The truth value algebra of type-2 fuzzy sets. (2016)

• Record Type: Book
• Further Information: Note: John Harding, Carol L. Walker, Elbert A. Walker.
• Authors: Harding, John, 1963-; Walker, Carol L, 1935-; Walker, E (Elbert), 1930-
• Contents: The Algebra of Truth Values; Preliminaries; Classical and fuzzy subsets; The truth value algebra of type-2 fuzzy sets; Simplifying the operations; Examples Properties of the Type-2 Truth Value Algebra ; Preliminaries; Basic observations; Properties of the operations; Two partial orderings; Fragments of distributivity Subalgebras of the Type-2 Truth Value Algebra ; Preliminaries; Type-1 fuzzy sets; Interval-valued fuzzy sets; Normal functions; Convex functions; Convex normal functions; Endmaximal functions; The algebra of sets; Functions with finite support Automorphisms ; Preliminaries; Sets, fuzzy sets, and interval-valued fuzzy sets; Automorphisms of M with the pointwise operations; Characterizing certain elements of M; Automorphisms of M with the convolution operations; Characteristic subalgebras of M T-Norms and T-Conorms ; Preliminaries; Triangular norms and conorms; T-norms and t-conorms on intervals; Convolutions of t-norms and t-conorms; Convolutions of continuous t-norms and t-conorms; T-norms and t-conorms on L Convex Normal Functions ; Preliminaries; Straightening the order; Realizing L as an algebra of decreasing functions; Completeness of L; Convex normal upper semicontinuous functions; Agreement convexly almost everywhere; Metric and topological properties; T-norms and t-conorms Varieties Related to M ; Preliminaries; The variety V(M); Local finiteness; A syntactic decision procedure; The algebra E of sets in M; Complex algebras of chains ; Varieties and complex algebras of chains; The algebras 23 and 25 revisited Type-2 Fuzzy Sets and Bichains ; Preliminaries; Birkhoff systems and bichains; Varieties of Birkhoff systems; Splitting bichains; Toward an equational basis Categories of Fuzzy Relations ; Preliminaries; Fuzzy relations; Rule bases and fuzzy control; Additional variables; The type-2 setting; Symmetric monoidal categories The Finite Case ; Preliminaries; Finite type-2 algebras; Subalgebras; The partial orders determined by convolutions; The double order; Varieties related to mn ; The automorphism group of mn ; Convex normal functions; The De Morgan algebras H(mn ) Appendix: Properties of the Operations on M Bibliography Index Summary and Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 511.3223; Fuzzy sets; Algebra
• Languages: English
• ISBNs: 9781498735292
• Related ISBNs: 9781498735278
• Notes: Note: Description based on CIP data; item not viewed.
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