Topological and Algebraic Structures in Fuzzy Sets : A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

Rodabaugh, Stephen Ernest (EDT); Klement, Erich Peter (EDT)

ISBN 10: 1402015151 / ISBN 13: 9781402015151

Published by Springer, 2003

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Bibliographic Details

• Title: Topological and Algebraic Structures in Fuzzy Sets : A Handbook of Recent Developments in the Mathematics of Fuzzy Sets
• Publisher: Springer
• Publication Date: 2003
• Language: English
• ISBN 10: 1402015151
• ISBN 13: 9781402015151
• Binding: Hardcover
• Condition: As New

About this title

Synopsis

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan­ dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish­ ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand­ book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand­ book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem­ inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti­ eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

Synopsis

"Topological and Algebraic Structures in Fuzzy Sets" has these unique features: strategically located at the juncture of fuzzy sets, topology, algebra, lattices, foundations of mathematics; major studies in uniformities and convergence structures, fundamental examples in lattice-valued topology, modifications and extensions of sobriety, categorical aspects of lattice-valued subsets, logic and foundations of mathematics, t-norms and associated algebraic and ordered structures; internationally recognized authorities clarify deep mathematical aspects of fuzzy sets, particularly those topological or algebraic in nature; comprehensive bibliographies and tutorial nature of longer chapters take readers to the frontier of each topic; extensively referenced introduction unifies volume and guides readers to chapters closest to their interests; annotated open questions direct future research in the mathematics of fuzzy sets; and suitable as a text for advanced graduate students.