Logical Algebraic Analytic And Probabilistic Aspects Of Triangular Norms
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Logical Algebraic Analytic And Probabilistic Aspects Of Triangular Norms
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Author : Erich Peter Klement
language : en
Publisher: Elsevier
Release Date : 2005-03-25
Logical Algebraic Analytic And Probabilistic Aspects Of Triangular Norms written by Erich Peter Klement and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-25 with Mathematics categories.
This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.Key Features:- Complete state of the art of the importance of triangular norms in various mathematical fields- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications- Chapter authors are leading authorities in their fields- Triangular norms on different domains (including discrete, partially ordered) are described- Not only triangular norms but also related operators (aggregation operators, copulas) are covered- Book contains many enlightening illustrations· Complete state of the art of the importance of triangular norms in various mathematical fields· 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications· Chapter authors are leading authorities in their fields· Triangular norms on different domains (including discrete, partially ordered) are described· Not only triangular norms but also related operators (aggregation operators, copulas) are covered· Book contains many enlightening illustrations
On Logical Algebraic And Probabilistic Aspects Of Fuzzy Set Theory
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Author : Susanne Saminger-Platz
language : en
Publisher: Springer
Release Date : 2016-01-11
On Logical Algebraic And Probabilistic Aspects Of Fuzzy Set Theory written by Susanne Saminger-Platz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-11 with Technology & Engineering categories.
The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.
Logic Language Information And Computation
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Author : Wilfrid Hodges
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-19
Logic Language Information And Computation written by Wilfrid Hodges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-19 with Philosophy categories.
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 4th volume of the FoLLI LNAI subline; containing the refereed proceedings of the 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008, held in Edinburgh, UK, in July 2008. The 21 revised full papers presented together with the abstracts of 7 tutorials and invited lectures were carefully reviewed and selected from numerous submissions. The papers cover all pertinent subjects in computer science with particular interest in cross-disciplinary topics. Typical areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection.
Triangular Norms
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Author : Erich Peter Klement
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Triangular Norms written by Erich Peter Klement and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.
Associative Functions Triangular Norms And Copulas
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Author : Claudi Alsina
language : en
Publisher: World Scientific
Release Date : 2006-02-22
Associative Functions Triangular Norms And Copulas written by Claudi Alsina and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-22 with Mathematics categories.
The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
Aggregation Functions In Theory And In Practise
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Author : Humberto Bustince Sola
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-20
Aggregation Functions In Theory And In Practise written by Humberto Bustince Sola and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Technology & Engineering categories.
This volume collects the extended abstracts of 45 contributions of participants to the Seventh International Summer School on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. These contributions cover a very broad range, from the purely theoretical ones to those with a more applied focus. Moreover, the summaries of the plenary talks and tutorials given at the same workshop are included. Together they provide a good overview of recent trends in research in aggregation functions which can be of interest to both researchers in Physics or Mathematics working on the theoretical basis of aggregation functions, and to engineers who require them for applications.
Beyond Traditional Probabilistic Data Processing Techniques Interval Fuzzy Etc Methods And Their Applications
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Author : Olga Kosheleva
language : en
Publisher: Springer Nature
Release Date : 2020-02-28
Beyond Traditional Probabilistic Data Processing Techniques Interval Fuzzy Etc Methods And Their Applications written by Olga Kosheleva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Computers categories.
Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitable for graduate students.
Fuzzy Mathematics
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Author : Apostolos Syropoulos
language : en
Publisher: Springer Nature
Release Date : 2025-02-25
Fuzzy Mathematics written by Apostolos Syropoulos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-25 with Mathematics categories.
This book aims to introduce readers without a strong mathematical background to the basic ideas of fuzzy set theory and logic. Fuzzy mathematics is the mathematics of vagueness, a universal property of this world. There are many objects that are called vague because they cannot be precisely defined. Since vagueness is so common, a tool is needed to describe it and to effectively deal with it. Fuzzy mathematics is such a tool, and it is used by most researchers and scholars. As such, this book provides a short overview of the field written for non-specialists. This book allows readers to delve into the theory of fuzzy sets and introduces core mathematical ideas without using the usual formalities of books in mathematics, i.e. theorems, proofs, etc.
Computational Intelligence For Knowledge Based System Design
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Author : Eyke Hüllermeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-17
Computational Intelligence For Knowledge Based System Design written by Eyke Hüllermeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-17 with Computers categories.
The book constitutes the refereed proceedings of the 13th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2010, held in Dortmund, Germany from June 28 - July 2, 2010. The 77 revised full papers were carefully reviewed and selected from 320 submissions and reflect the richness of research in the field of Computational Intelligence and represent developments on topics as: machine learning, data mining, pattern recognition, uncertainty handling, aggregation and fusion of information as well as logic and knowledge processing.
Computational Intelligence In Decision And Control Proceedings Of The 8th International Flins Conference
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Author : Da Ruan
language : en
Publisher: World Scientific
Release Date : 2008-08-08
Computational Intelligence In Decision And Control Proceedings Of The 8th International Flins Conference written by Da Ruan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-08 with Computers categories.
FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the eighth edition in the series of FLINS conferences cover state-of-the-art research, development, and technology for computational intelligence systems in general, and for intelligent decision and control in particular.