Relations: Concrete, Abstract, and Applied

The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:Contents: PART 1: Relations — Historical and Mathematical Preliminaries:A Short Look into (Relations') HistoryMathematical PrerequisitesPART 2: Relations — Concrete, Two-Valued:Binary Relations: Basic Properties and OperationsSome Basic Kinds of Binary RelationsRelations, Matrices, and GraphsSome Special Topics Around RelationsPART 3: Relations — Concrete, Many-Valued:Many-Valued Extensions: PreliminariesFuzzy Sets and Fuzzy RelationsPART 4: Relations — Abstract:Semigroups and Binary RelationsRelation AlgebrasRelations and CategoriesPART 5: Relations — Applied:Semiotics and SemanticsInformation Systems and Rough SetsFormal Concept AnalysisMereology and Qualitative Spatial and Temporal ReasoningArgumentation FrameworksDescribing Graphs and Transition SystemsOrder Relations and Preference ModellingRelations and Syllogisms Again
Readership: Students and researchers in mathematics and computer science.Relations;Order Relations;Tolerance Relations;Equivalence Relations;BandlerÔÇôKohout Product;Regular Relations;Difunctional Relations;Commuting Relations;Fuzzy Relations;Fuzzy Relation Equations and Inequalities;Semigroup of Binary Relations;Green's Relations;Relation Algebras;Regular Categories;Allegories' Semiotics and Semantics;Mereology;Mereotopology;Qualitative Spatial and Temporal Reasoning;QSTR;Transition Systems;Preference Modelling;Syllogisms0Key Features:Part 1 starts with a chapter giving a short overview on the historical development and also summarizes the mathematical prerequisites useful for the bookConcepts of universal algebra and category theory are included in order to make the text more self-contained and to give first impressions of the beauty and elegance of these two disciplines