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  • English  (5)
  • Latin
  • BTU Cottbus  (5)
  • Müncheberg ZALF
  • Höhle, Ulrich  (5)
  • 1
    UID:
    b3kat_BV045099531
    Format: 1 Online-Ressource (XXI, 326 Seiten)
    ISBN: 9783319789484
    Series Statement: Developments in mathematics volume 54
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-78947-7
    Language: English
    Subjects: Mathematics
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    URL: Volltext  (URL des Erstveröffentlichers)
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  • 2
    Online Resource
    Online Resource
    Boston, MA : Springer US
    UID:
    b3kat_BV042420859
    Format: 1 Online-Ressource (VII, 382 p)
    ISBN: 9781461516170 , 9781461356431
    Note: The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields
    Language: English
    Keywords: Topologie ; Monade
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
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  • 3
    UID:
    b3kat_BV042420899
    Format: 1 Online-Ressource (XII, 716 p)
    ISBN: 9781461550792 , 9781461373100
    Series Statement: The Handbooks of Fuzzy Sets Series 3
    Note: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. , Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. , Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton&endash;Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets
    Language: English
    Keywords: Fuzzy-Logik ; Fuzzy-Menge
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  • 4
    Online Resource
    Online Resource
    Dordrecht : Springer Netherlands
    UID:
    b3kat_BV046873878
    Format: 1 Online-Ressource (IX, 398 p)
    Edition: 1st ed. 1992
    ISBN: 9789401126168
    Series Statement: Theory and Decision Library B, Mathematical and Statistical Methods 14
    Content: This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. First, this volume is an extended account of the eleventh Seminar of 1989. Second, and more importantly, it is the culmination of the tradition of the preceding ten Seminars. The purpose of the Linz Seminar, since its inception, was and is to foster the development of the mathematical aspects of fuzzy sets. In the earlier years, this was accomplished by bringing together for a week small grou ps of mathematicians in various fields in an intimate, focused environment which promoted much informal, critical discussion in addition to formal presentations. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme; and participation was broadened to include both younger scholars within, and established mathematicians outside, the mathematical mainstream of fuzzy sets theory. Most of the material of this book was developed over the years in close association with the Seminar or influenced by what transpired at Linz. For much of the content, it played a crucial role in either stimulating this material or in providing feedback and the necessary screening of ideas. Thus we may fairly say that the book, and the eleventh Seminar to which it is directly related, are in many respects a culmination of the previous Seminars
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9789401051569
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780792315117
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9789401126175
    Language: English
    Subjects: Computer Science , Economics , Mathematics
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    Keywords: Fuzzy-Menge ; Kategorie ; Fuzzy-Menge ; Kategorientheorie ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 5
    UID:
    b3kat_BV046873912
    Format: 1 Online-Ressource (VIII, 392 p)
    Edition: 1st ed. 1995
    ISBN: 9789401102155
    Series Statement: Theory and Decision Library B, Mathematical and Statistical Methods 32
    Content: Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics. The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780792331940
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9789401040969
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9789401102162
    Language: English
    Subjects: Mathematics
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    Keywords: Nichtklassische Logik ; Fuzzy-Menge ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
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