June 23-24, 1997
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1. Hans-Heinrich Bothe:
Fuzzy - neural networks
Fuzzy Logic and Neural Networks have been applied to
numerious technical applications. Either methodic
family has well known advantages. An appropriate
combination of both can help to eliminate
disadvantages, leading to adaptible and interpretable
system behaviour. The tutorium will systematically
introduce and compare several sophisticated approaches.
It is addressed to applications in control or pattern
recognition.
2. Michel Grabisch:
Fuzzy measures and integrals for decision analysis
and pattern recognition
Fuzzy measure is a powerful tool for modeling
uncertainty and strength of coalitions in a decision
making problem. We introduce fuzzy measures among
various measures of uncertainty, and fuzzy integral as
a mean to compute overall evaluations or expected
values. Two aspects of decision making are examined
here, namely decision under uncertainty and
multicriteria decision making. In decision under
uncertainty, it is shown how the expected utiity model
is generalized to avoid well known oparadoxes as the
Ellsberg paradox. Some results are also given on
imprecise probabilities. In multicriteria decision
making, the concepts of Shapley value and interaction
index are introduced. It is shown that a fuzzy measure
can have several equivalent representations, which may
be truncated to cope with the exponential complexity of
fuzzy measures. Their use in multicriteria decision
making and in pattern recognition are detailed.
3. Petr Hajek, Lluis Godo:
Foundations of fuzzy logic
Foundations of fuzzy logic in the narrow sense, i.e.
formal deductive systems of fuzzy propositional and
predicate calculi will be presented and surveyed. First
an axiomatic system of Basic fuzzy propositional logic
is presented, sound for each fuzzy logic given by
a continuous t-norm. Then three stronger logics are
elaborated, corresponding to the three main t-norms
(Lukasiewicz, Godel, product). Completeness theorems
are discussed. Pavelka-like extension of Lukasiewicz
logic (for proving partially true conclusions from
partially true premisses) is presented in a very simple
form. Basic predicate logic is given a natural
semantics shown to be complete; Godel predicate logic
is also completely (recursively) axiomatizable, but
neither Lukasiewicz nor product predicate logic is;
nevertheless, all these systems have powerful axiomatic
systems from which most basic things are provable. The
aim of the tutorial is to show the participants that
fuzzy logic in the nerrow sense is indeed a fully
fledged logic, dealing with truth-preserving deduction.
As such it may well serve as foundation for fuzzy logic
applications.
4. Hans Hellendoorn:
Industrial applications of fuzzy control
We describe the use of fuzzy systems in several
divisions of a large industrial company. We will focus
on the use of pure fuzzy control, fuzzy classification,
and data analysis. We will present examples from
automobile industry, paper industry, traffic control,
power plants, telecommunications, domestic appliances,
etc.
5. Francisco Herrera, Louis Magdalena:
Genetic fuzzy systems
The automatic definition of a fuzzy system can be
considered in a lot of cases as an optimization or
search process. Genetic Algorithms (GAs) are the best
known and widely used global search technique with an
ability to explore and exploit a given operating space
using available performance measures. GAs are known to
be capable of finding near optimal solutions in complex
search spaces. A priori knowledge of a Fuzzy System may
be in form of known linguistic variables, fuzzy
membership function parameters, fuzzy rules, number of
rules, etc. The generic code structure and independent
performance features of GAs make them suitable
candidates for incorporating a priori knowledge.
The searching capabilities and its ability for
incorporating a priori knowledge have extended the use
of GAs in the development of a wide range of methods
for designing fuzzy systems in the last years. Systems
applying these design approaches have received the
general name of Genetic Fuzzy Systems (GFSs).
In this tutorial we summarize different GFSs
approaches, focusing our presentation on the genetic
fuzzy rule based systems.
6. Masahiro Inuiguchi:
Fuzzy linear programming: What, why and how ?
This tutorial is meant to be as an introduction for
interested beginners and general conceptual review for
advanced fuzzy researchers. We review some fuzzy linear
programming techniques from a practical point of view.
First, the general history and the approach of fuzzy
mathematical programming are described. Using
a concrete numerical example, a few models of the fuzzy
linear programming problem are explained. The
importance of taking care of uncertainty in the problem
setting is emphasized. Next, fuzzy mathematical
programming approaches are compared to stochastic
programming approaches. The advantages and
disadvantages of fuzzy mathematical programming
approaches are exemplified in the setting of
a portfolio selection problem. Finally, some newly
developed techniques in fuzzy mathematical programming
are briefly reviewed.
7. Erich Peter Klement, Radko Mesiar:
t-norms, foundations and applications
Definitions, basic properties. Important examples.
Additive and multiplicative generators. Strict and
nilpotent t-norms. Continuous t-norms. Related
operations. Fuzzy logic connectives. Generalized
extension principle. Relations to the composional rule
of inference. Applications on fuzzy control.
8. Witold Pedrycz:
Knowledge discovery and data mining in a framework
of fuzzy set technology
Knowledge Discovery (KD) and Data mining (DM) are aimed
at addressing genuine needs arising from a diversity of
data rich and knowledge poor information environments.
The role of fuzzy sets in knowledge discovery has not
been profoundly visible even though fuzzy sets are
inherently inclined towards coping with linguistic
domain knowledge. The paper re-examines the key issues
of knowledge discovery by putting them in the context
of the technology of fuzzy sets. Subsequently, we
reveal several interesting links between fuzzy data
mining and fuzzy sets. The study exploits
knowledge-oriented and context based modifications of
well known algorithms of fuzzy clustering. We also look
at the development of the fuzzy models from the
perspective of data mining - a prudent and user
- oriented sifting of data, qualitative observations,
and calibration of commonsense rules in an attempt to
establish meaningful and useful relationships between
systems variables.
9. Junzo Watada:
Fuzzy portfolio selection and its application
to decision making
In this tutorial, the basic concepts of fuzzy portfolio
selection is provided and its concept is applied to
several problems as the fuzzy mean-variance analysis.
The objective of this fuzzy portfolio selection is to
decide the best portfolio based on vague aspiration
level which decision makers have. The vague aspiration
level is expressed by a fuzzy number and maximized by
Bellman-Zadeh's maximization principle. In the method,
genetic algorithm is employed to efficiently reduce the
computational cost for obtaining its solution. As its
application the proposed method is applied to
a personal allocation problem.
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Vilem Novak, DSc., Associate Professor
University of Ostrava
IRAFM (Institute for Research and Applications of Fuzzy Modeling)
Brafova 7
701 03 Ostrava 1
Czech Republic
tel: +420-69-622 2808
fax: +420-69-22 28 28
e-mail: novakv@osu.cz
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