(GENERALIZED) FUZZY MATRICES AND RELATIONS

The book provides an overview of the main concepts and results related to fuzzy matrices and fuzzy relations, using 'fuzzy' in a general sense to mean many-valued. This overview, along with numerous references to original contributions dispersed across various journals, serves as a comprehensive guide for further exploration.

This volume can be viewed in two ways: (i) as a companion to the author's previous work, 'Relations: Concrete, Abstract, and Applied' (published by WSPC, 2020), but with a distinct emphasis on many-valued concepts; or (ii) as a standalone volume that can be read independently, which necessarily includes some repetition of material from the earlier book as preliminary or reference content.

Similar to the previous book, this one does not present new findings but offers a self-contained compilation of known results selected from the extensive research conducted over the past five decades, arranged in a systematic manner.

The topics covered in this text have been the subject of intensive research over the last two decades, yet there has been no book publication on this subject for over 15 years. This book aims to bridge that gap.

Contents:
Preliminaries and Classical Two-valued Concepts:Some Mathematical PrerequisitesRelationsBoolean Matrices(Generalized) Fuzzy Matrices:Various Structures for Many-Valued AlgebraAlgebraic PreliminariesMatrices over Arbitrary and Commutative SemiringsMatrices over Antirings and Path AlgebrasMatrices over Inclines and Various Kinds of LatticesFuzzy Relations and Fuzzy Graphs:Basic Properties of Fuzzy RelationsSome Basic Kinds of Fuzzy RelationsFuzzy Preference Structures and Social ChoiceFuzzy Relation Equations and InequalitiesFuzzy GraphsSome Abstract Algebra of Fuzzy Relations:Fuzzy Relation AlgebrasFuzzy Relations and Categories
Readership: Academic researchers, Postgraduate students, graduate students. The book is self-contained to a large extent and is thus suitable for self-study for students who want to learn about various aspects of binary relations in both their two- and many-valued form.

Herbert Toth, is a former software engineer (meanwhile retired for a couple of years) with a strong inclination to fuzzy/many-valued concepts and to the paradigm known as Design by Contract (DbC) or Correctness-by-Construction (CbC).Parallel to studying psychology at the University of Vienna, he earned an MSc in Applied Computer Science at the Technical University of Vienna, and later on a PhD in Mathematical Logic at the University of Vienna.