Non-Classical Logics and their Applications to Fuzzy Subsets, Softcover reprint of the original 1st ed. 1995
A Handbook of the Mathematical Foundations of Fuzzy Set Theory
Theory and Decision Library B Series, Vol. 32

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.

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.

This book is 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.Algebraic foundations of non-classical logics. Alpha-complete MV-algebras. On MV-algebras of continuous functions. Free and projective Heyting and monadic Heyting algebras. Commutative, residuated I-monoids. A proof of the completeness of the infinite-valued calculus of Lukasiewicz with one variable. Non-classical models and topos-like categories. Presheaves over GL-monoids. Quantales : quantales sets. Categories of fuzzy sets with values