Reliable Computing -- Special issue

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Date: Mon Dec 03 2001 - 12:37:43 MET

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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.

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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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</DIV>
    <DIV><FONT face="Arial Cyr" size=2>The following lists a few areas of
    interest.&nbsp; It is indicative and not<BR>exhaustive.</FONT></DIV>
    <DIV>&nbsp;</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>&nbsp; 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>&nbsp; neural networks<BR>- Interval and
    fuzzy ordering methods<BR>- The use of interval analysis and fuzzy set theory in
    neural<BR>&nbsp; networks<BR>- The use of interval analysis and fuzzy set theory
    in surface<BR>&nbsp; modeling, interpolation and approximation<BR>- The
    application of interval analysis to fuzzy algorithms and vice<BR>&nbsp;
    versa<BR>- The methods and relationship between interval and fuzzy<BR>&nbsp;
    optimization<BR>- Fuzzy and interval logic controllers<BR>- Computer systems in
    support of fuzzy number data types and<BR>&nbsp; associated numerical algorithms
    akin to such interval analysis computer<BR>&nbsp; systems as that of S.Rump,
    "INTLAB---Interval Laboratory" at:<BR>&nbsp; <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>&nbsp; solutions under
    computational and data errors. Is there a comparable use<BR>&nbsp; of fuzzy set
    and possibility theory in the validation of solutions under<BR>&nbsp;
    uncertainty?</FONT></DIV>
    <DIV>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</DIV>
    <DIV><FONT face="Arial Cyr" size=2></FONT>&nbsp;</DIV>
    <DIV>&nbsp;</DIV>
    <DIV><FONT face="Arial Cyr" size=2></FONT>&nbsp;</DIV></BODY></HTML>

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