On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory
Description
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.
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Content
Fuzzy Logic and the Linz Seminar:Themes and some Personal Reminiscences.- How I Saw and How I See Fuzzy Sets.- Modules in the Category.- A Geometric Approach to MV-algebras.- On the Equational Characterization of Continuous t-norms.- The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids.- Structure of Uninorms with Continuous Diagonal Functions.- The Notions of Overlap and Grouping Functions.- Asymmetric Copulas and Their Application in Design of Experiments.- Copulæ of Processes Related to the Brownian Motion: a Brief Survey.- Extensions of Capacities.- Multi-source Information Fusion Using Measure Representations.- Bases and Transforms of Set Functions.- Conditioning for Boolean Subsets, Indicator Functions, and Fuzzy Subsets.- Multivalued Functions Integration from Additive to Arbitrary Non-Negative Set Function.