On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

The book is a collection of contributionsby leading experts, developed around traditional themes discussed at the annualLinz Seminars on Fuzzy Set Theory. The different chapters have been written byformer PhD students, colleagues, co-authors and friends of Peter Klement, aleading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory.The book also includes advanced findings on topics inspired by Klement'sresearch activities, concerning copulas, measures and integrals, as well asaggregation problems. Some of the chapters reflect personal views andcontroversial aspects of traditional topics, while others deal with deepmathematical theories, such as the algebraic and logical foundations of fuzzyset theory and fuzzy logic. Originally thought as an homage to Peter Klement,the book also represents an advanced reference guide to the mathematicaltheories related to fuzzy logic and fuzzy set theory with the potential tostimulate important discussions on new research directions in the field.

Fuzzy Logic and the Linz Seminar:Themesand some Personal Reminiscences.- How I Saw and How I See Fuzzy Sets.- Modulesin the Category.- A Geometric Approach to MV-algebras.- On the Equational Characterizationof Continuous t-norms.- The Semantics of Fuzzy Logics: Two Approaches to FiniteTomonoids.- Structure of Uninorms with Continuous Diagonal Functions.- TheNotions of Overlap and Grouping Functions.- Asymmetric Copulas and TheirApplication in Design of Experiments.- Copulæ of Processes Related to theBrownian Motion: a Brief Survey.- Extensions of Capacities.- Multi-source InformationFusion Using Measure Representations.- Bases and Transforms of Set Functions.- Conditioningfor Boolean Subsets, Indicator Functions, and Fuzzy Subsets.- Multivalued FunctionsIntegration from Additive to Arbitrary Non-Negative Set Function.