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

By: Erich Peter Klement (Editor), Ulrich Hohle (Editor)

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406 Pages

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This 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 or 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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Authors and Editors
Preface	p. 1
Introduction	p. 3
[alpha]-Complete MV-algebras	p. 7
On MV-algebras of continuous functions	p. 23
Free and projective Heyting and monadic Heyting algebras	p. 33
Commutative, residuated I-monoids	p. 53
A Proof of the completeness of the infinite-valued calculus of Lukasiewicz with one varibale	p. 107
Presheaves over GL-monoids	p. 127
Quantales: Quantal sets	p. 159
Categories of fuzzy sets with values in a quantale or projectale	p. 219
Fuzzy logic and categories of fuzzy sets	p. 235
Prolog extensions to many-valued logics	p. 271
Epistemological aspects of many-valued logics and fuzzy structures	p. 291
Ultraproduct theorem and recursive properties of fuzzy logic	p. 341
Bibliography	p. 371
Index	p. 385
Table of Contents provided by Blackwell. All Rights Reserved.

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

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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