Fuzzy Sets and Probability Statistics Th
Editorial
A mixture of fuzziness and randomness often arises in real-life situations. As a
consequence, many studies have been focussed on the modeling, analysis and
discussion of a ‘combination’ of techniques involving Fuzzy Sets and Probability/Statistics Theories.
The papers gathered in this special issue represent only a selected sample,
but the research on related topics is much wider than the one which can be
collected in a few papers.
In this special issue a considerable part has been devoted to fuzzy random
variables. In accordance with our databases in connection with this journal,
most of papers on the topic of the issue refer to this concept. For the last two
decades, fuzzy random variables have been studied in depth from a probabilistic viewpoint, and at present a sound, rigorous, and well-supported theory has
been established about this concept. Papers by the Guest Editors of the special
issue, Ter´an, and Li and Ogura cover some probabilistic aspects.
Much more recently, the use of fuzzy random variables for statistical and
decision-making purposes has been considered. Among them, papers by Kr¨atschmer,
Stahl, Gonz´alez-Rodr´ıguez et al., and Yoshida et al. correspond to different
statistical/decision-making applications and developments of fuzzy random
variables.
Finally, possibilistic approaches to the statistical management of fuzzy data
have also been included. In this way, the papers by D’Urso and Santoro, Giordani, Hryniewicz and Kurano et al. deal with problems such as multiple linear
regression, multi-way component models and decision/testing of fuzzy data.
This issue has been prepared in the last three years. As Guest Editors we
wanted to integrate in it both probabilistic and statistical contributions in a
balanced way. For this reason some of the papers were received a long time ago
and their publication suffered a significant delay and sometimes they have to
be updated to take into account the recent literature. We wish to acknowledge
the authors for their patience and understanding in this respect.
Preprint submitted to Elsevier Science
6 May 2006
We are indebted to Didier Dubois who has encouraged us to prepare this issue.
Of course, and fortunately, this issue journal issue includes only a small part of
the current research activities and topics in the field of Probability/Statistics
with fuzzy data. Nevertheless, we hope that this issue represents yet another
proof of the statement coined by Zadeh “Probability Theory and Fuzzy Logic
are complementary rather than competitive.”
Oviedo, Cincinnati, February 2006
´
Mar´ıa Angeles
Gil
Departamento de Estad´ıstica e I.O. y D.M.
Universidad de Oviedo
C/ Calvo Sotelo, s/n, E-33007 Oviedo, Spain
Miguel L´opez D´ıaz
Departamento de Estad´ıstica e I.O. y D.M.
Universidad de Oviedo
C/ Calvo Sotelo, s/n, E-33007 Oviedo, Spain
Dan A. Ralescu
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, OH 45221-0025, USA
2
A mixture of fuzziness and randomness often arises in real-life situations. As a
consequence, many studies have been focussed on the modeling, analysis and
discussion of a ‘combination’ of techniques involving Fuzzy Sets and Probability/Statistics Theories.
The papers gathered in this special issue represent only a selected sample,
but the research on related topics is much wider than the one which can be
collected in a few papers.
In this special issue a considerable part has been devoted to fuzzy random
variables. In accordance with our databases in connection with this journal,
most of papers on the topic of the issue refer to this concept. For the last two
decades, fuzzy random variables have been studied in depth from a probabilistic viewpoint, and at present a sound, rigorous, and well-supported theory has
been established about this concept. Papers by the Guest Editors of the special
issue, Ter´an, and Li and Ogura cover some probabilistic aspects.
Much more recently, the use of fuzzy random variables for statistical and
decision-making purposes has been considered. Among them, papers by Kr¨atschmer,
Stahl, Gonz´alez-Rodr´ıguez et al., and Yoshida et al. correspond to different
statistical/decision-making applications and developments of fuzzy random
variables.
Finally, possibilistic approaches to the statistical management of fuzzy data
have also been included. In this way, the papers by D’Urso and Santoro, Giordani, Hryniewicz and Kurano et al. deal with problems such as multiple linear
regression, multi-way component models and decision/testing of fuzzy data.
This issue has been prepared in the last three years. As Guest Editors we
wanted to integrate in it both probabilistic and statistical contributions in a
balanced way. For this reason some of the papers were received a long time ago
and their publication suffered a significant delay and sometimes they have to
be updated to take into account the recent literature. We wish to acknowledge
the authors for their patience and understanding in this respect.
Preprint submitted to Elsevier Science
6 May 2006
We are indebted to Didier Dubois who has encouraged us to prepare this issue.
Of course, and fortunately, this issue journal issue includes only a small part of
the current research activities and topics in the field of Probability/Statistics
with fuzzy data. Nevertheless, we hope that this issue represents yet another
proof of the statement coined by Zadeh “Probability Theory and Fuzzy Logic
are complementary rather than competitive.”
Oviedo, Cincinnati, February 2006
´
Mar´ıa Angeles
Gil
Departamento de Estad´ıstica e I.O. y D.M.
Universidad de Oviedo
C/ Calvo Sotelo, s/n, E-33007 Oviedo, Spain
Miguel L´opez D´ıaz
Departamento de Estad´ıstica e I.O. y D.M.
Universidad de Oviedo
C/ Calvo Sotelo, s/n, E-33007 Oviedo, Spain
Dan A. Ralescu
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, OH 45221-0025, USA
2