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Full 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.
Contents
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.
