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The Truth Value Algebra of Type-2 Fuzzy Sets -- Order Convolutions of Functions on the Unit Interval

2型模糊集的真值代数

CRC Press Harding, John Walker, Carol L Walker, Elbert A

ISBN：9781498735278，出版年：2016，中图分类号：O15 被引 11次

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.

Algebra of sets Fuzzy set Basis (universal algebra) Membership function Variety (universal algebra) Fuzzy logic Automorphism Completeness (order theory) Discrete mathematics Algebra Mathematics

Summa (Quaestiones ordinariae) art. XXV-XXVII

亨利的《苏玛》二十五至二十七

Leuven University Press Henry of Ghent Silvia Negri

ISBN：9789462702349，出版年：2020，中图分类号：I1

First critical edition of articles XXV–XXVII of the Summa (Quaestiones ordinariae) of Henry of Ghent Das Buch bietet die erste kritische Edition der Artikel XXV-XXVII der Summa (Quaestiones ordinariae)  des Heinrich von Gent. Dabei leistet es einen Beitrag zur Geschichte der Formen und Pfade der Ideenvermittlung im Mittelalter und zur mittelalterlichen Buchkultur. Die Kollationierung der Handschriften der Artikel XXV-XXVII und die Untersuchung ihrer materiellen Überlieferung haben der Editorin erlaubt, den Prozess der Ausarbeitung, Publikation und Verbreitung einer Portion von Heinrichs Summa über einen längeren Zeitraum in großer Detailgenauigkeit zu rekonstruieren. Die hier edierten Artikel enthalten ein Kernstück von Heinrichs theologischem und metaphysischem System. In der Behandlung von Einheit, Natur und Leben Gottes entfalten sie eine rationale Darstellung des ersten Prinzips. This book offers the first critical edition of articles XXV–XXVII of the Summa (Quaestiones ordinariae) of Henry of Ghent. At the same time, it contributes to our understanding of the forms and trajectories through which ideas were transmitted throughout the Middle Ages and to medieval book culture. Collating the manuscripts of articles XXV–XXVII and studying their material tradition allowed the editor to reconstruct in great detail how a portion of Henry’s Summa was prepared, published and disseminated over a considerable number of years. The primary text presents an authoritative overview of Henry's theological and metaphysical system. In dealing with the unity, nature, and life of God, it unfolds a rational explanation of the first principle.This publication is GPRC-labeled (Guaranteed Peer-Reviewed Content).

Representation (arts) Taxonomy (general) Composition (visual arts) Ordinal number (linguistics) Style (visual arts) Indeterminacy (literature) Apostrophe (figure of speech) Context (archaeology) Section (typography) Variety (universal algebra)