Topological and Algebraic Structures in Fuzzy Sets

by Rodabaugh, Stephen Ernest; Klement, Erich Peter

• ISBN13: 9781402015151
• ISBN10: 1402015151
• Format: Hardcover
• Copyright: 2003-10-01
• Publisher: Kluwer Academic Pub

Summary

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; -suitable as a text for advanced graduate students.

Table of Contents

Volume Contributors	vii
Preface	xi
Introduction	1	(18)
Part I: Topological Structures in Fuzzy Sets
Uniform Completion In Pointfree Topology	19	(38)
B. Banaschewski
Monadic Convergence Structures	57	(24)
W. Gahler
A Unified Approach To The Concept Of Fuzzy L-Uniform Space	81	(34)
J. Gutierrez Garcia
M. A. de Prada Vicente
A. P. Sostak
Many Valued Topologies And Borel Probability Measures	115	(22)
U. Hohle
Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions	137	(16)
T. Kubiak
Lattice-Valued Frames, Functor Categories, And Classes of Sober Spaces	153	(46)
A. Pultr
S. E. Rodabaugh
Weakening The Requirement That L Be A Complete Chain	189	(10)
U. Hohle
S. E. Rodabaugh
Axiomatic Foundations For Uniform Operator Quasi-Uniformities	199	(36)
S. E. Rodabaugh
Fully Fuzzy Topology	235	(22)
L. N. Stout
Part II: Algebraic Structures in Fuzzy Sets
Fuzzy Logics Arising From Strict De Morgan Systems	257	(20)
M. Gehrke
C. Walker
E. Walker
Structure Of Girard Monoids on [0,1]	277	(32)
S. Jenei
On The Geometry Of Choice	309	(28)
C. J. Mulvey
On Some Fuzzy Categories Related To Category L-TOP Of L-Topological Spaces	337	(38)
A. P. Sostak
Part III: Related Topics in Topological and Algebraic Structures
Fuzzy Compactness Via Categorical Closure Operators	375	(14)
I. W. Alderton
Discrete Triangular Norms	389	(12)
B. De Baets
R. Mesiar
Powerset Operators Based Approach To Fuzzy Topologies On Fuzzy Sets	401	(14)
C. Guido
Lifting Of Sobriety Concepts With Particular Reference To (L, M)-Topological Spaces	415	(12)
W. Kotze
Examples For Different Sobrieties In Fixed-Basis Topology	427	(14)
A. Pultr
S. E. Rodabaugh
Additive Generators Of Non-Continuous Triangular Norms	441	(14)
P. Vicenik
Groups, T-Norms, And Families Of De Morgan Systems	455
C. Walker
E. Walker