Non-classical logics and their applications to fuzzy subsets : a handbook of the mathematical foundations of fuzzy set theory
著者
書誌事項
Non-classical logics and their applications to fuzzy subsets : a handbook of the mathematical foundations of fuzzy set theory
（Theory and decision library, ser. B . Mathematical and statistical methods ; v. 32）
Kluwer Academic Publishers, c1995
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注記
"Proceedings of the 14th Linz Seminar on Fuzzy Set Theory ... the second week of September 1992 at the Bildungszentrum St. Magdalena (Linz, Austria)"--P. 1
Includes bibliographical references and index
内容説明・目次
内容説明
This work is devoted to a study of various relations between non-classical logics and fuzzy sets. This volume is aimed at 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 should 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.
目次
Part A Algebraic Foundations of Non-Classical Logics: Complete MV-algebras, L.P. Belluce. On MV-algebras of continuous functions, A. Di Nola, S. Sessa. Free and projective Heyting and monadic Heyting algebras, R. Grigolia. Commutative, residuated l-monoids, U. Hohle. 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: Presheaves over GL-monoids, U. Hohle. Quantales - Quantal sets, C.J. Mulvey, M. Nawaz. Categories of fuzzy sets with values in a quantale or projectale, L.N. Stout. Fuzzy logic and categories of fuzzy sets, O. Wyler. Part C General Aspects of Non-Classical Logics: Prolog extensions to many-valued logics, F. Klawonn. Epistemological aspects of many-valued logics and fuzzy structures, L.J. Kohout. Ultraproduct theorem and recursive properties of fuzzy logic, V. Novak.
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