermann Pdf

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.

Author : H. J. Zimmerman
Publisher : Allied Publishers
Page : 430 pages
File Size : 52,6 Mb
Release : 1996
Category : Fuzzy sets
ISBN : 8170235251

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Fuzzy Set Theory and Its Applications by H. J. Zimmerman Pdf

Author : Przemyslaw Grzegorzewski,Olgierd Hryniewicz,Maria A. Gil
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 42,8 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783790817737

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Soft Methods in Probability, Statistics and Data Analysis by Przemyslaw Grzegorzewski,Olgierd Hryniewicz,Maria A. Gil Pdf

Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

Author : Nikolai Dokuchaev
Publisher : World Scientific Publishing Company
Page : 224 pages
File Size : 55,8 Mb
Release : 2015-06-12
Category : Business & Economics
ISBN : 9789814678056

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Probability Theory by Nikolai Dokuchaev Pdf

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

Author : Simona Salicone,Marco Prioli
Publisher : Springer
Page : 330 pages
File Size : 55,5 Mb
Release : 2018-04-23
Category : Mathematics
ISBN : 9783319741390

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Measuring Uncertainty within the Theory of Evidence by Simona Salicone,Marco Prioli Pdf

This monograph considers the evaluation and expression of measurement uncertainty within the mathematical framework of the Theory of Evidence. With a new perspective on the metrology science, the text paves the way for innovative applications in a wide range of areas. Building on Simona Salicone’s Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence, the material covers further developments of the Random Fuzzy Variable (RFV) approach to uncertainty and provides a more robust mathematical and metrological background to the combination of measurement results that leads to a more effective RFV combination method. While the first part of the book introduces measurement uncertainty, the Theory of Evidence, and fuzzy sets, the following parts bring together these concepts and derive an effective methodology for the evaluation and expression of measurement uncertainty. A supplementary downloadable program allows the readers to interact with the proposed approach by generating and combining RFVs through custom measurement functions. With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field.