Non-classical Logics And Their Applications To Fuzzy Subsets: A Handbook Of The Mathematical Foundations Of Fuzzy Set Theory by Ulrich HöhleNon-classical Logics And Their Applications To Fuzzy Subsets: A Handbook Of The Mathematical Foundations Of Fuzzy Set Theory by Ulrich Höhle

Non-classical Logics And Their Applications To Fuzzy Subsets: A Handbook Of The Mathematical…

byUlrich HöhleEditorErich Peter Klement

Paperback | October 20, 2012

Pricing and Purchase Info

$105.79 online 
$110.50 list price
Earn 529 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

Non-Classical Logics and their Applications to Fuzzy Subsetsis 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.
Title:Non-classical Logics And Their Applications To Fuzzy Subsets: A Handbook Of The Mathematical…Format:PaperbackDimensions:392 pages, 24 × 16 × 0.02 inPublished:October 20, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401040966

ISBN - 13:9789401040969

Reviews

Table of Contents

Preface. Introduction. Part A: Algebraic Foundations of Non-Classical Logics. I. alpha-Complete MV-algebras; L.P. Belluce. II. On MV-algebras of continuous functions; A. Di Nola, S. Sessa. III. Free and projective Heyting and monadic Heyting algebras; R. Grigolia. IV. Commutative, residuated l-monoids; U. Höhle. V. A proof of the completeness of the infinite-valued calculus of Lukasiewicz with one variable; D. Mundici, M. Pasquetto. Part B: Non-Classical Models and Topos-Like Categories. VI. Presheaves over GL-monoids; U. Höhle. VII. Quantales: Quantal sets; C.J. Mulvey, M. Nawaz. VIII. Categories of fuzzy sets with values in a quantale or projectale; L.N. Stout. IX. Fuzzy logic and categories of fuzzy sets; O. Wyler. Part C: General Aspects of Non-Classical Logics. X. Prolog extensions to many-valued logics; F. Klawonn. XI. Epistemological aspects of many-valued logics and fuzzy structures; L.J. Kohout. XII. Ultraproduct theorem and recursive properties of fuzzy logic; V. Novák. Bibliography. Index.