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Non-Classical Logics and their Applications to Fuzzy Subsets : a Handbook of the Mathematical Foundations of Fuzzy Set Theory

Author: Ulrich Höhle; E P Klement
Publisher: Dordrecht : Springer Netherlands, 1995.
Series: Theory and decision library., Series B,, Mathematical and statistical methods ;, 32.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ulrich Höhle; E P Klement
ISBN: 9789401102155 9401102155
OCLC Number: 851370642
Description: 1 online resource (viii, 392 pages).
Contents: A Algebraic Foundations of Non-Classical Logics --
I?-Complete MV-algebras --
II On MV-algebras of continuous functions --
III Free and projective Heyting and monadic Heyting algebras --
IV Commutative, residuated 1 --
monoids --
V A Proof of the completeness of the infinite-valued calculus of Lukasiewicz with one varibale --
B Non-Classical Models and Topos-Like Categories --
VI Presheaves Over GL-monoide --
VII Quantales: Quantal sets --
VIII Categories of fuzzy sets with values in a quantale or project ale --
IX Fuzzy logic and categories of fuzzy sets --
C General Aspects of Non-Classical Logics 269 --
X Prolog extensions to many-valued logics --
XI Epistemological aspects of many-valued logics and fuzzy structures --
XII Ultraproduct theorem and recursive properties of fuzzy logic.
Series Title: Theory and decision library., Series B,, Mathematical and statistical methods ;, 32.
Responsibility: edited by Ulrich Höhle, Erich Peter Klement.

Abstract:

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.

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