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From: "Vyacheslav Nesterov" <slavanest@yahoo.com>

To: "RC mailing list" <reliable_computing@interval.louisiana.edu>

Subject: Reliable Computing -- Special issue

Date: Mon, 12 Nov 2001 22:10:24 +0300

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Reliable Computing:

Special Issue on the Linkages Between Interval

Mathematics and Fuzzy Set Theory

Guest editor: Weldon A. Lodwick

Reliable Computing will devote a special issue to

papers that address the interrelationship between interval mathematics

and fuzzy set theory. The connection between interval mathematics and

fuzzy set theory is evident in the extension principle, arithmetic,

logic, and in the mathematics of uncertainty. Much of the research to

date has been in the use of interval mathematics in fuzzy set theory, in

particular fuzzy arithmetic and fuzzy interval analysis. This may be

because intervals can be considered as a particular type of fuzzy set.

The impact of fuzzy set theory on interval mathematics is not quite as

evident. For example, it is clear that fuzzy logic, fuzzy control, fuzzy

neural networks, and fuzzy cluster analysis, are four important areas of

fuzzy set theory. The impact of interval analysis on these four areas is

not as apparent. Can the development in these areas of fuzzy set theory

inform research in interval mathematics?

There are areas of interval mathematics and fuzzy set theory that have

developed in parallel with little or no interchange of ideas. In

particular the extension principle of Zadeh and the united extension of

R.E. Moore as well as subsequent research in this area has largely been

developed independently. Both are related to set-valued functions. Is

there a useful underlying unifying mathematics? Secondly, dependencies

and their effect on the resulting arithmetic has more recently been a

part of the fuzzy set theory literature and approaches independently

developed from what has been known in the interval analysis community

almost since the beginnings of interval analysis research. Are there

other areas of interval analysis research that would be useful for the

fuzzy set theory community to know about?

One of the paths of interval mathematics research has led to validation

analysis. Is there a useful comparable counterpart for fuzzy set theory?

Interval analysis is the way to model the uncertainty arising from

computer computations. Thus, interval analysis shares mathematical

uncertainty modeling with the field of fuzzy set theory. So,

fundamentally, what are the common points between interval analysis and

fuzzy set theory? In interval analysis, convergence of algorithms has

been an area of research. Are there extensions of these approaches to

fuzzy algorithms? In the area of interval analysis, much work has been

done in validation methods for differential equations. A few research

papers have appeared in this area in the fuzzy set theory setting. Are

there areas of cross-fertilization? There are many research papers in

the area of optimization in both interval analysis and fuzzy set theory.

What is the interrelationship between interval and fuzzy optimization?

Is there a fundamental mathematical foundation out of which both arise?

The following lists a few areas of interest. It is indicative and not

exhaustive.

- Fuzzy and interval mathematical analysis

- Comparative analysis of the interval and fuzzy logics

- Upper and lower dependency bounds in interval and fuzzy

mathematics

- Dependency analysis in interval and fuzzy computations

- Fuzzy and interval methods in classification (cluster) analysis

- The use of fuzzy set theory and interval analysis methods in

neural networks

- Interval and fuzzy ordering methods

- The use of interval analysis and fuzzy set theory in neural

networks

- The use of interval analysis and fuzzy set theory in surface

modeling, interpolation and approximation

- The application of interval analysis to fuzzy algorithms and vice

versa

- The methods and relationship between interval and fuzzy

optimization

- Fuzzy and interval logic controllers

- Computer systems in support of fuzzy number data types and

associated numerical algorithms akin to such interval analysis computer

systems as that of S.Rump, "INTLAB---Interval Laboratory" at:

http://www.ti3.tu-harburg.de/~rump/intlab/index.html

- Interval and fuzzy methods for differential equations

- Convergence and complexity analysis of interval and fuzzy algorithms

- One of the uses of interval analysis is in the validation of

solutions under computational and data errors. Is there a comparable use

of fuzzy set and possibility theory in the validation of solutions under

uncertainty?

In addition to new results in theoretical analysis, innovative

applications, and computer implementations, we invite insightful

surveys. Please send a copy of your manuscript (in electronic form

preferably---LATEX, including the style files required, postscript or

pdf format) to:

Professor Weldon A. Lodwick

Department of Mathematics---Campus Box 170

University of Colorado at Denver

P.O. Box 173364

Denver, Colorado 80217--3364

weldon.lodwick@cudenver.edu

Telephone: +1 303 556-8462

Schedule:

June 15, 2002: Deadline for submission of papers to the special issue.

December 15, 2002: Notification about acceptance of papers.

March 15, 2003: Revisions to accepted papers due.

Manuscripts will be subjected to the usual reviewing process

and should conform to the standards and formats as indicated in the

"Information for Authors" section inside the back cover of

Reliable Computing. Contributions should not exceed 32 pages.

------------- End Forwarded Message -------------

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<DIV><FONT face="Arial Cyr" size=2>Reliable Computing:<BR>Special Issue on the

Linkages Between Interval<BR>Mathematics and Fuzzy Set Theory<BR>Guest editor:

Weldon A. Lodwick</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>Reliable Computing will devote a special

issue to<BR>papers that address the interrelationship between interval

mathematics<BR>and fuzzy set theory. The connection between interval mathematics

and<BR>fuzzy set theory is evident in the extension principle,

arithmetic,<BR>logic, and in the mathematics of uncertainty. Much of the

research to<BR>date has been in the use of interval mathematics in fuzzy set

theory, in<BR>particular fuzzy arithmetic and fuzzy interval analysis. This may

be<BR>because intervals can be considered as a particular type of fuzzy

set.<BR>The impact of fuzzy set theory on interval mathematics is not quite

as<BR>evident. For example, it is clear that fuzzy logic, fuzzy control,

fuzzy<BR>neural networks, and fuzzy cluster analysis, are four important areas

of<BR>fuzzy set theory. The impact of interval analysis on these four areas

is<BR>not as apparent. Can the development in these areas of fuzzy set

theory<BR>inform research in interval mathematics?</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>There are areas of interval mathematics and

fuzzy set theory that have<BR>developed in parallel with little or no

interchange of ideas. In<BR>particular the extension principle of Zadeh and the

united extension of<BR>R.E. Moore as well as subsequent research in this area

has largely been<BR>developed independently. Both are related to set-valued

functions. Is<BR>there a useful underlying unifying mathematics? Secondly,

dependencies<BR>and their effect on the resulting arithmetic has more recently

been a<BR>part of the fuzzy set theory literature and approaches

independently<BR>developed from what has been known in the interval analysis

community<BR>almost since the beginnings of interval analysis research. Are

there<BR>other areas of interval analysis research that would be useful for

the<BR>fuzzy set theory community to know about?</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>One of the paths of interval mathematics

research has led to validation<BR>analysis. Is there a useful comparable

counterpart for fuzzy set theory?<BR>Interval analysis is the way to model the

uncertainty arising from<BR>computer computations. Thus, interval analysis

shares mathematical<BR>uncertainty modeling with the field of fuzzy set theory.

So,<BR>fundamentally, what are the common points between interval analysis

and<BR>fuzzy set theory? In interval analysis, convergence of algorithms

has<BR>been an area of research. Are there extensions of these approaches

to<BR>fuzzy algorithms? In the area of interval analysis, much work has

been<BR>done in validation methods for differential equations. A few

research<BR>papers have appeared in this area in the fuzzy set theory setting.

Are<BR>there areas of cross-fertilization? There are many research papers

in<BR>the area of optimization in both interval analysis and fuzzy set

theory.<BR>What is the interrelationship between interval and fuzzy

optimization?<BR>Is there a fundamental mathematical foundation out of which

both arise?</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>The following lists a few areas of

interest. It is indicative and not<BR>exhaustive.</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>- Fuzzy and interval mathematical

analysis<BR>- Comparative analysis of the interval and fuzzy logics<BR>- Upper

and lower dependency bounds in interval and fuzzy<BR> mathematics<BR>-

Dependency analysis in interval and fuzzy computations<BR>- Fuzzy and interval

methods in classification (cluster) analysis<BR>- The use of fuzzy set theory

and interval analysis methods in<BR> neural networks<BR>- Interval and

fuzzy ordering methods<BR>- The use of interval analysis and fuzzy set theory in

neural<BR> networks<BR>- The use of interval analysis and fuzzy set theory

in surface<BR> modeling, interpolation and approximation<BR>- The

application of interval analysis to fuzzy algorithms and vice<BR>

versa<BR>- The methods and relationship between interval and fuzzy<BR>

optimization<BR>- Fuzzy and interval logic controllers<BR>- Computer systems in

support of fuzzy number data types and<BR> associated numerical algorithms

akin to such interval analysis computer<BR> systems as that of S.Rump,

"INTLAB---Interval Laboratory" at:<BR> <A

href="http://www.ti3.tu-harburg.de/~rump/intlab/index.html">http://www.ti3.tu-harburg.de/~rump/intlab/index.html><BR>-

Interval and fuzzy methods for differential equations<BR>- Convergence and

complexity analysis of interval and fuzzy algorithms<BR>- One of the uses of

interval analysis is in the validation of<BR> solutions under

computational and data errors. Is there a comparable use<BR> of fuzzy set

and possibility theory in the validation of solutions under<BR>

uncertainty?</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>In addition to new results in theoretical

analysis, innovative<BR>applications, and computer implementations, we invite

insightful<BR>surveys. Please send a copy of your manuscript (in electronic

form<BR>preferably---LATEX, including the style files required, postscript

or<BR>pdf format) to:</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>Professor Weldon A. Lodwick<BR>Department of

Mathematics---Campus Box 170<BR>University of Colorado at Denver<BR>P.O. Box

173364<BR>Denver, Colorado 80217--3364<BR><A

href="mailto:weldon.lodwick@cudenver.edu">weldon.lodwick@cudenver.edu</A><BR>Telephone:

+1 303 556-8462</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>Schedule:<BR>June 15, 2002: Deadline for

submission of papers to the special issue.<BR>December 15, 2002: Notification

about acceptance of papers.<BR>March 15, 2003: Revisions to accepted papers

due.</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2>Manuscripts will be subjected to the usual

reviewing process<BR>and should conform to the standards and formats as

indicated in the<BR>"Information for Authors" section inside the back cover

of<BR>Reliable Computing. Contributions should not exceed 32 pages.</FONT></DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2></FONT> </DIV>

<DIV> </DIV>

<DIV><FONT face="Arial Cyr" size=2></FONT> </DIV></BODY></HTML>

--Den_of_Snakes_471_000--

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