Christian G. Fermüller (Austria)
Technische Universität Wien, Wien
Fuzzy Logic and Theories of Vagueness
Abstract:
Fuzzy Logic has been successfully applied to all kinds of scenarios, where degrees of membership and truth can be systematically discerned. However it is highly contentious whether this fact renders Fuzzy Logic an ideal tool for modelling reasoning with vague concepts and propositions. There is a lively and prolific debate in analytic philosophy about so-called theories of vagueness. Interestingly, degree based approaches don't fare well among most contemporary philosophers. In this talk we will survey this discourse on vagueness from a logician's perspective and try to explain why various alternatives to many valued logics are deemed necessary to model human reasoning under vagueness. We maintain that deductive Fuzzy Logic in itself is hardly a full-blown theory of vagueness, but may play an important role in formalizing and quantifying different aspects of handling logically complex vague information.
Joan Gispert (Spain)
Facultat de Matemàtiques, Universitat de Barcelona, Barcelona
Algebraic semantics for t-norm based fuzzy logic
Abstract:
In this talk we present from an algebraic point of view the general framework of core and \Delta-core fuzzy logics. We consider three types of completeness with respect to any semantics of linearly orderd algebras and we give useful algebraic characterizations of these completeness. Moreover we distinguish some special semantics for these logics and we survey the known completeness methods and results for prominent logics.
Petr Hájek (Czech Republic)
Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague
Mathematical fuzzy logic - a survey and some news
Abstract:
Mathematical fuzzy logic (or fuzzy logic in a narrow sense) is a many-valued
symbolic logic with a comparative notion of truth. The present state of
development of t-norm based fuzzy propositional and predicate logic will be
surveyed and some recent results will be discribed (on witnessed models and
others).
Sándor Jenei (Hungary)
Institute of Mathematics and Informatics, University of Pécs, Pécs
Recent Advances in the Field of Left-continuous T-norms
Abstract:
The recent advances in the research of left-continuous t-norms is summarized in this talk. The main focus is on construction methods, geometric description, and structural characterization. We point out further research directions and open problems.
Extended abstract in PDF can be found here.
Michel Minoux (France)
Systems for Decision Aiding and Formation, University of Paris 6, Paris
Semirings, Dioids and their links to Fuzzy Sets and other Applications
Abstract:
Algebraic structures such as Bottleneck Algebras (R, Max, Min), Fuzzy Algebras ((0,1), Max,Min) or more generally ((0,1), Max, T) where T is a t-norm have been extensively used as relevant tools for modeling and solving problems related to Fuzzy Sets, Fuzzy relations and systems. Many of these algebraic structures may be viewed as special instances of canonically ordered Semirings, (i.e. semirings in which the preorder relation induced by addition is an order), these being frequently referred to as Dioids. Though Semirings or Dioids do not enjoy all the classical properties of rings or fields in ordinary algebra, many classical results can be shown to be still valid in those structures. The talk will provide an overview of some of the most important properties of Semirings and Dioids in particulat those related to solving linear systems, computing eigenvalues and eigenvectors, testing linear dependence or independence. Special emphasis will be put on the subclasses of Dioids more closely related to Fuzzy Set theory and applications.
Da Ruan (Belgium)
Belgian Nuclear Research Centre, Mol
Lessons learned from fuzzy logic applications in complex systems
Abstract:
In recent years there has been a growing interest in the need for designing intelligent systems to address complex engineering problems. One of the most challenging issues for the intelligent system is to effectively handle real-world uncertainties that cannot be eliminated. These uncertainties include sensor imprecision, instrumentation and process noise and disturbances, unpredictable environmental factors, to name a few. These uncertainties result in a lack of the full and precise knowledge of the system including its state, dynamics, and interaction with the environment. Fuzzy logic (FL) and soft computing (SC) techniques, as complimentary to the existing traditional techniques, have shown great potential to solve these demanding, real-world problems that exist in uncertain and unpredictable environments. These technologies have formed the foundation for intelligent systems. An overview on FL and SC in control and decision making for complex systems will be given over the last four decades. Some real-world cases on power plant operation, information–driven safeguards, cost estimation under uncertainty for a large engineering project, and decision support for long-term options of energy policy will be illustrated for the potential use of FL related techniques in complex systems. Essential steps on implementing FL related techniques in industry will be presented via R&D, demonstration, and commercialization. Challenges and future research directions will be concluded in this talk.
Abstract in DOC including author's short bio can be found here.
Lotfi A. Zadeh (USA)
Berkeley Initiative in Soft Computing, University of California, Berkeley
Fuzzy Logic—A New Direction. The Concept of f-Validity.
Abstract:
Science deals not with reality but with models of reality. In this perspective, fuzzy logic may be viewed as a system of concepts and techniques aimed at construction of models of reality which are better than those which can be constructed through the use of methods based on bivalent logic and bivalent-logic-based probability theory.
What lies beyond the boundaries of fuzzy logic? An uncharted territory which is explored involves settings in which precision is not an attainable objective. In such settings, it is necessary to retreat from precision and accept what may be called f-validity. The concept of f-validity has wide-ranging ramifications.