On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory (Studies in Fuzziness and Soft Computing, 336)

"The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement's research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field" -- OhioLink Library Catalog Front Matter....Pages i-xii Fuzzy Logic and the Linz Seminar: Themes and Some Personal Reminiscences....Pages 1-11 How I Saw, and How I See Fuzzy Sets....Pages 13-22 Modules in the Category \(\mathtt {\mathbf{Sup}}\) ....Pages 23-56 A Geometric Approach to MV-Algebras....Pages 57-70 On the Equational Characterization of Continuous t-Norms....Pages 71-82 The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids....Pages 83-108 Structure of Uninorms with Continuous Diagonal Functions....Pages 109-135 The Notions of Overlap and Grouping Functions....Pages 137-156 Asymmetric Copulas and Their Application in Design of Experiments....Pages 157-172 Copulæ of Processes Related to the Brownian Motion: A Brief Survey....Pages 173-180 Extensions of Capacities....Pages 181-198 Multi-source Information Fusion Using Measure Representations....Pages 199-214 Bases and Transforms of Set Functions....Pages 215-231 Conditioning for Boolean Subsets, Indicator Functions and Fuzzy Subsets....Pages 233-256 Multivalued Functions Integration: from Additive to Arbitrary Non-negative Set Function....Pages 257-274 Back Matter....Pages 275-275